[{"data":1,"prerenderedAt":5574},["ShallowReactive",2],{"subject-categories-math":3,"formula-de\u002Fformulas\u002Fmath\u002Fmultivariable-calculus\u002Fsatz-von-stokes":546,"formula-related-de\u002Fformulas\u002Fmath\u002Fmultivariable-calculus\u002Fsatz-von-stokes":5561},[4,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,173,174,175,176,177,178,179,180,181,182,183,184,185,186,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,512,513,514,515,516,517,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545],{"category":5},"algebra",{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":65},"arithmetic",{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":101},"calculus",{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":172},"differential-equations",{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":187},"discrete-math",{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":208},"functions",{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":247},"geometry",{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":312},"linear-algebra",{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":368},"multivariable-calculus",{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":391},"numerics",{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":412},"sequences-series",{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":441},"stochastics",{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":518},"trigonometry",{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"id":547,"title":548,"aliases":549,"body":555,"category":368,"checks":5492,"conditions":5511,"conditionsHtml":5512,"deprecated":5513,"description":5486,"extension":5514,"figure":5513,"figureCaption":5513,"figureHtml":5513,"formulaId":5515,"latex":5516,"latexHtml":5517,"level":5518,"meta":5519,"navigation":5520,"path":5521,"redirectFrom":5522,"related":5523,"seo":5528,"stem":5529,"subject":585,"summary":5530,"tags":5531,"variables":5537,"__hash__":5560},"formulas_de\u002Fde\u002Fformulas\u002Fmath\u002Fmultivariable-calculus\u002Fsatz-von-stokes.md","Satz von Stokes",[550,551,552,553,554],"Stokesscher Integralsatz","Integralsatz von Stokes","Zirkulation und Rotation","Satz von Green","Greensche Formel in der Ebene",{"type":556,"value":557,"toc":5485},"minimark",[558,563,684,988,1335,1548,1554,2192,2196,2782,3025,3992,4554,4914,4918],[559,560,562],"h2",{"id":561},"erklärung","Erklärung",[564,565,566,567,570,571,574,575,683],"p",{},"Der ",[568,569,548],"strong",{}," verbindet ein Flächenintegral mit einem Kurvenintegral über den Rand der Fläche. Rechts steht die ",[568,572,573],{},"Zirkulation"," von ",[576,577,580,611],"span",{"className":578},[579],"katex",[576,581,584],{"className":582},[583],"katex-mathml",[585,586,588],"math",{"xmlns":587},"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML",[589,590,591,606],"semantics",{},[592,593,594],"mrow",{},[595,596,598,602],"mover",{"accent":597},"true",[599,600,601],"mi",{},"F",[603,604,605],"mo",{},"⃗",[607,608,610],"annotation",{"encoding":609},"application\u002Fx-tex","\\vec F",[576,612,615],{"className":613,"ariaHidden":597},[614],"katex-html",[576,616,619,624],{"className":617},[618],"base",[576,620],{"className":621,"style":623},[622],"strut","height:0.9663em;",[576,625,629],{"className":626},[627,628],"mord","accent",[576,630,633],{"className":631},[632],"vlist-t",[576,634,637],{"className":635},[636],"vlist-r",[576,638,641,654],{"className":639,"style":623},[640],"vlist",[576,642,644,649],{"style":643},"top:-3em;",[576,645],{"className":646,"style":648},[647],"pstrut","height:3em;",[576,650,601],{"className":651,"style":653},[627,652],"mathnormal","margin-right:0.1389em;",[576,655,657,660],{"style":656},"top:-3.2523em;",[576,658],{"className":659,"style":648},[647],[576,661,665],{"className":662,"style":664},[663],"accent-body","left:-0.1522em;",[576,666,670],{"className":667,"style":669},[668],"overlay","height:0.714em;width:0.471em;",[671,672,679],"svg",{"xmlns":673,"width":674,"height":675,"style":676,"viewBox":677,"preserveAspectRatio":678},"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg","0.471em","0.714em","width:0.471em","0 0 471 714","xMinYMin",[680,681],"path",{"d":682},"M377 20c0-5.333 1.833-10 5.5-14S391 0 397 0c4.667 0 8.667 1.667 12 5\n3.333 2.667 6.667 9 10 19 6.667 24.667 20.333 43.667 41 57 7.333 4.667 11\n10.667 11 18 0 6-1 10-3 12s-6.667 5-14 9c-28.667 14.667-53.667 35.667-75 63\n-1.333 1.333-3.167 3.5-5.5 6.5s-4 4.833-5 5.5c-1 .667-2.5 1.333-4.5 2s-4.333 1\n-7 1c-4.667 0-9.167-1.833-13.5-5.5S337 184 337 178c0-12.667 15.667-32.333 47-59\nH213l-171-1c-8.667-6-13-12.333-13-19 0-4.667 4.333-11.333 13-20h359\nc-16-25.333-24-45-24-59z"," längs der Randkurve, links der Fluss der Rotation durch die Fläche. Anschaulich: Die Summe der kleinen Wirbel auf der Fläche ergibt den Umlauf am Rand, weil sich die Beiträge im Inneren gegenseitig aufheben.",[564,685,686,687,718,719,757,758,822,823,851,852,987],{},"Genau gilt der Satz für eine orientierte, stückweise glatte Fläche ",[576,688,690,704],{"className":689},[579],[576,691,693],{"className":692},[583],[585,694,695],{"xmlns":587},[589,696,697,702],{},[592,698,699],{},[599,700,701],{},"S",[607,703,701],{"encoding":609},[576,705,707],{"className":706,"ariaHidden":597},[614],[576,708,710,714],{"className":709},[618],[576,711],{"className":712,"style":713},[622],"height:0.6833em;",[576,715,701],{"className":716,"style":717},[627,652],"margin-right:0.0576em;"," mit stückweise glatter Randkurve ",[576,720,722,740],{"className":721},[579],[576,723,725],{"className":724},[583],[585,726,727],{"xmlns":587},[589,728,729,737],{},[592,730,731,735],{},[599,732,734],{"mathvariant":733},"normal","∂",[599,736,701],{},[607,738,739],{"encoding":609},"\\partial S",[576,741,743],{"className":742,"ariaHidden":597},[614],[576,744,746,750,754],{"className":745},[618],[576,747],{"className":748,"style":749},[622],"height:0.6944em;",[576,751,734],{"className":752,"style":753},[627],"margin-right:0.0556em;",[576,755,701],{"className":756,"style":717},[627,652]," und ein Feld ",[576,759,761,778],{"className":760},[579],[576,762,764],{"className":763},[583],[585,765,766],{"xmlns":587},[589,767,768,776],{},[592,769,770],{},[595,771,772,774],{"accent":597},[599,773,601],{},[603,775,605],{},[607,777,610],{"encoding":609},[576,779,781],{"className":780,"ariaHidden":597},[614],[576,782,784,787],{"className":783},[618],[576,785],{"className":786,"style":623},[622],[576,788,790],{"className":789},[627,628],[576,791,793],{"className":792},[632],[576,794,796],{"className":795},[636],[576,797,799,807],{"className":798,"style":623},[640],[576,800,801,804],{"style":643},[576,802],{"className":803,"style":648},[647],[576,805,601],{"className":806,"style":653},[627,652],[576,808,809,812],{"style":656},[576,810],{"className":811,"style":648},[647],[576,813,815],{"className":814,"style":664},[663],[576,816,818],{"className":817,"style":669},[668],[671,819,820],{"xmlns":673,"width":674,"height":675,"style":676,"viewBox":677,"preserveAspectRatio":678},[680,821],{"d":682},", das auf einer Umgebung von ",[576,824,826,839],{"className":825},[579],[576,827,829],{"className":828},[583],[585,830,831],{"xmlns":587},[589,832,833,837],{},[592,834,835],{},[599,836,701],{},[607,838,701],{"encoding":609},[576,840,842],{"className":841,"ariaHidden":597},[614],[576,843,845,848],{"className":844},[618],[576,846],{"className":847,"style":713},[622],[576,849,701],{"className":850,"style":717},[627,652]," stetig differenzierbar ist (",[576,853,855,886],{"className":854},[579],[576,856,858],{"className":857},[583],[585,859,860],{"xmlns":587},[589,861,862,883],{},[592,863,864,870,873],{},[595,865,866,868],{"accent":597},[599,867,601],{},[603,869,605],{},[603,871,872],{},"∈",[874,875,876,879],"msup",{},[599,877,878],{},"C",[880,881,882],"mn",{},"1",[607,884,885],{"encoding":609},"\\vec F \\in C^1",[576,887,889,943],{"className":888,"ariaHidden":597},[614],[576,890,892,896,931,936,940],{"className":891},[618],[576,893],{"className":894,"style":895},[622],"height:1.0054em;vertical-align:-0.0391em;",[576,897,899],{"className":898},[627,628],[576,900,902],{"className":901},[632],[576,903,905],{"className":904},[636],[576,906,908,916],{"className":907,"style":623},[640],[576,909,910,913],{"style":643},[576,911],{"className":912,"style":648},[647],[576,914,601],{"className":915,"style":653},[627,652],[576,917,918,921],{"style":656},[576,919],{"className":920,"style":648},[647],[576,922,924],{"className":923,"style":664},[663],[576,925,927],{"className":926,"style":669},[668],[671,928,929],{"xmlns":673,"width":674,"height":675,"style":676,"viewBox":677,"preserveAspectRatio":678},[680,930],{"d":682},[576,932],{"className":933,"style":935},[934],"mspace","margin-right:0.2778em;",[576,937,872],{"className":938},[939],"mrel",[576,941],{"className":942,"style":935},[934],[576,944,946,950],{"className":945},[618],[576,947],{"className":948,"style":949},[622],"height:0.8141em;",[576,951,953,957],{"className":952},[627],[576,954,878],{"className":955,"style":956},[627,652],"margin-right:0.0715em;",[576,958,961],{"className":959},[960],"msupsub",[576,962,964],{"className":963},[632],[576,965,967],{"className":966},[636],[576,968,970],{"className":969,"style":949},[640],[576,971,973,977],{"style":972},"top:-3.063em;margin-right:0.05em;",[576,974],{"className":975,"style":976},[647],"height:2.7em;",[576,978,984],{"className":979},[980,981,982,983],"sizing","reset-size6","size3","mtight",[576,985,882],{"className":986},[627,983],").",[564,989,990,991,1059,1060,1093,1094,1124,1125,1156,1157,1334],{},"Die Orientierungen müssen zusammenpassen: Zeigt der Daumen der rechten Hand in Richtung ",[576,992,994,1013],{"className":993},[579],[576,995,997],{"className":996},[583],[585,998,999],{"xmlns":587},[589,1000,1001,1010],{},[592,1002,1003],{},[595,1004,1005,1008],{"accent":597},[599,1006,1007],{},"n",[603,1009,605],{},[607,1011,1012],{"encoding":609},"\\vec n",[576,1014,1016],{"className":1015,"ariaHidden":597},[614],[576,1017,1019,1023],{"className":1018},[618],[576,1020],{"className":1021,"style":1022},[622],"height:0.714em;",[576,1024,1026],{"className":1025},[627,628],[576,1027,1029],{"className":1028},[632],[576,1030,1032],{"className":1031},[636],[576,1033,1035,1043],{"className":1034,"style":1022},[640],[576,1036,1037,1040],{"style":643},[576,1038],{"className":1039,"style":648},[647],[576,1041,1007],{"className":1042},[627,652],[576,1044,1045,1048],{"style":643},[576,1046],{"className":1047,"style":648},[647],[576,1049,1052],{"className":1050,"style":1051},[663],"left:-0.2355em;",[576,1053,1055],{"className":1054,"style":669},[668],[671,1056,1057],{"xmlns":673,"width":674,"height":675,"style":676,"viewBox":677,"preserveAspectRatio":678},[680,1058],{"d":682},", geben die gekrümmten Finger die Durchlaufrichtung von ",[576,1061,1063,1078],{"className":1062},[579],[576,1064,1066],{"className":1065},[583],[585,1067,1068],{"xmlns":587},[589,1069,1070,1076],{},[592,1071,1072,1074],{},[599,1073,734],{"mathvariant":733},[599,1075,701],{},[607,1077,739],{"encoding":609},[576,1079,1081],{"className":1080,"ariaHidden":597},[614],[576,1082,1084,1087,1090],{"className":1083},[618],[576,1085],{"className":1086,"style":749},[622],[576,1088,734],{"className":1089,"style":753},[627],[576,1091,701],{"className":1092,"style":717},[627,652]," an. Bei einer Fläche in der ",[576,1095,1097,1111],{"className":1096},[579],[576,1098,1100],{"className":1099},[583],[585,1101,1102],{"xmlns":587},[589,1103,1104,1109],{},[592,1105,1106],{},[599,1107,1108],{},"x",[607,1110,1108],{"encoding":609},[576,1112,1114],{"className":1113,"ariaHidden":597},[614],[576,1115,1117,1121],{"className":1116},[618],[576,1118],{"className":1119,"style":1120},[622],"height:0.4306em;",[576,1122,1108],{"className":1123},[627,652],"-",[576,1126,1128,1142],{"className":1127},[579],[576,1129,1131],{"className":1130},[583],[585,1132,1133],{"xmlns":587},[589,1134,1135,1140],{},[592,1136,1137],{},[599,1138,1139],{},"y",[607,1141,1139],{"encoding":609},[576,1143,1145],{"className":1144,"ariaHidden":597},[614],[576,1146,1148,1152],{"className":1147},[618],[576,1149],{"className":1150,"style":1151},[622],"height:0.625em;vertical-align:-0.1944em;",[576,1153,1139],{"className":1154,"style":1155},[627,652],"margin-right:0.0359em;","-Ebene mit ",[576,1158,1160,1194],{"className":1159},[579],[576,1161,1163],{"className":1162},[583],[585,1164,1165],{"xmlns":587},[589,1166,1167,1191],{},[592,1168,1169,1175,1178],{},[595,1170,1171,1173],{"accent":597},[599,1172,1007],{},[603,1174,605],{},[603,1176,1177],{},"=",[1179,1180,1181,1188],"msub",{},[595,1182,1183,1186],{"accent":597},[599,1184,1185],{},"e",[603,1187,605],{},[599,1189,1190],{},"z",[607,1192,1193],{"encoding":609},"\\vec