[{"data":1,"prerenderedAt":3476},["ShallowReactive",2],{"subject-categories-math":3,"formula-de\u002Fformulas\u002Fmath\u002Fmultivariable-calculus\u002Fdivergenz":546,"formula-related-de\u002Fformulas\u002Fmath\u002Fmultivariable-calculus\u002Fdivergenz":3463},[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":556,"category":368,"checks":3407,"conditions":3419,"conditionsHtml":3420,"deprecated":3421,"description":3401,"extension":3422,"figure":3421,"figureCaption":3421,"figureHtml":3421,"formulaId":3423,"latex":3424,"latexHtml":3425,"level":3426,"meta":3427,"navigation":3428,"path":3429,"redirectFrom":3430,"related":3431,"seo":3436,"stem":3437,"subject":582,"summary":3438,"tags":3439,"variables":3445,"__hash__":3462},"formulas_de\u002Fde\u002Fformulas\u002Fmath\u002Fmultivariable-calculus\u002Fdivergenz.md","Divergenz",[550,551,552,553,554,555],"div F","Divergenz eines Vektorfelds","Quellendichte","Divergenz berechnen","quellenfreies Vektorfeld","Nabla mal F",{"type":557,"value":558,"toc":3400},"minimark",[559,564,1187,1194,1522,1649,1653,1902,2076,2248,2500,2983,2987],[560,561,563],"h2",{"id":562},"erklärung","Erklärung",[565,566,567,568,571,572,680,681,1051,1052,1116,1117,1186],"p",{},"Die ",[569,570,548],"strong",{}," macht aus einem Vektorfeld ",[573,574,577,608],"span",{"className":575},[576],"katex",[573,578,581],{"className":579},[580],"katex-mathml",[582,583,585],"math",{"xmlns":584},"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML",[586,587,588,603],"semantics",{},[589,590,591],"mrow",{},[592,593,595,599],"mover",{"accent":594},"true",[596,597,598],"mi",{},"F",[600,601,602],"mo",{},"⃗",[604,605,607],"annotation",{"encoding":606},"application\u002Fx-tex","\\vec F",[573,609,612],{"className":610,"ariaHidden":594},[611],"katex-html",[573,613,616,621],{"className":614},[615],"base",[573,617],{"className":618,"style":620},[619],"strut","height:0.9663em;",[573,622,626],{"className":623},[624,625],"mord","accent",[573,627,630],{"className":628},[629],"vlist-t",[573,631,634],{"className":632},[633],"vlist-r",[573,635,638,651],{"className":636,"style":620},[637],"vlist",[573,639,641,646],{"style":640},"top:-3em;",[573,642],{"className":643,"style":645},[644],"pstrut","height:3em;",[573,647,598],{"className":648,"style":650},[624,649],"mathnormal","margin-right:0.1389em;",[573,652,654,657],{"style":653},"top:-3.2523em;",[573,655],{"className":656,"style":645},[644],[573,658,662],{"className":659,"style":661},[660],"accent-body","left:-0.1522em;",[573,663,667],{"className":664,"style":666},[665],"overlay","height:0.714em;width:0.471em;",[668,669,676],"svg",{"xmlns":670,"width":671,"height":672,"style":673,"viewBox":674,"preserveAspectRatio":675},"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg","0.471em","0.714em","width:0.471em","0 0 471 714","xMinYMin",[677,678],"path",{"d":679},"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"," ein Skalarfeld. Man kann sie sich als Skalarprodukt des Nabla-Operators ",[573,682,684,751],{"className":683},[576],[573,685,687],{"className":686},[580],[582,688,689],{"xmlns":584},[586,690,691,748],{},[589,692,693,697,700],{},[596,694,696],{"mathvariant":695},"normal","∇",[600,698,699],{},"=",[589,701,702,705,718,721,732,734,745],{},[600,703,704],{"fence":594},"(",[706,707,708,711],"mfrac",{},[596,709,710],{"mathvariant":695},"∂",[589,712,713,715],{},[596,714,710],{"mathvariant":695},[596,716,717],{},"x",[600,719,720],{"separator":594},",",[706,722,723,725],{},[596,724,710],{"mathvariant":695},[589,726,727,729],{},[596,728,710],{"mathvariant":695},[596,730,731],{},"y",[600,733,720],{"separator":594},[706,735,736,738],{},[596,737,710],{"mathvariant":695},[589,739,740,742],{},[596,741,710],{"mathvariant":695},[596,743,744],{},"z",[600,746,747],{"fence":594},")",[604,749,750],{"encoding":606},"\\nabla = \\left( \\frac{\\partial}{\\partial x}, \\frac{\\partial}{\\partial y}, \\frac{\\partial}{\\partial z} \\right)",[573,752,754,776],{"className":753,"ariaHidden":594},[611],[573,755,757,761,764,769,773],{"className":756},[615],[573,758],{"className":759,"style":760},[619],"height:0.6833em;",[573,762,696],{"className":763},[624],[573,765],{"className":766,"style":768},[767],"mspace","margin-right:0.2778em;",[573,770,699],{"className":771},[772],"mrel",[573,774],{"className":775,"style":768},[767],[573,777,779,783],{"className":778},[615],[573,780],{"className":781,"style":782},[619],"height:1.8em;vertical-align:-0.65em;",[573,784,787,798,886,890,894,967,970,973,1045],{"className":785},[786],"minner",[573,788,793],{"className":789,"style":792},[790,791],"mopen","delimcenter","top:0em;",[573,794,704],{"className":795},[796,797],"delimsizing","size2",[573,799,801,805,882],{"className":800},[624],[573,802],{"className":803},[790,804],"nulldelimiter",[573,806,808],{"className":807},[706],[573,809,812,873],{"className":810},[629,811],"vlist-t2",[573,813,815,868],{"className":814},[633],[573,816,819,842,853],{"className":817,"style":818},[637],"height:0.8801em;",[573,820,822,825],{"style":821},"top:-2.655em;",[573,823],{"className":824,"style":645},[644],[573,826,832],{"className":827},[828,829,830,831],"sizing","reset-size6","size3","mtight",[573,833,835,839],{"className":834},[624,831],[573,836,710],{"className":837,"style":838},[624,831],"margin-right:0.0556em;",[573,840,717],{"className":841},[624,649,831],[573,843,845,848],{"style":844},"top:-3.23em;",[573,846],{"className":847,"style":645},[644],[573,849],{"className":850,"style":852},[851],"frac-line","border-bottom-width:0.04em;",[573,854,856,859],{"style":855},"top:-3.394em;",[573,857],{"className":858,"style":645},[644],[573,860,862],{"className":861},[828,829,830,831],[573,863,865],{"className":864},[624,831],[573,866,710],{"className":867,"style":838},[624,831],[573,869,872],{"className":870},[871],"vlist-s","​",[573,874,876],{"className":875},[633],[573,877,880],{"className":878,"style":879},[637],"height:0.345em;",[573,881],{