n = \\vec e_z",[576,1195,1197,1247],{"className":1196,"ariaHidden":597},[614],[576,1198,1200,1203,1238,1241,1244],{"className":1199},[618],[576,1201],{"className":1202,"style":1022},[622],[576,1204,1206],{"className":1205},[627,628],[576,1207,1209],{"className":1208},[632],[576,1210,1212],{"className":1211},[636],[576,1213,1215,1223],{"className":1214,"style":1022},[640],[576,1216,1217,1220],{"style":643},[576,1218],{"className":1219,"style":648},[647],[576,1221,1007],{"className":1222},[627,652],[576,1224,1225,1228],{"style":643},[576,1226],{"className":1227,"style":648},[647],[576,1229,1231],{"className":1230,"style":1051},[663],[576,1232,1234],{"className":1233,"style":669},[668],[671,1235,1236],{"xmlns":673,"width":674,"height":675,"style":676,"viewBox":677,"preserveAspectRatio":678},[680,1237],{"d":682},[576,1239],{"className":1240,"style":935},[934],[576,1242,1177],{"className":1243},[939],[576,1245],{"className":1246,"style":935},[934],[576,1248,1250,1254],{"className":1249},[618],[576,1251],{"className":1252,"style":1253},[622],"height:0.864em;vertical-align:-0.15em;",[576,1255,1257,1293],{"className":1256},[627],[576,1258,1260],{"className":1259},[627,628],[576,1261,1263],{"className":1262},[632],[576,1264,1266],{"className":1265},[636],[576,1267,1269,1277],{"className":1268,"style":1022},[640],[576,1270,1271,1274],{"style":643},[576,1272],{"className":1273,"style":648},[647],[576,1275,1185],{"className":1276},[627,652],[576,1278,1279,1282],{"style":643},[576,1280],{"className":1281,"style":648},[647],[576,1283,1286],{"className":1284,"style":1285},[663],"left:-0.1799em;",[576,1287,1289],{"className":1288,"style":669},[668],[671,1290,1291],{"xmlns":673,"width":674,"height":675,"style":676,"viewBox":677,"preserveAspectRatio":678},[680,1292],{"d":682},[576,1294,1296],{"className":1295},[960],[576,1297,1300,1325],{"className":1298},[632,1299],"vlist-t2",[576,1301,1303,1320],{"className":1302},[636],[576,1304,1307],{"className":1305,"style":1306},[640],"height:0.1514em;",[576,1308,1310,1313],{"style":1309},"top:-2.55em;margin-left:0em;margin-right:0.05em;",[576,1311],{"className":1312,"style":976},[647],[576,1314,1316],{"className":1315},[980,981,982,983],[576,1317,1190],{"className":1318,"style":1319},[627,652,983],"margin-right:0.044em;",[576,1321,1324],{"className":1322},[1323],"vlist-s","​",[576,1326,1328],{"className":1327},[636],[576,1329,1332],{"className":1330,"style":1331},[640],"height:0.15em;",[576,1333],{}," läuft der Rand also gegen den Uhrzeigersinn.",[564,1336,1337,1338,1402,1403,1547],{},"Das Ergebnis hängt nur von der Randkurve ab. Alle Flächen mit demselben Rand, z.B. eine Kreisscheibe und eine Halbkugel darüber, liefern denselben Wert, sofern ",[576,1339,1341,1358],{"className":1340},[579],[576,1342,1344],{"className":1343},[583],[585,1345,1346],{"xmlns":587},[589,1347,1348,1356],{},[592,1349,1350],{},[595,1351,1352,1354],{"accent":597},[599,1353,601],{},[603,1355,605],{},[607,1357,610],{"encoding":609},[576,1359,1361],{"className":1360,"ariaHidden":597},[614],[576,1362,1364,1367],{"className":1363},[618],[576,1365],{"className":1366,"style":623},[622],[576,1368,1370],{"className":1369},[627,628],[576,1371,1373],{"className":1372},[632],[576,1374,1376],{"className":1375},[636],[576,1377,1379,1387],{"className":1378,"style":623},[640],[576,1380,1381,1384],{"style":643},[576,1382],{"className":1383,"style":648},[647],[576,1385,601],{"className":1386,"style":653},[627,652],[576,1388,1389,1392],{"style":656},[576,1390],{"className":1391,"style":648},[647],[576,1393,1395],{"className":1394,"style":664},[663],[576,1396,1398],{"className":1397,"style":669},[668],[671,1399,1400],{"xmlns":673,"width":674,"height":675,"style":676,"viewBox":677,"preserveAspectRatio":678},[680,1401],{"d":682}," auf allen diesen Flächen stetig differenzierbar ist. Folgerung: Ist ",[576,1404,1406,1439],{"className":1405},[579],[576,1407,1409],{"className":1408},[583],[585,1410,1411],{"xmlns":587},[589,1412,1413,1436],{},[592,1414,1415,1418,1421,1427,1429],{},[599,1416,1417],{"mathvariant":733},"rot",[603,1419,1420],{},"⁡",[595,1422,1423,1425],{"accent":597},[599,1424,601],{},[603,1426,605],{},[603,1428,1177],{},[595,1430,1431,1434],{"accent":597},[880,1432,1433],{},"0",[603,1435,605],{},[607,1437,1438],{"encoding":609},"\\operatorname{rot} \\vec F = \\vec 0",[576,1440,1442,1504],{"className":1441,"ariaHidden":597},[614],[576,1443,1445,1448,1456,1460,1495,1498,1501],{"className":1444},[618],[576,1446],{"className":1447,"style":623},[622],[576,1449,1452],{"className":1450},[1451],"mop",[576,1453,1417],{"className":1454},[627,1455],"mathrm",[576,1457],{"className":1458,"style":1459},[934],"margin-right:0.1667em;",[576,1461,1463],{"className":1462},[627,628],[576,1464,1466],{"className":1465},[632],[576,1467,1469],{"className":1468},[636],[576,1470,1472,1480],{"className":1471,"style":623},[640],[576,1473,1474,1477],{"style":643},[576,1475],{"className":1476,"style":648},[647],[576,1478,601],{"className":1479,"style":653},[627,652],[576,1481,1482,1485],{"style":656},[576,1483],{"className":1484,"style":648},[647],[576,1486,1488],{"className":1487,"style":664},[663],[576,1489,1491],{"className":1490,"style":669},[668],[671,1492,1493],{"xmlns":673,"width":674,"height":675,"style":676,"viewBox":677,"preserveAspectRatio":678},[680,1494],{"d":682},[576,1496],{"className":1497,"style":935},[934],[576,1499,1177],{"className":1500},[939],[576,1502],{"className":1503,"style":935},[934],[576,1505,1507,1511],{"className":1506},[618],[576,1508],{"className":1509,"style":1510},[622],"height:0.9274em;",[576,1512,1514],{"className":1513},[627,628],[576,1515,1517],{"className":1516},[632],[576,1518,1520],{"className":1519},[636],[576,1521,1523,1531],{"className":1522,"style":1510},[640],[576,1524,1525,1528],{"style":643},[576,1526],{"className":1527,"style":648},[647],[576,1529,1433],{"className":1530},[627],[576,1532,1534,1537],{"style":1533},"top:-3.2134em;",[576,1535],{"className":1536,"style":648},[647],[576,1538,1540],{"className":1539,"style":1051},[663],[576,1541,1543],{"className":1542,"style":669},[668],[671,1544,1545],{"xmlns":673,"width":674,"height":675,"style":676,"viewBox":677,"preserveAspectRatio":678},[680,1546],{"d":682},", ist die Zirkulation längs jeder Randkurve null.",[564,1549,1550,1551,1553],{},"Der ebene Sonderfall ist der ",[568,1552,553],{},":",[576,1555,1558],{"className":1556},[1557],"katex-display",[576,1559,1561,1684],{"className":1560},[579],[576,1562,1564],{"className":1563},[583],[585,1565,1567],{"xmlns":587,"display":1566},"block",[589,1568,1569,1681],{},[592,1570,1571,1579,1628,1631,1634,1636,1647,1650,1656,1660,1662,1664,1667,1673,1675,1677,1679],{},[1179,1572,1573,1576],{},[603,1574,1575],{},"∬",[599,1577,1578],{},"D",[592,1580,1581,1584,1604,1607,1625],{},[603,1582,1583],{"fence":597},"(",[1585,1586,1587,1598],"mfrac",{},[592,1588,1589,1591],{},[599,1590,734],{"mathvariant":733},[1179,1592,1593,1595],{},[599,1594,601],{},[880,1596,1597],{},"2",[592,1599,1600,1602],{},[599,1601,734],{"mathvariant":733},[599,1603,1108],{},[603,1605,1606],{},"−",[1585,1608,1609,1619],{},[592,1610,1611,1613],{},[599,1612,734],{"mathvariant":733},[1179,1614,1615,1617],{},[599,1616,601],{},[880,1618,882],{},[592,1620,1621,1623],{},[599,1622,734],{"mathvariant":733},[599,1624,1139],{},[603,1626,1627],{"fence":597},")",[599,1629,1630],{},"d",[599,1632,1633],{},"A",[603,1635,1177],{},[1179,1637,1638,1641],{},[603,1639,1640],{},"∮",[592,1642,1643,1645],{},[599,1644,734],{"mathvariant":733},[599,1646,1578],{},[603,1648,1583],{"stretchy":1649},"false",[1179,1651,1652,1654],{},[599,1653,601],{},[880,1655,882],{},[1657,1658,1659],"mtext",{}," ",[599,1661,1630],{},[599,1663,1108],{},[603,1665,1666],{},"+",[1179,1668,1669,1671],{},[599,1670,601],{},[880,1672,1597],{},[1657,1674,1659],{},[599,1676,1630],{},[599,1678,1139],{},[603,1680,1627],{"stretchy":1649},[607,1682,1683],{"encoding":609},"\\iint_D \\left( \\frac{\\partial F_2}{\\partial x} - \\frac{\\partial F_1}{\\partial y} \\right) dA = \\oint_{\\partial D} (F_1\\, dx + F_2\\, dy)",[576,1685,1687,2015,2133],{"className":1686,"ariaHidden":597},[614],[576,1688,1690,1694,1741,1744,1997,2000,2003,2006,2009,2012],{"className":1689},[618],[576,1691],{"className":1692,"style":1693},[622],"height:2.4em;vertical-align:-0.95em;",[576,1695,1697,1703],{"className":1696},[1451],[576,1698,1575],{"className":1699,"style":1702},[1451,1700,1701],"op-symbol","large-op","margin-right:0.4445em;position:relative;top:-0.001em;",[576,1704,1706],{"className":1705},[960],[576,1707,1709,1732],{"className":1708},[632,1299],[576,1710,1712,1729],{"className":1711},[636],[576,1713,1716],{"className":1714,"style":1715},[640],"height:-0.4334em;",[576,1717,1719,1722],{"style":1718},"top:-1.7883em;margin-left:-0.4445em;margin-right:0.05em;",[576,1720],{"className":1721,"style":976},[647],[576,1723,1725],{"className":1724},[980,981,982,983],[576,1726,1578],{"className":1727,"style":1728},[627,652,983],"margin-right:0.0278em;",[576,1730,1324],{"className":1731},[1323],[576,1733,1735],{"className":1734},[636],[576,1736,1739],{"className":1737,"style":1738},[640],"height:0.9117em;",[576,1740],{},[576,1742],{"className":1743,"style":1459},[934],[576,1745,1748,1758,1874,1878,1882,1885,1991],{"className":1746},[1747],"minner",[576,1749,1754],{"className":1750,"style":1753},[1751,1752],"mopen","delimcenter","top:0em;",[576,1755,1583],{"className":1756},[1757,982],"delimsizing",[576,1759,1761,1765,1870],{"className":1760},[627],[576,1762],{"className":1763},[1751,1764],"nulldelimiter",[576,1766,1768],{"className":1767},[1585],[576,1769,1771,1861],{"className":1770},[632,1299],[576,1772,1774,1858],{"className":1773},[636],[576,1775,1778,1793,1804],{"className":1776,"style":1777},[640],"height:1.3714em;",[576,1779,1781,1784],{"style":1780},"top:-2.314em;",[576,1782],{"className":1783,"style":648},[647],[576,1785,1787,1790],{"className":1786},[627],[576,1788,734],{"className":1789,"style":753},[627],[576,1791,1108],{"className":1792},[627,652],[576,1794,1796,1799],{"style":1795},"top:-3.23em;",[576,1797],{"className":1798,"style":648},[647],[576,1800],{"className":1801,"style":1803},[1802],"frac-line","border-bottom-width:0.04em;",[576,1805,1807,1810],{"style":1806},"top:-3.677em;",[576,1808],{"className":1809,"style":648},[647],[576,1811,1813,1816],{"className":1812},[627],[576,1814,734],{"className":1815,"style":753},[627],[576,1817,1819,1822],{"className":1818},[627],[576,1820,601],{"className":1821,"style":653},[627,652],[576,1823,1825],{"className":1824},[960],[576,1826,1828,1850],{"className":1827},[632,1299],[576,1829,1831,1847],{"className":1830},[636],[576,1832,1835],{"className":1833,"style":1834},[640],"height:0.3011em;",[576,1836,1838,1841],{"style":1837},"top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;",[576,1839],{"className":1840,"style":976},[647],[576,1842,1844],{"className":1843},[980,981,982,983],[576,1845,1597],{"className":1846},[627,983],[576,1848,1324],{"className":1849},[1323],[576,1851,1853],{"className":1852},[636],[576,1854,1856],{"className":1855,"style":1331},[640],[576,1857],{},[576,1859,1324],{"className":1860},[1323],[576,1862,1864],{"className":1863},[636],[576,1865,1868],{"className":1866,"style":1867},[640],"height:0.686em;",[576,1869],{},[576,1871],{"className":1872},[1873,1764],"mclose",[576,1875],{"className":1876,"style":1877},[934],"margin-right:0.2222em;",[576,1879,1606],{"className":1880},[1881],"mbin",[576,1883],{"className":1884,"style":1877},[934],[576,1886,1888,1891,1988],{"className":1887},[627],[576,1889],{"className":1890},[1751,1764],[576,1892,1894],{"className":1893},[1585],[576,1895,1897,1979],{"className":1896},[632,1299],[576,1898,1900,1976],{"className":1899},[636],[576,1901,1903,1917,1925],{"className":1902,"style":1777},[640],[576,1904,1905,1908],{"style":1780},[576,1906],{"className":1907,"style":648},[647],[576,1909,1911,1914],{"className":1910},[627],[576,1912,734],{"className":1913,"style":753},[627],[576,1915,1139],{"className":1916,"style":1155},[627,652],[576,1918,1919,1922],{"style":1795},[576,1920],{"className":1921,"style":648},[647],[576,1923],{"className":1924,"style":1803},[1802],[576,1926,1927,1930],{"style":1806},[576,1928],{"className":1929,"style":648},[647],[576,1931,1933,1936],{"className":1932},[627],[576,1934,734],{"className":1935,"style":753},[627],[576,1937,1939,1942],{"className":1938},[627],[576,1940,601],{"className":1941,"style":653},[627,652],[576,1943,1945],{"className":1944},[960],[576,1946,1948,1968],{"className":1947},[632,1299],[576,1949,1951,1965],{"className":1950},[636],[576,1952,1954],{"className":1953,"style":1834},[640],[576,1955,1956,1959],{"style":1837},[576,1957],{"className":1958,"style":976},[647],[576,1960,1962],{"className":1961},[980,981,982,983],[576,1963,882],{"className":1964},[627,983],[576,1966,1324],{"className":1967},[1323],[576,1969,1971],{"className":1970},[636],[576,1972,1974],{"className":1973,"style":1331},[640],[576,1975],{},[576,1977,1324],{"className":1978},[1323],[576,1980,1982],{"className":1981},[636],[576,1983,1986],{"className":1984,"style":1985},[640],"height:0.8804em;",[576,1987],{},[576,1989],{"className":1990},[1873,1764],[576,1992,1994],{"className":1993,"style":1753},[1873,1752],[576,1995,1627],{"className":1996},[1757,982],[576,1998],{"className":1999,"style":1459},[934],[576,2001,1630],{"className":2002},[627,652],[576,2004,1633],{"className":2005},[627,652],[576,2007],{"className":2008,"style":935},[934],[576,2010,1177],{"className":2011},[939],[576,2013],{"className":2014,"style":935},[934],[576,2016,2018,2022,2072,2075,2115,2118,2121,2124,2127,2130],{"className":2017},[618],[576,2019],{"className":2020,"style":2021},[622],"height:2.2719em;vertical-align:-0.9119em;",[576,2023,2025,2029],{"className":2024},[1451],[576,2026,1640],{"className":2027,"style":2028},[1451,1700,1701],"margin-right:0.4445em;position:relative;top:-0.0011em;",[576,2030,2032],{"className":2031},[960],[576,2033,2035,2063],{"className":2034},[632,1299],[576,2036,2038,2060],{"className":2037},[636],[576,2039,2042],{"className":2040,"style":2041},[640],"height:-0.4258em;",[576,2043,2045,2048],{"style":2044},"top:-1.7881em;margin-left:-0.4445em;margin-right:0.05em;",[576,2046],{"className":2047,"style":976},[647],[576,2049,2051],{"className":2050},[980,981,982,983],[576,2052,2054,2057],{"className":2053},[627,983],[576,2055,734],{"className":2056,"style":753},[627,983],[576,2058,1578],{"className":2059,"style":1728},[627,652,983],[576,2061,1324],{"className":2062},[1323],[576,2064,2066],{"className":2065},[636],[576,2067,2070],{"className":2068,"style":2069},[640],"height:0.9119em;",[576,2071],{},[576,2073,1583],{"className":2074},[1751],[576,2076,2078,2081],{"className":2077},[627],[576,2079,601],{"className":2080,"style":653},[627,652],[576,2082,2084],{"className":2083},[960],[576,2085,2087,2107],{"className":2086},[632,1299],[576,2088,2090,2104],{"className":2089},[636],[576,2091,2093],{"className":2092,"style":1834},[640],[576,2094,2095,2098],{"style":1837},[576,2096],{"className":2097,"style":976},[647],[576,2099,2101],{"className":2100},[980,981,982,983],[576,2102,882],{"className":2103},[627,983],[576,2105,1324],{"className":2106},[1323],[576,2108,2110],{"className":2109},[636],[576,2111,2113],{"className":2112,"style":1331},[640],[576,2114],{},[576,2116],{"className":2117,"style":1459},[934],[576,2119,1630],{"className":2120},[627,652],[576,2122,1108],{"className":2123},[627,652],[576,2125],{"className":2126,"style":1877},[934],[576,2128,1666],{"className":2129},[1881],[576,2131],{"className":2132,"style":1877},[934],[576,2134,2136,2140,2180,2183,2186,2189],{"className":2135},[618],[576,2137],{"className":2138,"style":2139},[622],"height:1em;vertical-align:-0.25em;",[576,2141,2143,2146],{"className":2142},[627],[576,2144,601],{"className":2145,"style":653},[627,652],[576,2147,2149],{"className":2148},[960],[576,2150,2152,2172],{"className":2151},[632,1299],[576,2153,2155,2169],{"className":2154},[636],[576,2156,2158],{"className":2157,"style":1834},[640],[576,2159,2160,2163],{"style":1837},[576,2161],{"className":2162,"style":976},[647],[576,2164,2166],{"className":2165},[980,981,982,983],[576,2167,1597],{"className":2168},[627,983],[576,2170,1324],{"className":2171},[1323],[576,2173,2175],{"className":2174},[636],[576,2176,2178],{"className":2177,"style":1331},[640],[576,2179],{},[576,2181],{"className":2182,"style":1459},[934],[576,2184,1630],{"className":2185},[627,652],[576,2187,1139],{"className":2188,"style":1155},[627,652],[576,2190,1627],{"className":2191},[1873],[559,2193,2195],{"id":2194},"beispiele","Beispiele",[564,2197,2198,2199,2373,2374,2404,2405,1124,2433,2461,2462,2628,2629,1553],{},"Für ",[576,2200,2202,2249],{"className":2201},[579],[576,2203,2205],{"className":2204},[583],[585,2206,2207],{"xmlns":587},[589,2208,2209,2246],{},[592,2210,2211,2217,2219,2221,2223,2225,2228,2231,2233,2235,2237,2239],{},[595,2212,2213,2215],{"accent":597},[599,2214,601],{},[603,2216,605],{},[603,2218,1177],{},[603,2220,1583],{"stretchy":1649},[603,2222,1606],{},[599,2224,1139],{},[603,2226,2227],{"separator":597},",",[1657,2229,2230],{}," ",[599,2232,1108],{},[603,2234,2227],{"separator":597},[1657,2236,2230],{},[880,2238,1433],{},[874,2240,2241,2243],{},[603,2242,1627],{"stretchy":1649},[599,2244,2245],{},"T",[607,2247,2248],{"encoding":609},"\\vec F = (-y,\\ x,\\ 0)^T",[576,2250,2252,2302],{"className":2251,"ariaHidden":597},[614],[576,2253,2255,2258,2293,2296,2299],{"className":2254},[618],[576,2256],{"className":2257,"style":623},[622],[576,2259,2261],{"className":2260},[627,628],[576,2262,2264],{"className":2263},[632],[576,2265,2267],{"className":2266},[636],[576,2268,2270,2278],{"className":2269,"style":623},[640],[576,2271,2272,2275],{"style":643},[576,2273],{"className":2274,"style":648},[647],[576,2276,601],{"className":2277,"style":653},[627,652],[576,2279,2280,2283],{"style":656},[576,2281],{"className":2282,"style":648},[647],[576,2284,2286],{"className":2285,"style":664},[663],[576,2287,2289],{"className":2288,"style":669},[668],[671,2290,2291],{"xmlns":673,"width":674,"height":675,"style":676,"viewBox":677,"preserveAspectRatio":678},[680,2292],{"d":682},[576,2294],{"className":2295,"style":935},[934],[576,2297,1177],{"className":2298},[939],[576,2300],{"className":2301,"style":935},[934],[576,2303,2305,2309,2312,2315,2318,2322,2325,2328,2331,2334,2337,2340,2343],{"className":2304},[618],[576,2306],{"className":2307,"style":2308},[622],"height:1.0913em;vertical-align:-0.25em;",[576,2310,1583],{"className":2311},[1751],[576,2313,1606],{"className":2314},[627],[576,2316,1139],{"className":2317,"style":1155},[627,652],[576,2319,2227],{"className":2320},[2321],"mpunct",[576,2323,2230],{"className":2324},[934],[576,2326],{"className":2327,"style":1459},[934],[576,2329,1108],{"className":2330},[627,652],[576,2332,2227],{"className":2333},[2321],[576,2335,2230],{"className":2336},[934],[576,2338],{"className":2339,"style":1459},[934],[576,2341,1433],{"className":2342},[627],[576,2344,2346,2349],{"className":2345},[1873],[576,2347,1627],{"className":2348},[1873],[576,2350,2352],{"className":2351},[960],[576,2353,2355],{"className":2354},[632],[576,2356,2358],{"className":2357},[636],[576,2359,2362],{"className":2360,"style":2361},[640],"height:0.8413em;",[576,2363,2364,2367],{"style":972},[576,2365],{"className":2366,"style":976},[647],[576,2368,2370],{"className":2369},[980,981,982,983],[576,2371,2245],{"className":2372,"style":653},[627,652,983]," und die Kreisscheibe mit Radius ",[576,2375,2377,2391],{"className":2376},[579],[576,2378,2380],{"className":2379},[583],[585,2381,2382],{"xmlns":587},[589,2383,2384,2389],{},[592,2385,2386],{},[599,2387,2388],{},"R",[607,2390,2388],{"encoding":609},[576,2392,2394],{"className":2393,"ariaHidden":597},[614],[576,2395,2397,2400],{"className":2396},[618],[576,2398],{"className":2399,"style":713},[622],[576,2401,2388],{"className":2402,"style":2403},[627,652],"margin-right:0.0077em;"," in der ",[576,2406,2408,2421],{"className":2407},[579],[576,2409,2411],{"className":2410},[583],[585,2412,2413],{"xmlns":587},[589,2414,2415,2419],{},[592,2416,2417],{},[599,2418,1108],{},[607,2420,1108],{"encoding":609},[576,2422,2424],{"className":2423,"ariaHidden":597},[614],[576,2425,2427,2430],{"className":2426},[618],[576,2428],{"className":2429,"style":1120},[622],[576,2431,1108],{"className":2432},[627,652],[576,2434,2436,2449],{"className":2435},[579],[576,2437,2439],{"className":2438},[583],[585,2440,2441],{"xmlns":587},[589,2442,2443,2447],{},[592,2444,2445],{},[599,2446,1139],{},[607,2448,1139],{"encoding":609},[576,2450,2452],{"className":2451,"ariaHidden":597},[614],[576,2453,2455,2458],{"className":2454},[618],[576,2456],{"className":2457,"style":1151},[622],[576,2459,1139],{"className":2460,"style":1155},[627,652],"-Ebene ist ",[576,2463,2465,2507],{"className":2464},[579],[576,2466,2468],{"className":2467},[583],[585,2469,2470],{"xmlns":587},[589,2471,2472,2504],{},[592,2473,2474,2476,2478,2484,2486,2488,2490,2492,2494,2496,2498],{},[599,2475,1417],{"mathvariant":733},[603,2477,1420],{},[595,2479,2480,2482],{"accent":597},[599,2481,601],{},[603,2483,605],{},[603,2485,1177],{},[603,2487,1583],{"stretchy":1649},[880,2489,1433],{},[603,2491,2227],{"separator":597},[880,2493,1433],{},[603,2495,2227],{"separator":597},[880,2497,1597],{},[874,2499,2500,2502],{},[603,2501,1627],{"stretchy":1649},[599,2503,2245],{},[607,2505,2506],{"encoding":609},"\\operatorname{rot} \\vec F = (0, 0, 2)^T",[576,2508,2510,2569],{"className":2509,"ariaHidden":597},[614],[576,2511,2513,2516,2522,2525,2560,2563,2566],{"className":2512},[618],[576,2514],{"className":2515,"style":623},[622],[576,2517,2519],{"className":2518},[1451],[576,2520,1417],{"className":2521},[627,1455],[576,2523],{"className":2524,"style":1459},[934],[576,2526,2528],{"className":2527},[627,628],[576,2529,2531],{"className":2530},[632],[576,2532,2534],{"className":2533},[636],[576,2535,2537,2545],{"className":2536,"style":623},[640],[576,2538,2539,2542],{"style":643},[576,2540],{"className":2541,"style":648},[647],[576,2543,601],{"className":2544,"style":653},[627,652],[576,2546,2547,2550],{"style":656},[576,2548],{"className":2549,"style":648},[647],[576,2551,2553],{"className":2552,"style":664},[663],[576,2554,2556],{"className":2555,"style":669},[668],[671,2557,2558],{"xmlns":673,"width":674,"height":675,"style":676,"viewBox":677,"preserveAspectRatio":678},[680,2559],{"d":682},[576,2561],{"className":2562,"style":935},[934],[576,2564,1177],{"className":2565},[939],[576,2567],{"className":2568,"style":935},[934],[576,2570,2572,2575,2578,2581,2584,2587,2590,2593,2596,2599],{"className":2571},[618],[576,2573],{"className":2574,"style":2308},[622],[576,2576,1583],{"className":2577},[1751],[576,2579,1433],{"className":2580},[627],[576,2582,2227],{"className":2583},[2321],[576,2585],{"className":2586,"style":1459},[934],[576,2588,1433],{"className":2589},[627],[576,2591,2227],{"className":2592},[2321],[576,2594],{"className":2595,"style":1459},[934],[576,2597,1597],{"className":2598},[627],[576,2600,2602,2605],{"className":2601},[1873],[576,2603,1627],{"className":2604},[1873],[576,2606,2608],{"className":2607},[960],[576,2609,2611],{"className":2610},[632],[576,2612,2614],{"className":2613},[636],[576,2615,2617],{"className":2616,"style":2361},[640],[576,2618,2619,2622],{"style":972},[576,2620],{"className":2621,"style":976},[647],[576,2623,2625],{"className":2624},[980,981,982,983],[576,2626,2245],{"className":2627,"style":653},[627,652,983]," und ",[576,2630,2632,2670],{"className":2631},[579],[576,2633,2635],{"className":2634},[583],[585,2636,2637],{"xmlns":587},[589,2638,2639,2667],{},[592,2640,2641,2647,2649,2651,2653,2655,2657,2659,2661],{},[595,2642,2643,2645],{"accent":597},[599,2644,1007],{},[603,2646,605],{},[603,2648,1177],{},[603,2650,1583],{"stretchy":1649},[880,2652,1433],{},[603,2654,2227],{"separator":597},[880,2656,1433],{},[603,2658,2227],{"separator":597},[880,2660,882],{},[874,2662,2663,2665],{},[603,2664,1627],{"stretchy":1649},[599,2666,2245],{},[607,2668,2669],{"encoding":609},"\\vec n = (0, 0, 1)^T",[576,2671,2673,2723],{"className":2672,"ariaHidden":597},[614],[576,2674,2676,2679,2714,2717,2720],{"className":2675},[618],[576,2677],{"className":2678,"style":1022},[622],[576,2680,2682],{"className":2681},[627,628],[576,2683,2685],{"className":2684},[632],[576,2686,2688],{"className":2687},[636],[576,2689,2691,2699],{"className":2690,"style":1022},[640],[576,2692,2693,2696],{"style":643},[576,2694],{"className":2695,"style":648},[647],[576,2697,1007],{"className":2698},[627,652],[576,2700,2701,2704],{"style":643},[576,2702],{"className":2703,"style":648},[647],[576,2705,2707],{"className":2706,"style":1051},[663],[576,2708,2710],{"className":2709,"style":669},[668],[671,2711,2712],{"xmlns":673,"width":674,"height":675,"style":676,"viewBox":677,"preserveAspectRatio":678},[680,2713],{"d":682},[576,2715],{"className":2716,"style":935},[934],[576,2718,1177],{"className":2719},[939],[576,2721],{"className":2722,"style":935},[934],[576,2724,2726,2729,2732,2735,2738,2741,2744,2747,2750,2753],{"className":2725},[618],[576,2727],{"className":2728,"style":2308},[622],[576,2730,1583],{"className":2731},[1751],[576,2733,1433],{"className":2734},[627],[576,2736,2227],{"className":2737},[2321],[576,2739],{"className":2740,"style":1459},[934],[576,2742,1433],{"className":2743},[627],[576,2745,2227],{"className":2746},[2321],[576,2748],{"className":2749,"style":1459},[934],[576,2751,882],{"className":2752},[627],[576,2754,2756,2759],{"className":2755},[1873],[576,2757,1627],{"className":2758},[1873],[576,2760,2762],{"className":2761},[960],[576,2763,2765],{"className":2764},[632],[576,2766,2768],{"className":2767},[636],[576,2769,2771],{"className":2770,"style":2361},[640],[576,2772,2773,2776],{"style":972},[576,2774],{"className":2775,"style":976},[647],[576,2777,2779],{"className":2778},[980,981,982,983],[576,2780,2245],{"className":2781,"style":653},[627,652,983],[576,2783,2785],{"className":2784},[1557],[576,2786,2788,2842],{"className":2787},[579],[576,2789,2791],{"className":2790},[583],[585,2792,2793],{"xmlns":587,"display":1566},[589,2794,2795,2839],{},[592,2796,2797,2803,2805,2807,2809,2811,2813,2815,2818,2821,2827,2829,2831,2833],{},[1179,2798,2799,2801],{},[603,2800,1575],{},[599,2802,701],{},[880,2804,1597],{},[1657,2806,1659],{},[599,2808,1630],{},[599,2810,701],{},[603,2812,1177],{},[880,2814,1597],{},[603,2816,2817],{},"⋅",[599,2819,2820],{},"π",[874,2822,2823,2825],{},[599,2824,2388],{},[880,2826,1597],{},[603,2828,1177],{},[880,2830,1597],{},[599,2832,2820],{},[874,2834,2835,2837],{},[599,2836,2388],{},[880,2838,1597],{},[607,2840,2841],{"encoding":609},"\\iint_S 2\\, dS = 2 \\cdot \\pi R^2 = 2\\pi R^2",[576,2843,2845,2916,2935,2984],{"className":2844,"ariaHidden":597},[614],[576,2846,2848,2852,2892,2895,2898,2901,2904,2907,2910,2913],{"className":2847},[618],[576,2849],{"className":2850,"style":2851},[622],"height:2.2717em;vertical-align:-0.9117em;",[576,2853,2855,2858],{"className":2854},[1451],[576,2856,1575],{"className":2857,"style":1702},[1451,1700,1701],[576,2859,2861],{"className":2860},[960],[576,2862,2864,2884],{"className":2863},[632,1299],[576,2865,2867,2881],{"className":2866},[636],[576,2868,2870],{"className":2869,"style":1715},[640],[576,2871,2872,2875],{"style":1718},[576,2873],{"className":2874,"style":976},[647],[576,2876,2878],{"className":2877},[980,981,982,983],[576,2879,701],{"className":2880,"style":717},[627,652,983],[576,2882,1324],{"className":2883},[1323],[576,2885,2887],{"className":2886},[636],[576,2888,2890],{"className":2889,"style":1738},[640],[576,2891],{},[576,2893],{"className":2894,"style":1459},[934],[576,2896,1597],{"className":2897},[627],[576,2899],{"className":2900,"style":1459},[934],[576,2902,1630],{"className":2903},[627,652],[576,2905,701],{"className":2906,"style":717},[627,652],[576,2908],{"className":2909,"style":935},[934],[576,2911,1177],{"className":2912},[939],[576,2914],{"className":2915,"style":935},[934],[576,2917,2919,2923,2926,2929,2932],{"className":2918},[618],[576,2920],{"className":2921,"style":2922},[622],"height:0.6444em;",[576,2924,1597],{"className":2925},[627],[576,2927],{"className":2928,"style":1877},[934],[576,2930,2817],{"className":2931},[1881],[576,2933],{"className":2934,"style":1877},[934],[576,2936,2938,2942,2945,2975,2978,2981],{"className":2937},[618],[576,2939],{"className":2940,"style":2941},[622],"height:0.8641em;",[576,2943,2820],{"className":2944,"style":1155},[627,652],[576,2946,2948,2951],{"className":2947},[627],[576,2949,2388],{"className":2950,"style":2403},[627,652],[576,2952,2954],{"className":2953},[960],[576,2955,2957],{"className":2956},[632],[576,2958,2960],{"className":2959},[636],[576,2961,2963],{"className":2962,"style":2941},[640],[576,2964,2966,2969],{"style":2965},"top:-3.113em;margin-right:0.05em;",[576,2967],{"className":2968,"style":976},[647],[576,2970,2972],{"className":2971},[980,981,982,983],[576,2973,1597],{"className":2974},[627,983],[576,2976],{"className":2977,"style":935},[934],[576,2979,1177],{"className":2980},[939],[576,2982],{"className":2983,"style":935},[934],[576,2985,2987,2990,2993,2996],{"className":2986},[618],[576,2988],{"className":2989,"style":2941},[622],[576,2991,1597],{"className":2992},[627],[576,2994,2820],{"className":2995,"style":1155},[627,652],[576,2997,2999,3002],{"className":2998},[627],[576,3000,2388],{"className":3001,"style":2403},[627,652],[576,3003,3005],{"className":3004},[960],[576,3006,3008],{"className":3007},[632],[576,3009,3011],{"className":3010},[636],[576,3012,3014],{"className":3013,"style":2941},[640],[576,3015,3016,3019],{"style":2965},[576,3017],{"className":3018,"style":976},[647],[576,3020,3022],{"className":3021},[980,981,982,983],[576,3023,1597],{"className":3024},[627,983],[564,3026,3027,3028,3246,3247,3665,3666,3867,3868,3919,3920,3991],{},"Am Rand ",[576,3029,3031,3095],{"className":3030},[579],[576,3032,3034],{"className":3033},[583],[585,3035,3036],{"xmlns":587},[589,3037,3038,3092],{},[592,3039,3040,3047,3049,3052,3054,3056,3058,3060,3063,3065,3067,3069,3071,3073,3076,3078,3080,3082,3084,3086],{},[595,3041,3042,3045],{"accent":597},[599,3043,3044],{},"r",[603,3046,605],{},[603,3048,1583],{"stretchy":1649},[599,3050,3051],{},"t",[603,3053,1627],{"stretchy":1649},[603,3055,1177],{},[603,3057,1583],{"stretchy":1649},[599,3059,2388],{},[599,3061,3062],{},"cos",[603,3064,1420],{},[599,3066,3051],{},[603,3068,2227],{"separator":597},[1657,3070,2230],{},[599,3072,2388],{},[599,3074,3075],{},"sin",[603,3077,1420],{},[599,3079,3051],{},[603,3081,2227],{"separator":597},[1657,3083,2230],{},[880,3085,1433],{},[874,3087,3088,3090],{},[603,3089,1627],{"stretchy":1649},[599,3091,2245],{},[607,3093,3094],{"encoding":609},"\\vec r(t) = (R\\cos t,\\ R\\sin t,\\ 0)^T",[576,3096,3098,3157],{"className":3097,"ariaHidden":597},[614],[576,3099,3101,3104,3139,3142,3145,3148,3151,3154],{"className":3100},[618],[576,3102],{"className":3103,"style":2139},[622],[576,3105,3107],{"className":3106},[627,628],[576,3108,3110],{"className":3109},[632],[576,3111,3113],{"className":3112},[636],[576,3114,3116,3124],{"className":3115,"style":1022},[640],[576,3117,3118,3121],{"style":643},[576,3119],{"className":3120,"style":648},[647],[576,3122,3044],{"className":3123,"style":1728},[627,652],[576,3125,3126,3129],{"style":643},[576,3127],{"className":3128,"style":648},[647],[576,3130,3132],{"className":3131,"style":1285},[663],[576,3133,3135],{"className":3134,"style":669},[668],[671,3136,3137],{"xmlns":673,"width":674,"height":675,"style":676,"viewBox":677,"preserveAspectRatio":678},[680,3138],{"d":682},[576,3140,1583],{"className":3141},[1751],[576,3143,3051],{"className":3144},[627,652],[576,3146,1627],{"className":3147},[1873],[576,3149],{"className":3150,"style":935},[934],[576,3152,1177],{"className":3153},[939],[576,3155],{"className":3156,"style":935},[934],[576,3158,3160,3163,3166,3169,3172,3175,3178,3181,3184,3187,3190,3193,3196,3199,3202,3205,3208,3211,3214,3217],{"className":3159},[618],[576,3161],{"className":3162,"style":2308},[622],[576,3164,1583],{"className":3165},[1751],[576,3167,2388],{"className":3168,"style":2403},[627,652],[576,3170],{"className":3171,"style":1459},[934],[576,3173,3062],{"className":3174},[1451],[576,3176],{"className":3177,"style":1459},[934],[576,3179,3051],{"className":3180},[627,652],[576,3182,2227],{"className":3183},[2321],[576,3185,2230],{"className":3186},[934],[576,3188],{"className":3189,"style":1459},[934],[576,3191,2388],{"className":3192,"style":2403},[627,652],[576,3194],{"className":3195,"style":1459},[934],[576,3197,3075],{"className":3198},[1451],[576,3200],{"className":3201,"style":1459},[934],[576,3203,3051],{"className":3204},[627,652],[576,3206,2227],{"className":3207},[2321],[576,3209,2230],{"className":3210},[934],[576,3212],{"className":3213,"style":1459},[934],[576,3215,1433],{"className":3216},[627],[576,3218,3220,3223],{"className":3219},[1873],[576,3221,1627],{"className":3222},[1873],[576,3224,3226],{"className":3225},[960],[576,3227,3229],{"className":3228},[632],[576,3230,3232],{"className":3231},[636],[576,3233,3235],{"className":3234,"style":2361},[640],[576,3236,3237,3240],{"style":972},[576,3238],{"className":3239,"style":976},[647],[576,3241,3243],{"className":3242},[980,981,982,983],[576,3244,2245],{"className":3245,"style":653},[627,652,983]," ist ",[576,3248,3250,3329],{"className":3249},[579],[576,3251,3253],{"className":3252},[583],[585,3254,3255],{"xmlns":587},[589,3256,3257,3326],{},[592,3258,3259,3265,3267,3278,3280,3286,3296,3298,3300,3306,3316,3318,3320],{},[595,3260,3261,3263],{"accent":597},[599,3262,601],{},[603,3264,605],{},[603,3266,2817],{},[595,3268,3269,3275],{"accent":597},[595,3270,3271,3273],{"accent":597},[599,3272,3044],{},[603,3274,605],{},[603,3276,3277],{},"˙",[603,3279,1177],{},[874,3281,3282,3284],{},[599,3283,2388],{},[880,3285,1597],{},[874,3287,3288,3294],{},[592,3289,3290,3292],{},[599,3291,3075],{},[603,3293,1420],{},[880,3295,1597],{},[599,3297,3051],{},[603,3299,1666],{},[874,3301,3302,3304],{},[599,3303,2388],{},[880,3305,1597],{},[874,3307,3308,3314],{},[592,3309,3310,3312],{},[599,3311,3062],{},[603,3313,1420],{},[880,3315,1597],{},[599,3317,3051],{},[603,3319,1177],{},[874,3321,3322,3324],{},[599,3323,2388],{},[880,3325,1597],{},[607,3327,3328],{"encoding":609},"\\vec F \\cdot \\dot{\\vec r} = R^2 \\sin^2 t + R^2 \\cos^2 t = R^2",[576,3330,3332,3382,3463,3548,3630],{"className":3331,"ariaHidden":597},[614],[576,3333,3335,3338,3373,3376,3379],{"className":3334},[618],[576,3336],{"className":3337,"style":623},[622],[576,3339,3341],{"className":3340},[627,628],[576,3342,3344],{"className":3343},[632],[576,3345,3347],{"className":3346},[636],[576,3348,3350,3358],{"className":3349,"style":623},[640],[576,3351,3352,3355],{"style":643},[576,3353],{"className":3354,"style":648},[647],[576,3356,601],{"className":3357,"style":653},[627,652],[576,3359,3360,3363],{"style":656},[576,3361],{"className":3362,"style":648},[647],[576,3364,3366],{"className":3365,"style":664},[663],[576,3367,3369],{"className":3368,"style":669},[668],[671,3370,3371],{"xmlns":673,"width":674,"height":675,"style":676,"viewBox":677,"preserveAspectRatio":678},[680,3372],{"d":682},[576,3374],{"className":3375,"style":1877},[934],[576,3377,2817],{"className":3378},[1881],[576,3380],{"className":3381,"style":1877},[934],[576,3383,3385,3389,3454,3457,3460],{"className":3384},[618],[576,3386],{"className":3387,"style":3388},[622],"height:0.9509em;",[576,3390,3392],{"className":3391},[627,628],[576,3393,3395],{"className":3394},[632],[576,3396,3398],{"className":3397},[636],[576,3399,3401,3441],{"className":3400,"style":3388},[640],[576,3402,3403,3406],{"style":643},[576,3404],{"className":3405,"style":648},[647],[576,3407,3409],{"className":3408},[627,628],[576,3410,3412],{"className":3411},[632],[576,3413,3415],{"className":3414},[636],[576,3416,3418,3426],{"className":3417,"style":1022},[640],[576,3419,3420,3423],{"style":643},[576,3421],{"className":3422,"style":648},[647],[576,3424,3044],{"className":3425,"style":1728},[627,652],[576,3427,3428,3431],{"style":643},[576,3429],{"className":3430,"style":648},[647],[576,3432,3434],{"className":3433,"style":1285},[663],[576,3435,3437],{"className":3436,"style":669},[668],[671,3438,3439],{"xmlns":673,"width":674,"height":675,"style":676,"viewBox":677,"preserveAspectRatio":678},[680,3440],{"d":682},[576,3442,3444,3447],{"style":3443},"top:-3.283em;",[576,3445],{"className":3446,"style":648},[647],[576,3448,3451],{"className":3449,"style":3450},[663],"left:-0.1389em;",[576,3452,3277],{"className":3453},[627],[576,3455],{"className":3456,"style":935},[934],[576,3458,1177],{"className":3459},[939],[576,3461],{"className":3462,"style":935},[934],[576,3464,3466,3470,3499,3502,3533,3536,3539,3542,3545],{"className":3465},[618],[576,3467],{"className":3468,"style":3469},[622],"height:0.9552em;vertical-align:-0.0833em;",[576,3471,3473,3476],{"className":3472},[627],[576,3474,2388],{"className":3475,"style":2403},[627,652],[576,3477,3479],{"className":3478},[960],[576,3480,3482],{"className":3481},[632],[576,3483,3485],{"className":3484},[636],[576,3486,3488],{"className":3487,"style":949},[640],[576,3489,3490,3493],{"style":972},[576,3491],{"className":3492,"style":976},[647],[576,3494,3496],{"className":3495},[980,981,982,983],[576,3497,1597],{"className":3498},[627,983],[576,3500],{"className":3501,"style":1459},[934],[576,3503,3505,3508],{"className":3504},[1451],[576,3506,3075],{"className":3507},[1451],[576,3509,3511],{"className":3510},[960],[576,3512,3514],{"className":3513},[632],[576,3515,3517],{"className":3516},[636],[576,3518,3521],{"className":3519,"style":3520},[640],"height:0.8719em;",[576,3522,3524,3527],{"style":3523},"top:-3.1208em;margin-right:0.05em;",[576,3525],{"className":3526,"style":976},[647],[576,3528,3530],{"className":3529},[980,981,982,983],[576,3531,1597],{"className":3532},[627,983],[576,3534],{"className":3535,"style":1459},[934],[576,3537,3051],{"className":3538},[627,652],[576,3540],{"className":3541,"style":1877},[934],[576,3543,1666],{"className":3544},[1881],[576,3546],{"className":3547,"style":1877},[934],[576,3549,3551,3554,3583,3586,3615,3618,3621,3624,3627],{"className":3550},[618],[576,3552],{"className":3553,"style":949},[622],[576,3555,3557,3560],{"className":3556},[627],[576,3558,2388],{"className":3559,"style":2403},[627,652],[576,3561,3563],{"className":3562},[960],[576,3564,3566],{"className":3565},[632],[576,3567,3569],{"className":3568},[636],[576,3570,3572],{"className":3571,"style":949},[640],[576,3573,3574,3577],{"style":972},[576,3575],{"className":3576,"style":976},[647],[576,3578,3580],{"className":3579},[980,981,982,983],[576,3581,1597],{"className":3582},[627,983],[576,3584],{"className":3585,"style":1459},[934],[576,3587,3589,3592],{"className":3588},[1451],[576,3590,3062],{"className":3591},[1451],[576,3593,3595],{"className":3594},[960],[576,3596,3598],{"className":3597},[632],[576,3599,3601],{"className":3600},[636],[576,3602,3604],{"className":3603,"style":949},[640],[576,3605,3606,3609],{"style":972},[576,3607],{"className":3608,"style":976},[647],[576,3610,3612],{"className":3611},[980,981,982,983],[576,3613,1597],{"className":3614},[627,983],[576,3616],{"className":3617,"style":1459},[934],[576,3619,3051],{"className":3620},[627,652],[576,3622],{"className":3623,"style":935},[934],[576,3625,1177],{"className":3626},[939],[576,3628],{"className":3629,"style":935},[934],[576,3631,3633,3636],{"className":3632},[618],[576,3634],{"className":3635,"style":949},[622],[576,3637,3639,3642],{"className":3638},[627],[576,3640,2388],{"className":3641,"style":2403},[627,652],[576,3643,3645],{"className":3644},[960],[576,3646,3648],{"className":3647},[632],[576,3649,3651],{"className":3650},[636],[576,3652,3654],{"className":3653,"style":949},[640],[576,3655,3656,3659],{"style":972},[576,3657],{"className":3658,"style":976},[647],[576,3660,3662],{"className":3661},[980,981,982,983],[576,3663,1597],{"className":3664},[627,983],", also ",[576,3667,3669,3711],{"className":3668},[579],[576,3670,3672],{"className":3671},[583],[585,3673,3674],{"xmlns":587},[589,3675,3676,3708],{},[592,3677,3678,3680,3686,3688,3690,3696,3698,3700,3702],{},[603,3679,1640],{},[595,3681,3682,3684],{"accent":597},[599,3683,601],{},[603,3685,605],{},[603,3687,2817],{},[599,3689,1630],{},[595,3691,3692,3694],{"accent":597},[599,3693,3044],{},[603,3695,605],{},[603,3697,1177],{},[880,3699,1597],{},[599,3701,2820],{},[874,3703,3704,3706],{},[599,3705,2388],{},[880,3707,1597],{},[607,3709,3710],{"encoding":609},"\\oint \\vec F \\cdot d\\vec r = 2\\pi R^2",[576,3712,3714,3773,3826],{"className":3713,"ariaHidden":597},[614],[576,3715,3717,3721,3726,3729,3764,3767,3770],{"className":3716},[618],[576,3718],{"className":3719,"style":3720},[622],"height:1.2724em;vertical-align:-0.3061em;",[576,3722,1640],{"className":3723,"style":3725},[1451,1700,3724],"small-op","margin-right:0.1945em;position:relative;top:-0.0006em;",[576,3727],{"className":3728,"style":1459},[934],[576,3730,3732],{"className":3731},[627,628],[576,3733,3735],{"className":3734},[632],[576,3736,3738],{"className":3737},[636],[576,3739,3741,3749],{"className":3740,"style":623},[640],[576,3742,3743,3746],{"style":643},[576,3744],{"className":3745,"style":648},[647],[576,3747,601],{"className":3748,"style":653},[627,652],[576,3750,3751,3754],{"style":656},[576,3752],{"className":3753,"style":648},[647],[576,3755,3757],{"className":3756,"style":664},[663],[576,3758,3760],{"className":3759,"style":669},[668],[671,3761,3762],{"xmlns":673,"width":674,"height":675,"style":676,"viewBox":677,"preserveAspectRatio":678},[680,3763],{"d":682},[576,3765],{"className":3766,"style":1877},[934],[576,3768,2817],{"className":3769},[1881],[576,3771],{"className":3772,"style":1877},[934],[576,3774,3776,3779,3782,3817,3820,3823],{"className":3775},[618],[576,3777],{"className":3778,"style":1022},[622],[576,3780,1630],{"className":3781},[627,652],[576,3783,3785],{"className":3784},[627,628],[576,3786,3788],{"className":3787},[632],[576,3789,3791],{"className":3790},[636],[576,3792,3794,3802],{"className":3793,"style":1022},[640],[576,3795,3796,3799],{"style":643},[576,3797],{"className":3798,"style":648},[647],[576,3800,3044],{"className":3801,"style":1728},[627,652],[576,3803,3804,3807],{"style":643},[576,3805],{"className":3806,"style":648},[647],[576,3808,3810],{"className":3809,"style":1285},[663],[576,3811,3813],{"className":3812,"style":669},[668],[671,3814,3815],{"xmlns":673,"width":674,"height":675,"style":676,"viewBox":677,"preserveAspectRatio":678},[680,3816],{"d":682},[576,3818],{"className":3819,"style":935},[934],[576,3821,1177],{"className":3822},[939],[576,3824],{"className":3825,"style":935},[934],[576,3827,3829,3832,3835,3838],{"className":3828},[618],[576,3830],{"className":3831,"style":949},[622],[576,3833,1597],{"className":3834},[627],[576,3836,2820],{"className":3837,"style":1155},[627,652],[576,3839,3841,3844],{"className":3840},[627],[576,3842,2388],{"className":3843,"style":2403},[627,652],[576,3845,3847],{"className":3846},[960],[576,3848,3850],{"className":3849},[632],[576,3851,3853],{"className":3852},[636],[576,3854,3856],{"className":3855,"style":949},[640],[576,3857,3858,3861],{"style":972},[576,3859],{"className":3860,"style":976},[647],[576,3862,3864],{"className":3863},[980,981,982,983],[576,3865,1597],{"className":3866},[627,983],". Für ",[576,3869,3871,3889],{"className":3870},[579],[576,3872,3874],{"className":3873},[583],[585,3875,3876],{"xmlns":587},[589,3877,3878,3886],{},[592,3879,3880,3882,3884],{},[599,3881,2388],{},[603,3883,1177],{},[880,3885,1597],{},[607,3887,3888],{"encoding":609},"R = 2",[576,3890,3892,3910],{"className":3891,"ariaHidden":597},[614],[576,3893,3895,3898,3901,3904,3907],{"className":3894},[618],[576,3896],{"className":3897,"style":713},[622],[576,3899,2388],{"className":3900,"style":2403},[627,652],[576,3902],{"className":3903,"style":935},[934],[576,3905,1177],{"className":3906},[939],[576,3908],{"className":3909,"style":935},[934],[576,3911,3913,3916],{"className":3912},[618],[576,3914],{"className":3915,"style":2922},[622],[576,3917,1597],{"className":3918},[627]," ergibt sich ",[576,3921,3923,3946],{"className":3922},[579],[576,3924,3926],{"className":3925},[583],[585,3927,3928],{"xmlns":587},[589,3929,3930,3943],{},[592,3931,3932,3935,3937,3940],{},[880,3933,3934],{},"8",[599,3936,2820],{},[603,3938,3939],{},"≈",[880,3941,3942],{},"25,13",[607,3944,3945],{"encoding":609},"8\\pi \\approx 25{,}13",[576,3947,3949,3970],{"className":3948,"ariaHidden":597},[614],[576,3950,3952,3955,3958,3961,3964,3967],{"className":3951},[618],[576,3953],{"className":3954,"style":2922},[622],[576,3956,3934],{"className":3957},[627],[576,3959,2820],{"className":3960,"style":1155},[627,652],[576,3962],{"className":3963,"style":935},[934],[576,3965,3939],{"className":3966},[939],[576,3968],{"className":3969,"style":935},[934],[576,3971,3973,3977,3981,3987],{"className":3972},[618],[576,3974],{"className":3975,"style":3976},[622],"height:0.8389em;vertical-align:-0.1944em;",[576,3978,3980],{"className":3979},[627],"25",[576,3982,3984],{"className":3983},[627],[576,3985,2227],{"className":3986},[2321],[576,3988,3990],{"className":3989},[627],"13",".",[564,3993,3994,3995,4189,4190,4218,4219,3246,4387,4553],{},"Mit dem Satz von Green lassen sich Flächeninhalte als Randintegrale berechnen: Für ",[576,3996,3998,4036],{"className":3997},[579],[576,3999,4001],{"className":4000},[583],[585,4002,4003],{"xmlns":587},[589,4004,4005,4033],{},[592,4006,4007,4013,4015,4021,4023,4025,4027,4029,4031],{},[595,4008,4009,4011],{"accent":597},[599,4010,601],{},[603,4012,605],{},[603,4014,1177],{},[1585,4016,4017,4019],{},[880,4018,882],{},[880,4020,1597],{},[603,4022,1583],{"stretchy":1649},[603,4024,1606],{},[599,4026,1139],{},[603,4028,2227],{"separator":597},[599,4030,1108],{},[603,4032,1627],{"stretchy":1649},[607,4034,4035],{"encoding":609},"\\vec F = \\frac{1}{2}(-y, x)",[576,4037,4039,4089],{"className":4038,"ariaHidden":597},[614],[576,4040,4042,4045,4080,4083,4086],{"className":4041},[618],[576,4043],{"className":4044,"style":623},[622],[576,4046,4048],{"className":4047},[627,628],[576,4049,4051],{"className":4050},[632],[576,4052,4054],{"className":4053},[636],[576,4055,4057,4065],{"className":4056,"style":623},[640],[576,4058,4059,4062],{"style":643},[576,4060],{"className":4061,"style":648},[647],[576,4063,601],{"className":4064,"style":653},[627,652],[576,4066,4067,4070],{"style":656},[576,4068],{"className":4069,"style":648},[647],[576,4071,4073],{"className":4072,"style":664},[663],[576,4074,4076],{"className":4075,"style":669},[668],[671,4077,4078],{"xmlns":673,"width":674,"height":675,"style":676,"viewBox":677,"preserveAspectRatio":678},[680,4079],{"d":682},[576,4081],{"className":4082,"style":935},[934],[576,4084,1177],{"className":4085},[939],[576,4087],{"className":4088,"style":935},[934],[576,4090,4092,4096,4168,4171,4174,4177,4180,4183,4186],{"className":4091},[618],[576,4093],{"className":4094,"style":4095},[622],"height:1.1901em;vertical-align:-0.345em;",[576,4097,4099,4102,4165],{"className":4098},[627],[576,4100],{"className":4101},[1751,1764],[576,4103,4105],{"className":4104},[1585],[576,4106,4108,4156],{"className":4107},[632,1299],[576,4109,4111,4153],{"className":4110},[636],[576,4112,4115,4130,4138],{"className":4113,"style":4114},[640],"height:0.8451em;",[576,4116,4118,4121],{"style":4117},"top:-2.655em;",[576,4119],{"className":4120,"style":648},[647],[576,4122,4124],{"className":4123},[980,981,982,983],[576,4125,4127],{"className":4126},[627,983],[576,4128,1597],{"className":4129},[627,983],[576,4131,4132,4135],{"style":1795},[576,4133],{"className":4134,"style":648},[647],[576,4136],{"className":4137,"style":1803},[1802],[576,4139,4141,4144],{"style":4140},"top:-3.394em;",[576,4142],{"className":4143,"style":648},[647],[576,4145,4147],{"className":4146},[980,981,982,983],[576,4148,4150],{"className":4149},[627,983],[576,4151,882],{"className":4152},[627,983],[576,4154,1324],{"className":4155},[1323],[576,4157,4159],{"className":4158},[636],[576,4160,4163],{"className":4161,"style":4162},[640],"height:0.345em;",[576,4164],{},[576,4166],{"className":4167},[1873,1764],[576,4169,1583],{"className":4170},[1751],[576,4172,1606],{"className":4173},[627],[576,4175,1139],{"className":4176,"style":1155},[627,652],[576,4178,2227],{"className":4179},[2321],[576,4181],{"className":4182,"style":1459},[934],[576,4184,1108],{"className":4185},[627,652],[576,4187,1627],{"className":4188},[1873]," ist der Integrand links gleich ",[576,4191,4193,4206],{"className":4192},[579],[576,4194,4196],{"className":4195},[583],[585,4197,4198],{"xmlns":587},[589,4199,4200,4204],{},[592,4201,4202],{},[880,4203,882],{},[607,4205,882],{"encoding":609},[576,4207,4209],{"className":4208,"ariaHidden":597},[614],[576,4210,4212,4215],{"className":4211},[618],[576,4213],{"className":4214,"style":2922},[622],[576,4216,882],{"className":4217},[627],". Für die Ellipse ",[576,4220,4222,4274],{"className":4221},[579],[576,4223,4225],{"className":4224},[583],[585,4226,4227],{"xmlns":587},[589,4228,4229,4271],{},[592,4230,4231,4237,4239,4241,4243,4245,4247,4250,4252,4254,4256,4258,4260,4263,4265,4267,4269],{},[595,4232,4233,4235],{"accent":597},[599,4234,3044],{},[603,4236,605],{},[603,4238,1583],{"stretchy":1649},[599,4240,3051],{},[603,4242,1627],{"stretchy":1649},[603,4244,1177],{},[603,4246,1583],{"stretchy":1649},[599,4248,4249],{},"a",[599,4251,3062],{},[603,4253,1420],{},[599,4255,3051],{},[603,4257,2227],{"separator":597},[1657,4259,2230],{},[599,4261,4262],{},"b",[599,4264,3075],{},[603,4266,1420],{},[599,4268,3051],{},[603,4270,1627],{"stretchy":1649},[607,4272,4273],{"encoding":609},"\\vec r(t) = (a\\cos t,\\ b\\sin t)",[576,4275,4277,4336],{"className":4276,"ariaHidden":597},[614],[576,4278,4280,4283,4318,4321,4324,4327,4330,4333],{"className":4279},[618],[576,4281],{"className":4282,"style":2139},[622],[576,4284,4286],{"className":4285},[627,628],[576,4287,4289],{"className":4288},[632],[576,4290,4292],{"className":4291},[636],[576,4293,4295,4303],{"className":4294,"style":1022},[640],[576,4296,4297,4300],{"style":643},[576,4298],{"className":4299,"style":648},[647],[576,4301,3044],{"className":4302,"style":1728},[627,652],[576,4304,4305,4308],{"style":643},[576,4306],{"className":4307,"style":648},[647],[576,4309,4311],{"className":4310,"style":1285},[663],[576,4312,4314],{"className":4313,"style":669},[668],[671,4315,4316],{"xmlns":673,"width":674,"height":675,"style":676,"viewBox":677,"preserveAspectRatio":678},[680,4317],{"d":682},[576,4319,1583],{"className":4320},[1751],[576,4322,3051],{"className":4323},[627,652],[576,4325,1627],{"className":4326},[1873],[576,4328],{"className":4329,"style":935},[934],[576,4331,1177],{"className":4332},[939],[576,4334],{"className":4335,"style":935},[934],[576,4337,4339,4342,4345,4348,4351,4354,4357,4360,4363,4366,4369,4372,4375,4378,4381,4384],{"className":4338},[618],[576,4340],{"className":4341,"style":2139},[622],[576,4343,1583],{"className":4344},[1751],[576,4346,4249],{"className":4347},[627,652],[576,4349],{"className":4350,"style":1459},[934],[576,4352,3062],{"className":4353},[1451],[576,4355],{"className":4356,"style":1459},[934],[576,4358,3051],{"className":4359},[627,652],[576,4361,2227],{"className":4362},[2321],[576,4364,2230],{"className":4365},[934],[576,4367],{"className":4368,"style":1459},[934],[576,4370,4262],{"className":4371},[627,652],[576,4373],{"className":4374,"style":1459},[934],[576,4376,3075],{"className":4377},[1451],[576,4379],{"className":4380,"style":1459},[934],[576,4382,3051],{"className":4383},[627,652],[576,4385,1627],{"className":4386},[1873],[576,4388,4390,4426],{"className":4389},[579],[576,4391,4393],{"className":4392},[583],[585,4394,4395],{"xmlns":587},[589,4396,4397,4423],{},[592,4398,4399,4401,4407,4409,4411,4417,4419,4421],{},[599,4400,1108],{},[595,4402,4403,4405],{"accent":597},[599,4404,1139],{},[603,4406,3277],{},[603,4408,1606],{},[599,4410,1139],{},[595,4412,4413,4415],{"accent":597},[599,4414,1108],{},[603,4416,3277],{},[603,4418,1177],{},[599,4420,4249],{},[599,4422,4262],{},[607,4424,4425],{"encoding":609},"x \\dot y - y \\dot x = ab",[576,4427,4429,4493,4543],{"className":4428,"ariaHidden":597},[614],[576,4430,4432,4436,4439,4484,4487,4490],{"className":4431},[618],[576,4433],{"className":4434,"style":4435},[622],"height:0.8623em;vertical-align:-0.1944em;",[576,4437,1108],{"className":4438},[627,652],[576,4440,4442],{"className":4441},[627,628],[576,4443,4445,4475],{"className":4444},[632,1299],[576,4446,4448,4472],{"className":4447},[636],[576,4449,4452,4460],{"className":4450,"style":4451},[640],"height:0.6679em;",[576,4453,4454,4457],{"style":643},[576,4455],{"className":4456,"style":648},[647],[576,4458,1139],{"className":4459,"style":1155},[627,652],[576,4461,4462,4465],{"style":643},[576,4463],{"className":4464,"style":648},[647],[576,4466,4469],{"className":4467,"style":4468},[663],"left:-0.0833em;",[576,4470,3277],{"className":4471},[627],[576,4473,1324],{"className":4474},[1323],[576,4476,4478],{"className":4477},[636],[576,4479,4482],{"className":4480,"style":4481},[640],"height:0.1944em;",[576,4483],{},[576,4485],{"className":4486,"style":1877},[934],[576,4488,1606],{"className":4489},[1881],[576,4491],{"className":4492,"style":1877},[934],[576,4494,4496,4499,4502,4534,4537,4540],{"className":4495},[618],[576,4497],{"className":4498,"style":4435},[622],[576,4500,1139],{"className":4501,"style":1155},[627,652],[576,4503,4505],{"className":4504},[627,628],[576,4506,4508],{"className":4507},[632],[576,4509,4511],{"className":4510},[636],[576,4512,4514,4522],{"className":4513,"style":4451},[640],[576,4515,4516,4519],{"style":643},[576,4517],{"className":4518,"style":648},[647],[576,4520,1108],{"className":4521},[627,652],[576,4523,4524,4527],{"style":643},[576,4525],{"className":4526,"style":648},[647],[576,4528,4531],{"className":4529,"style":4530},[663],"left:-0.1111em;",[576,4532,3277],{"className":4533},[627],[576,4535],{"className":4536,"style":935},[934],[576,4538,1177],{"className":4539},[939],[576,4541],{"className":4542,"style":935},[934],[576,4544,4546,4549],{"className":4545},[618],[576,4547],{"className":4548,"style":749},[622],[576,4550,4552],{"className":4551},[627,652],"ab",", also",[576,4555,4557],{"className":4556},[1557],[576,4558,4560,4634],{"className":4559},[579],[576,4561,4563],{"className":4562},[583],[585,4564,4565],{"xmlns":587,"display":1566},[589,4566,4567,4631],{},[592,4568,4569,4571,4573,4579,4581,4583,4585,4587,4589,4591,4593,4595,4597,4599,4601,4603,4605,4611,4613,4615,4617,4619,4621,4623,4625,4627,4629],{},[599,4570,1633],{},[603,4572,1177],{},[1585,4574,4575,4577],{},[880,4576,882],{},[880,4578,1597],{},[603,4580,1640],{},[603,4582,1583],{"stretchy":1649},[599,4584,1108],{},[1657,4586,1659],{},[599,4588,1630],{},[599,4590,1139],{},[603,4592,1606],{},[599,4594,1139],{},[1657,4596,1659],{},[599,4598,1630],{},[599,4600,1108],{},[603,4602,1627],{"stretchy":1649},[603,4604,1177],{},[1585,4606,4607,4609],{},[880,4608,882],{},[880,4610,1597],{},[603,4612,2817],{},[599,4614,4249],{},[599,4616,4262],{},[603,4618,2817],{},[880,4620,1597],{},[599,4622,2820],{},[603,4624,1177],{},[599,4626,2820],{},[599,4628,4249],{},[599,4630,4262],{},[607,4632,4633],{"encoding":609},"A = \\frac{1}{2} \\oint (x\\, dy - y\\, dx) = \\frac{1}{2} \\cdot ab \\cdot 2\\pi = \\pi ab",[576,4635,4637,4655,4755,4785,4863,4881,4902],{"className":4636,"ariaHidden":597},[614],[576,4638,4640,4643,4646,4649,4652],{"className":4639},[618],[576,4641],{"className":4642,"style":713},[622],[576,4644,1633],{"className":4645},[627,652],[576,4647],{"className":4648,"style":935},[934],[576,4650,1177],{"className":4651},[939],[576,4653],{"className":4654,"style":935},[934],[576,4656,4658,4662,4725,4728,4731,4734,4737,4740,4743,4746,4749,4752],{"className":4657},[618],[576,4659],{"className":4660,"style":4661},[622],"height:2.2222em;vertical-align:-0.8622em;",[576,4663,4665,4668,4722],{"className":4664},[627],[576,4666],{"className":4667},[1751,1764],[576,4669,4671],{"className":4670},[1585],[576,4672,4674,4714],{"className":4673},[632,1299],[576,4675,4677,4711],{"className":4676},[636],[576,4678,4681,4692,4700],{"className":4679,"style":4680},[640],"height:1.3214em;",[576,4682,4683,4686],{"style":1780},[576,4684],{"className":4685,"style":648},[647],[576,4687,4689],{"className":4688},[627],[576,4690,1597],{"className":4691},[627],[576,4693,4694,4697],{"style":1795},[576,4695],{"className":4696,"style":648},[647],[576,4698],{"className":4699,"style":1803},[1802],[576,4701,4702,4705],{"style":1806},[576,4703],{"className":4704,"style":648},[647],[576,4706,4708],{"className":4707},[627],[576,4709,882],{"className":4710},[627],[576,4712,1324],{"className":4713},[1323],[576,4715,4717],{"className":4716},[636],[576,4718,4720],{"className":4719,"style":1867},[640],[576,4721],{},[576,4723],{"className":4724},[1873,1764],[576,4726],{"className":4727,"style":1459},[934],[576,4729,1640],{"className":4730,"style":2028},[1451,1700,1701],[576,4732,1583],{"className":4733},[1751],[576,4735,1108],{"className":4736},[627,652],[576,4738],{"className":4739,"style":1459},[934],[576,4741,1630],{"className":4742},[627,652],[576,4744,1139],{"className":4745,"style":1155},[627,652],[576,4747],{"className":4748,"style":1877},[934],[576,4750,1606],{"className":4751},[1881],[576,4753],{"className":4754,"style":1877},[934],[576,4756,4758,4761,4764,4767,4770,4773,4776,4779,4782],{"className":4757},[618],[576,4759],{"className":4760,"style":2139},[622],[576,4762,1139],{"className":4763,"style":1155},[627,652],[576,4765],{"className":4766,"style":1459},[934],[576,4768,1630],{"className":4769},[627,652],[576,4771,1108],{"className":4772},[627,652],[576,4774,1627],{"className":4775},[1873],[576,4777],{"className":4778,"style":935},[934],[576,4780,1177],{"className":4781},[939],[576,4783],{"className":4784,"style":935},[934],[576,4786,4788,4792,4854,4857,4860],{"className":4787},[618],[576,4789],{"className":4790,"style":4791},[622],"height:2.0074em;vertical-align:-0.686em;",[576,4793,4795,4798,4851],{"className":4794},[627],[576,4796],{"className":4797},[1751,1764],[576,4799,4801],{"className":4800},[1585],[576,4802,4804,4843],{"className":4803},[632,1299],[576,4805,4807,4840],{"className":4806},[636],[576,4808,4810,4821,4829],{"className":4809,"style":4680},[640],[576,4811,4812,4815],{"style":1780},[576,4813],{"className":4814,"style":648},[647],[576,4816,4818],{"className":4817},[627],[576,4819,1597],{"className":4820},[627],[576,4822,4823,4826],{"style":1795},[576,4824],{"className":4825,"style":648},[647],[576,4827],{"className":4828,"style":1803},[1802],[576,4830,4831,4834],{"style":1806},[576,4832],{"className":4833,"style":648},[647],[576,4835,4837],{"className":4836},[627],[576,4838,882],{"className":4839},[627],[576,4841,1324],{"className":4842},[1323],[576,4844,4846],{"className":4845},[636],[576,4847,4849],{"className":4848,"style":1867},[640],[576,4850],{},[576,4852],{"className":4853},[1873,1764],[576,4855],{"className":4856,"style":1877},[934],[576,4858,2817],{"className":4859},[1881],[576,4861],{"className":4862,"style":1877},[934],[576,4864,4866,4869,4872,4875,4878],{"className":4865},[618],[576,4867],{"className":4868,"style":749},[622],[576,4870,4552],{"className":4871},[627,652],[576,4873],{"className":4874,"style":1877},[934],[576,4876,2817],{"className":4877},[1881],[576,4879],{"className":4880,"style":1877},[934],[576,4882,4884,4887,4890,4893,4896,4899],{"className":4883},[618],[576,4885],{"className":4886,"style":2922},[622],[576,4888,1597],{"className":4889},[627],[576,4891,2820],{"className":4892,"style":1155},[627,652],[576,4894],{"className":4895,"style":935},[934],[576,4897,1177],{"className":4898},[939],[576,4900],{"className":4901,"style":935},[934],[576,4903,4905,4908,4911],{"className":4904},[618],[576,4906],{"className":4907,"style":749},[622],[576,4909,2820],{"className":4910,"style":1155},[627,652],[576,4912,4552],{"className":4913},[627,652],[559,4915,4917],{"id":4916},"typische-fehler","Typische Fehler",[4919,4920,4921,4925,5130],"ul",{},[4922,4923,4924],"li",{},"Die Randkurve gegen die Normale orientieren. Dann ändert sich das Vorzeichen.",[4922,4926,4927,4928,5006,5007,3991],{},"Den Satz auf eine geschlossene Fläche ohne Rand anwenden. Dort gibt es keinen Rand, die rechte Seite ist null. Der Fluss von ",[576,4929,4931,4953],{"className":4930},[579],[576,4932,4934],{"className":4933},[583],[585,4935,4936],{"xmlns":587},[589,4937,4938,4950],{},[592,4939,4940,4942,4944],{},[599,4941,1417],{"mathvariant":733},[603,4943,1420],{},[595,4945,4946,4948],{"accent":597},[599,4947,601],{},[603,4949,605],{},[607,4951,4952],{"encoding":609},"\\operatorname{rot} \\vec F",[576,4954,4956],{"className":4955,"ariaHidden":597},[614],[576,4957,4959,4962,4968,4971],{"className":4958},[618],[576,4960],{"className":4961,"style":623},[622],[576,4963,4965],{"className":4964},[1451],[576,4966,1417],{"className":4967},[627,1455],[576,4969],{"className":4970,"style":1459},[934],[576,4972,4974],{"className":4973},[627,628],[576,4975,4977],{"className":4976},[632],[576,4978,4980],{"className":4979},[636],[576,4981,4983,4991],{"className":4982,"style":623},[640],[576,4984,4985,4988],{"style":643},[576,4986],{"className":4987,"style":648},[647],[576,4989,601],{"className":4990,"style":653},[627,652],[576,4992,4993,4996],{"style":656},[576,4994],{"className":4995,"style":648},[647],[576,4997,4999],{"className":4998,"style":664},[663],[576,5000,5002],{"className":5001,"style":669},[668],[671,5003,5004],{"xmlns":673,"width":674,"height":675,"style":676,"viewBox":677,"preserveAspectRatio":678},[680,5005],{"d":682}," durch eine geschlossene Fläche verschwindet tatsächlich, das folgt aus dem Satz von Gauß und ",[576,5008,5010,5045],{"className":5009},[579],[576,5011,5013],{"className":5012},[583],[585,5014,5015],{"xmlns":587},[589,5016,5017,5042],{},[592,5018,5019,5022,5024,5026,5028,5030,5036,5038,5040],{},[599,5020,5021],{"mathvariant":733},"div",[603,5023,1420],{},[603,5025,1583],{"stretchy":1649},[599,5027,1417],{"mathvariant":733},[603,5029,1420],{},[595,5031,5032,5034],{"accent":597},[599,5033,601],{},[603,5035,605],{},[603,5037,1627],{"stretchy":1649},[603,5039,1177],{},[880,5041,1433],{},[607,5043,5044],{"encoding":609},"\\operatorname{div}(\\operatorname{rot} \\vec F) = 0",[576,5046,5048,5121],{"className":5047,"ariaHidden":597},[614],[576,5049,5051,5055,5062,5065,5071,5074,5109,5112,5115,5118],{"className":5050},[618],[576,5052],{"className":5053,"style":5054},[622],"height:1.2163em;vertical-align:-0.25em;",[576,5056,5058],{"className":5057},[1451],[576,5059,5021],{"className":5060,"style":5061},[627,1455],"margin-right:0.0139em;",[576,5063,1583],{"className":5064},[1751],[576,5066,5068],{"className":5067},[1451],[576,5069,1417],{"className":5070},[627,1455],[576,5072],{"className":5073,"style":1459},[934],[576,5075,5077],{"className":5076},[627,628],[576,5078,5080],{"className":5079},[632],[576,5081,5083],{"className":5082},[636],[576,5084,5086,5094],{"className":5085,"style":623},[640],[576,5087,5088,5091],{"style":643},[576,5089],{"className":5090,"style":648},[647],[576,5092,601],{"className":5093,"style":653},[627,652],[576,5095,5096,5099],{"style":656},[576,5097],{"className":5098,"style":648},[647],[576,5100,5102],{"className":5101,"style":664},[663],[576,5103,5105],{"className":5104,"style":669},[668],[671,5106,5107],{"xmlns":673,"width":674,"height":675,"style":676,"viewBox":677,"preserveAspectRatio":678},[680,5108],{"d":682},[576,5110,1627],{"className":5111},[1873],[576,5113],{"className":5114,"style":935},[934],[576,5116,1177],{"className":5117},[939],[576,5119],{"className":5120,"style":935},[934],[576,5122,5124,5127],{"className":5123},[618],[576,5125],{"className":5126,"style":2922},[622],[576,5128,1433],{"className":5129},[627],[4922,5131,5132,5133,5197,5198,5421,5422,5450,5451,3991],{},"Bei einer Singularität auf der Fläche rechnen, als wäre ",[576,5134,5136,5153],{"className":5135},[579],[576,5137,5139],{"className":5138},[583],[585,5140,5141],{"xmlns":587},[589,5142,5143,5151],{},[592,5144,5145],{},[595,5146,5147,5149],{"accent":597},[599,5148,601],{},[603,5150,605],{},[607,5152,610],{"encoding":609},[576,5154,5156],{"className":5155,"ariaHidden":597},[614],[576,5157,5159,5162],{"className":5158},[618],[576,5160],{"className":5161,"style":623},[622],[576,5163,5165],{"className":5164},[627,628],[576,5166,5168],{"className":5167},[632],[576,5169,5171],{"className":5170},[636],[576,5172,5174,5182],{"className":5173,"style":623},[640],[576,5175,5176,5179],{"style":643},[576,5177],{"className":5178,"style":648},[647],[576,5180,601],{"className":5181,"style":653},[627,652],[576,5183,5184,5187],{"style":656},[576,5185],{"className":5186,"style":648},[647],[576,5188,5190],{"className":5189,"style":664},[663],[576,5191,5193],{"className":5192,"style":669},[668],[671,5194,5195],{"xmlns":673,"width":674,"height":675,"style":676,"viewBox":677,"preserveAspectRatio":678},[680,5196],{"d":682}," glatt. Für ",[576,5199,5201,5249],{"className":5200},[579],[576,5202,5204],{"className":5203},[583],[585,5205,5206],{"xmlns":587},[589,5207,5208,5246],{},[592,5209,5210,5230,5232,5234,5236,5238,5240,5242,5244],{},[1585,5211,5212,5214],{},[880,5213,882],{},[592,5215,5216,5222,5224],{},[874,5217,5218,5220],{},[599,5219,1108],{},[880,5221,1597],{},[603,5223,1666],{},[874,5225,5226,5228],{},[599,5227,1139],{},[880,5229,1597],{},[603,5231,1583],{"stretchy":1649},[603,5233,1606],{},[599,5235,1139],{},[603,5237,2227],{"separator":597},[599,5239,1108],{},[603,5241,2227],{"separator":597},[880,5243,1433],{},[603,5245,1627],{"stretchy":1649},[607,5247,5248],{"encoding":609},"\\frac{1}{x^2 + y^2}(-y, x, 0)",[576,5250,5252],{"className":5251,"ariaHidden":597},[614],[576,5253,5255,5259,5391,5394,5397,5400,5403,5406,5409,5412,5415,5418],{"className":5254},[618],[576,5256],{"className":5257,"style":5258},[622],"height:1.3262em;vertical-align:-0.4811em;",[576,5260,5262,5265,5388],{"className":5261},[627],[576,5263],{"className":5264},[1751,1764],[576,5266,5268],{"className":5267},[1585],[576,5269,5271,5379],{"className":5270},[632,1299],[576,5272,5274,5376],{"className":5273},[636],[576,5275,5277,5354,5362],{"className":5276,"style":4114},[640],[576,5278,5279,5282],{"style":4117},[576,5280],{"className":5281,"style":648},[647],[576,5283,5285],{"className":5284},[980,981,982,983],[576,5286,5288,5322,5325],{"className":5287},[627,983],[576,5289,5291,5294],{"className":5290},[627,983],[576,5292,1108],{"className":5293},[627,652,983],[576,5295,5297],{"className":5296},[960],[576,5298,5300],{"className":5299},[632],[576,5301,5303],{"className":5302},[636],[576,5304,5307],{"className":5305,"style":5306},[640],"height:0.7463em;",[576,5308,5310,5314],{"style":5309},"top:-2.786em;margin-right:0.0714em;",[576,5311],{"className":5312,"style":5313},[647],"height:2.5em;",[576,5315,5319],{"className":5316},[980,5317,5318,983],"reset-size3","size1",[576,5320,1597],{"className":5321},[627,983],[576,5323,1666],{"className":5324},[1881,983],[576,5326,5328,5331],{"className":5327},[627,983],[576,5329,1139],{"className":5330,"style":1155},[627,652,983],[576,5332,5334],{"className":5333},[960],[576,5335,5337],{"className":5336},[632],[576,5338,5340],{"className":5339},[636],[576,5341,5343],{"className":5342,"style":5306},[640],[576,5344,5345,5348],{"style":5309},[576,5346],{"className":5347,"style":5313},[647],[576,5349,5351],{"className":5350},[980,5317,5318,983],[576,5352,1597],{"className":5353},[627,983],[576,5355,5356,5359],{"style":1795},[576,5357],{"className":5358,"style":648},[647],[576,5360],{"className":5361,"style":1803},[1802],[576,5363,5364,5367],{"style":4140},[576,5365],{"className":5366,"style":648},[647],[576,5368,5370],{"className":5369},[980,981,982,983],[576,5371,5373],{"className":5372},[627,983],[576,5374,882],{"className":5375},[627,983],[576,5377,1324],{"className":5378},[1323],[576,5380,5382],{"className":5381},[636],[576,5383,5386],{"className":5384,"style":5385},[640],"height:0.4811em;",[576,5387],{},[576,5389],{"className":5390},[1873,1764],[576,5392,1583],{"className":5393},[1751],[576,5395,1606],{"className":5396},[627],[576,5398,1139],{"className":5399,"style":1155},[627,652],[576,5401,2227],{"className":5402},[2321],[576,5404],{"className":5405,"style":1459},[934],[576,5407,1108],{"className":5408},[627,652],[576,5410,2227],{"className":5411},[2321],[576,5413],{"className":5414,"style":1459},[934],[576,5416,1433],{"className":5417},[627],[576,5419,1627],{"className":5420},[1873]," ist die Rotation außerhalb der ",[576,5423,5425,5438],{"className":5424},[579],[576,5426,5428],{"className":5427},[583],[585,5429,5430],{"xmlns":587},[589,5431,5432,5436],{},[592,5433,5434],{},[599,5435,1190],{},[607,5437,1190],{"encoding":609},[576,5439,5441],{"className":5440,"ariaHidden":597},[614],[576,5442,5444,5447],{"className":5443},[618],[576,5445],{"className":5446,"style":1120},[622],[576,5448,1190],{"className":5449,"style":1319},[627,652],"-Achse null, die Zirkulation um die Achse aber ",[576,5452,5454,5470],{"className":5453},[579],[576,5455,5457],{"className":5456},[583],[585,5458,5459],{"xmlns":587},[589,5460,5461,5467],{},[592,5462,5463,5465],{},[880,5464,1597],{},[599,5466,2820],{},[607,5468,5469],{"encoding":609},"2\\pi",[576,5471,5473],{"className":5472,"ariaHidden":597},[614],[576,5474,5476,5479,5482],{"className":5475},[618],[576,5477],{"className":5478,"style":2922},[622],[576,5480,1597],{"className":5481},[627],[576,5483,2820],{"className":5484,"style":1155},[627,652],{"title":5486,"searchDepth":5487,"depth":5487,"links":5488},"",2,[5489,5490,5491],{"id":561,"depth":5487,"text":562},{"id":2194,"depth":5487,"text":2195},{"id":4916,"depth":5487,"text":4917},[5493,5496,5499,5502,5505,5508],{"lhs":5494,"rhs":5495},"2 * pi*R^2","2*pi*R^2",{"lhs":5497,"rhs":5498},"(-R*sin(t))*(-R*sin(t)) + R*cos(t)*R*cos(t)","R^2",{"lhs":5500,"rhs":5501},"round(sum(map(0:999, f(k) = 2^2*(sin((k + 0.5)*2*pi\u002F1000)^2 + cos((k + 0.5)*2*pi\u002F1000)^2))) * 2*pi\u002F1000, 6)","round(8*pi, 6)",{"lhs":5503,"rhs":5504},"round(8*pi, 2)","25.13",{"lhs":5506,"rhs":5507},"a*cos(t)*b*cos(t) - b*sin(t)*(-a*sin(t))","a*b",{"lhs":5509,"rhs":5510},"1\u002F2 * a*b * 2*pi","pi*a*b","S \\text{ orientierte Fläche},\\ \\partial S \\text{ nach Rechte-Hand-Regel},\\ {\\vec{F} \\in C^1}","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>S\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">S\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0576em;\">S\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">orientierte\u003C\u002Fspan> \u003Cspan style=\"white-space: nowrap\">\u003Cspan class=\"katex\">Fläche\u003C\u002Fspan>\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">,\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.3em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi mathvariant=\"normal\">∂\u003C\u002Fmi>\u003Cmi>S\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\partial S\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\" style=\"margin-right:0.0556em;\">∂\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0576em;\">S\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">nach\u003C\u002Fspan> \u003Cspan style=\"white-space: nowrap\">\u003Cspan class=\"katex\">Rechte-Hand-Regel\u003C\u002Fspan>\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">,\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.3em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmover accent=\"true\">\u003Cmi>F\u003C\u002Fmi>\u003Cmo>⃗\u003C\u002Fmo>\u003C\u002Fmover>\u003Cmo>∈\u003C\u002Fmo>\u003Cmsup>\u003Cmi>C\u003C\u002Fmi>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmsup>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">{\\vec{F} \\in C^1}\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1.0054em;vertical-align:-0.0391em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord katex-accent\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.9663em;\">\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.1389em;\">F\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.2523em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"accent-body\" style=\"left:-0.1522em;\">\u003Cspan class=\"katex-overlay\" style=\"height:0.714em;width:0.471em;\">\u003Csvg xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" width=\"0.471em\" height=\"0.714em\" style=\"width:0.471em\" viewBox=\"0 0 471 714\" preserveAspectRatio=\"xMinYMin\">\u003Cpath d=\"M377 20c0-5.333 1.833-10 5.5-14S391 0 397 0c4.667 0 8.667 1.667 12 5\n3.333 2.667 6.667 9 10 19 6.667 24.667 20.333 43.667 41 57 7.333 4.667 11\n10.667 11 18 0 6-1 10-3 12s-6.667 5-14 9c-28.667 14.667-53.667 35.667-75 63\n-1.333 1.333-3.167 3.5-5.5 6.5s-4 4.833-5 5.5c-1 .667-2.5 1.333-4.5 2s-4.333 1\n-7 1c-4.667 0-9.167-1.833-13.5-5.5S337 184 337 178c0-12.667 15.667-32.333 47-59\nH213l-171-1c-8.667-6-13-12.333-13-19 0-4.667 4.333-11.333 13-20h359\nc-16-25.333-24-45-24-59z\"\u002F>\u003C\u002Fsvg>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">∈\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0715em;\">C\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8141em;\">\u003Cspan style=\"top:-3.063em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">1\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",null,"md","stokes-theorem","\\iint_S (\\operatorname{rot} \\vec{F}) \\cdot \\vec{n}\\, dS = \\oint_{\\partial S} \\vec{F} \\cdot d\\vec{r}","\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" display=\"block\">\u003Csemantics>\u003Cmrow>\u003Cmsub>\u003Cmo>∬\u003C\u002Fmo>\u003Cmi>S\u003C\u002Fmi>\u003C\u002Fmsub>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi mathvariant=\"normal\">rot\u003C\u002Fmi>\u003Cmo>⁡\u003C\u002Fmo>\u003Cmover accent=\"true\">\u003Cmi>F\u003C\u002Fmi>\u003Cmo>⃗\u003C\u002Fmo>\u003C\u002Fmover>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmo>⋅\u003C\u002Fmo>\u003Cmover accent=\"true\">\u003Cmi>n\u003C\u002Fmi>\u003Cmo>⃗\u003C\u002Fmo>\u003C\u002Fmover>\u003Cmtext> \u003C\u002Fmtext>\u003Cmi>d\u003C\u002Fmi>\u003Cmi>S\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmsub>\u003Cmo>∮\u003C\u002Fmo>\u003Cmrow>\u003Cmi mathvariant=\"normal\">∂\u003C\u002Fmi>\u003Cmi>S\u003C\u002Fmi>\u003C\u002Fmrow>\u003C\u002Fmsub>\u003Cmover accent=\"true\">\u003Cmi>F\u003C\u002Fmi>\u003Cmo>⃗\u003C\u002Fmo>\u003C\u002Fmover>\u003Cmo>⋅\u003C\u002Fmo>\u003Cmi>d\u003C\u002Fmi>\u003Cmover accent=\"true\">\u003Cmi>r\u003C\u002Fmi>\u003Cmo>⃗\u003C\u002Fmo>\u003C\u002Fmover>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\iint_S (\\operatorname{rot} \\vec{F}) \\cdot \\vec{n}\\, dS = \\oint_{\\partial S} \\vec{F} \\cdot d\\vec{r}\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:2.2717em;vertical-align:-0.9117em;\">\u003C\u002Fspan>\u003Cspan class=\"mop\">\u003Cspan class=\"mop op-symbol large-op\" style=\"margin-right:0.4445em;position:relative;top:-0.001em;\">∬\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:-0.4334em;\">\u003Cspan style=\"top:-1.7883em;margin-left:-0.4445em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mathnormal mtight\" style=\"margin-right:0.0576em;\">S\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.9117em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mop\">\u003Cspan class=\"mord mathrm\">rot\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord katex-accent\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.9663em;\">\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.1389em;\">F\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.2523em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"accent-body\" style=\"left:-0.1522em;\">\u003Cspan class=\"katex-overlay\" style=\"height:0.714em;width:0.471em;\">\u003Csvg xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" width=\"0.471em\" height=\"0.714em\" style=\"width:0.471em\" viewBox=\"0 0 471 714\" preserveAspectRatio=\"xMinYMin\">\u003Cpath d=\"M377 20c0-5.333 1.833-10 5.5-14S391 0 397 0c4.667 0 8.667 1.667 12 5\n3.333 2.667 6.667 9 10 19 6.667 24.667 20.333 43.667 41 57 7.333 4.667 11\n10.667 11 18 0 6-1 10-3 12s-6.667 5-14 9c-28.667 14.667-53.667 35.667-75 63\n-1.333 1.333-3.167 3.5-5.5 6.5s-4 4.833-5 5.5c-1 .667-2.5 1.333-4.5 2s-4.333 1\n-7 1c-4.667 0-9.167-1.833-13.5-5.5S337 184 337 178c0-12.667 15.667-32.333 47-59\nH213l-171-1c-8.667-6-13-12.333-13-19 0-4.667 4.333-11.333 13-20h359\nc-16-25.333-24-45-24-59z\"\u002F>\u003C\u002Fsvg>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">⋅\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.714em;\">\u003C\u002Fspan>\u003Cspan class=\"mord katex-accent\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.714em;\">\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">n\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"accent-body\" style=\"left:-0.2355em;\">\u003Cspan class=\"katex-overlay\" style=\"height:0.714em;width:0.471em;\">\u003Csvg xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" width=\"0.471em\" height=\"0.714em\" style=\"width:0.471em\" viewBox=\"0 0 471 714\" preserveAspectRatio=\"xMinYMin\">\u003Cpath d=\"M377 20c0-5.333 1.833-10 5.5-14S391 0 397 0c4.667 0 8.667 1.667 12 5\n3.333 2.667 6.667 9 10 19 6.667 24.667 20.333 43.667 41 57 7.333 4.667 11\n10.667 11 18 0 6-1 10-3 12s-6.667 5-14 9c-28.667 14.667-53.667 35.667-75 63\n-1.333 1.333-3.167 3.5-5.5 6.5s-4 4.833-5 5.5c-1 .667-2.5 1.333-4.5 2s-4.333 1\n-7 1c-4.667 0-9.167-1.833-13.5-5.5S337 184 337 178c0-12.667 15.667-32.333 47-59\nH213l-171-1c-8.667-6-13-12.333-13-19 0-4.667 4.333-11.333 13-20h359\nc-16-25.333-24-45-24-59z\"\u002F>\u003C\u002Fsvg>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">d\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0576em;\">S\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:2.2719em;vertical-align:-0.9119em;\">\u003C\u002Fspan>\u003Cspan class=\"mop\">\u003Cspan class=\"mop op-symbol large-op\" style=\"margin-right:0.4445em;position:relative;top:-0.0011em;\">∮\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:-0.4258em;\">\u003Cspan style=\"top:-1.7881em;margin-left:-0.4445em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mtight\" style=\"margin-right:0.0556em;\">∂\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal mtight\" style=\"margin-right:0.0576em;\">S\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.9119em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord katex-accent\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.9663em;\">\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.1389em;\">F\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.2523em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"accent-body\" style=\"left:-0.1522em;\">\u003Cspan class=\"katex-overlay\" style=\"height:0.714em;width:0.471em;\">\u003Csvg xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" width=\"0.471em\" height=\"0.714em\" style=\"width:0.471em\" viewBox=\"0 0 471 714\" preserveAspectRatio=\"xMinYMin\">\u003Cpath d=\"M377 20c0-5.333 1.833-10 5.5-14S391 0 397 0c4.667 0 8.667 1.667 12 5\n3.333 2.667 6.667 9 10 19 6.667 24.667 20.333 43.667 41 57 7.333 4.667 11\n10.667 11 18 0 6-1 10-3 12s-6.667 5-14 9c-28.667 14.667-53.667 35.667-75 63\n-1.333 1.333-3.167 3.5-5.5 6.5s-4 4.833-5 5.5c-1 .667-2.5 1.333-4.5 2s-4.333 1\n-7 1c-4.667 0-9.167-1.833-13.5-5.5S337 184 337 178c0-12.667 15.667-32.333 47-59\nH213l-171-1c-8.667-6-13-12.333-13-19 0-4.667 4.333-11.333 13-20h359\nc-16-25.333-24-45-24-59z\"\u002F>\u003C\u002Fsvg>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">⋅\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.714em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">d\u003C\u002Fspan>\u003Cspan class=\"mord katex-accent\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.714em;\">\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0278em;\">r\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"accent-body\" style=\"left:-0.1799em;\">\u003Cspan class=\"katex-overlay\" style=\"height:0.714em;width:0.471em;\">\u003Csvg xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" width=\"0.471em\" height=\"0.714em\" style=\"width:0.471em\" viewBox=\"0 0 471 714\" preserveAspectRatio=\"xMinYMin\">\u003Cpath d=\"M377 20c0-5.333 1.833-10 5.5-14S391 0 397 0c4.667 0 8.667 1.667 12 5\n3.333 2.667 6.667 9 10 19 6.667 24.667 20.333 43.667 41 57 7.333 4.667 11\n10.667 11 18 0 6-1 10-3 12s-6.667 5-14 9c-28.667 14.667-53.667 35.667-75 63\n-1.333 1.333-3.167 3.5-5.5 6.5s-4 4.833-5 5.5c-1 .667-2.5 1.333-4.5 2s-4.333 1\n-7 1c-4.667 0-9.167-1.833-13.5-5.5S337 184 337 178c0-12.667 15.667-32.333 47-59\nH213l-171-1c-8.667-6-13-12.333-13-19 0-4.667 4.333-11.333 13-20h359\nc-16-25.333-24-45-24-59z\"\u002F>\u003C\u002Fsvg>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","university",{},true,"\u002Fde\u002Fformulas\u002Fmath\u002Fmultivariable-calculus\u002Fsatz-von-stokes",[],[5524,5525,5526,5527],"curl","line-integral","divergence-theorem","double-integral",{"title":548,"description":5486},"de\u002Fformulas\u002Fmath\u002Fmultivariable-calculus\u002Fsatz-von-stokes","Die Zirkulation eines Vektorfelds längs einer Randkurve ist gleich dem Fluss seiner Rotation durch die eingeschlossene Fläche.",[5532,5533,5534,5535,5536],"satz von stokes","rotation","kurvenintegral","zirkulation","integralsatz",[5538,5541,5544,5548,5552,5556],{"symbol":701,"meaning":5539,"symbolHtml":5540},"Fläche im Raum mit Rand","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>S\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">S\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0576em;\">S\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":739,"meaning":5542,"symbolHtml":5543},"Randkurve der Fläche","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi mathvariant=\"normal\">∂\u003C\u002Fmi>\u003Cmi>S\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\partial S\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\" style=\"margin-right:0.0556em;\">∂\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0576em;\">S\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":5545,"meaning":5546,"symbolHtml":5547},"\\vec{F}","Vektorfeld","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmover accent=\"true\">\u003Cmi>F\u003C\u002Fmi>\u003Cmo>⃗\u003C\u002Fmo>\u003C\u002Fmover>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\vec{F}\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.9663em;\">\u003C\u002Fspan>\u003Cspan class=\"mord katex-accent\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.9663em;\">\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.1389em;\">F\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.2523em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"accent-body\" style=\"left:-0.1522em;\">\u003Cspan class=\"katex-overlay\" style=\"height:0.714em;width:0.471em;\">\u003Csvg xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" width=\"0.471em\" height=\"0.714em\" style=\"width:0.471em\" viewBox=\"0 0 471 714\" preserveAspectRatio=\"xMinYMin\">\u003Cpath d=\"M377 20c0-5.333 1.833-10 5.5-14S391 0 397 0c4.667 0 8.667 1.667 12 5\n3.333 2.667 6.667 9 10 19 6.667 24.667 20.333 43.667 41 57 7.333 4.667 11\n10.667 11 18 0 6-1 10-3 12s-6.667 5-14 9c-28.667 14.667-53.667 35.667-75 63\n-1.333 1.333-3.167 3.5-5.5 6.5s-4 4.833-5 5.5c-1 .667-2.5 1.333-4.5 2s-4.333 1\n-7 1c-4.667 0-9.167-1.833-13.5-5.5S337 184 337 178c0-12.667 15.667-32.333 47-59\nH213l-171-1c-8.667-6-13-12.333-13-19 0-4.667 4.333-11.333 13-20h359\nc-16-25.333-24-45-24-59z\"\u002F>\u003C\u002Fsvg>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":5549,"meaning":5550,"symbolHtml":5551},"\\operatorname{rot} \\vec{F}","Rotation des Vektorfelds","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi mathvariant=\"normal\">rot\u003C\u002Fmi>\u003Cmo>⁡\u003C\u002Fmo>\u003Cmover accent=\"true\">\u003Cmi>F\u003C\u002Fmi>\u003Cmo>⃗\u003C\u002Fmo>\u003C\u002Fmover>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\operatorname{rot} \\vec{F}\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.9663em;\">\u003C\u002Fspan>\u003Cspan class=\"mop\">\u003Cspan class=\"mord mathrm\">rot\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord katex-accent\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.9663em;\">\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.1389em;\">F\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.2523em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"accent-body\" style=\"left:-0.1522em;\">\u003Cspan class=\"katex-overlay\" style=\"height:0.714em;width:0.471em;\">\u003Csvg xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" width=\"0.471em\" height=\"0.714em\" style=\"width:0.471em\" viewBox=\"0 0 471 714\" preserveAspectRatio=\"xMinYMin\">\u003Cpath d=\"M377 20c0-5.333 1.833-10 5.5-14S391 0 397 0c4.667 0 8.667 1.667 12 5\n3.333 2.667 6.667 9 10 19 6.667 24.667 20.333 43.667 41 57 7.333 4.667 11\n10.667 11 18 0 6-1 10-3 12s-6.667 5-14 9c-28.667 14.667-53.667 35.667-75 63\n-1.333 1.333-3.167 3.5-5.5 6.5s-4 4.833-5 5.5c-1 .667-2.5 1.333-4.5 2s-4.333 1\n-7 1c-4.667 0-9.167-1.833-13.5-5.5S337 184 337 178c0-12.667 15.667-32.333 47-59\nH213l-171-1c-8.667-6-13-12.333-13-19 0-4.667 4.333-11.333 13-20h359\nc-16-25.333-24-45-24-59z\"\u002F>\u003C\u002Fsvg>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":5553,"meaning":5554,"symbolHtml":5555},"\\vec{n}","Einheitsnormalenvektor der Fläche","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmover accent=\"true\">\u003Cmi>n\u003C\u002Fmi>\u003Cmo>⃗\u003C\u002Fmo>\u003C\u002Fmover>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\vec{n}\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.714em;\">\u003C\u002Fspan>\u003Cspan class=\"mord katex-accent\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.714em;\">\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">n\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"accent-body\" style=\"left:-0.2355em;\">\u003Cspan class=\"katex-overlay\" style=\"height:0.714em;width:0.471em;\">\u003Csvg xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" width=\"0.471em\" height=\"0.714em\" style=\"width:0.471em\" viewBox=\"0 0 471 714\" preserveAspectRatio=\"xMinYMin\">\u003Cpath d=\"M377 20c0-5.333 1.833-10 5.5-14S391 0 397 0c4.667 0 8.667 1.667 12 5\n3.333 2.667 6.667 9 10 19 6.667 24.667 20.333 43.667 41 57 7.333 4.667 11\n10.667 11 18 0 6-1 10-3 12s-6.667 5-14 9c-28.667 14.667-53.667 35.667-75 63\n-1.333 1.333-3.167 3.5-5.5 6.5s-4 4.833-5 5.5c-1 .667-2.5 1.333-4.5 2s-4.333 1\n-7 1c-4.667 0-9.167-1.833-13.5-5.5S337 184 337 178c0-12.667 15.667-32.333 47-59\nH213l-171-1c-8.667-6-13-12.333-13-19 0-4.667 4.333-11.333 13-20h359\nc-16-25.333-24-45-24-59z\"\u002F>\u003C\u002Fsvg>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":5557,"meaning":5558,"symbolHtml":5559},"dS","Flächenelement","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>d\u003C\u002Fmi>\u003Cmi>S\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">dS\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">d\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0576em;\">S\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","mg4VFiTskEEKSJ3gNqdf5IqKoAMuM5X51XpYCsvbD7g",[5562,5565,5568,5571],{"stem":5563,"title":5564,"category":368},"de\u002Fformulas\u002Fmath\u002Fmultivariable-calculus\u002Fdoppelintegral","Doppelintegral und Satz von Fubini",{"stem":5566,"title":5567,"category":368},"de\u002Fformulas\u002Fmath\u002Fmultivariable-calculus\u002Fkurvenintegral","Kurvenintegral",{"stem":5569,"title":5570,"category":368},"de\u002Fformulas\u002Fmath\u002Fmultivariable-calculus\u002Frotation","Rotation",{"stem":5572,"title":5573,"category":368},"de\u002Fformulas\u002Fmath\u002Fmultivariable-calculus\u002Fsatz-von-gauss","Satz von Gauß",1793824267786]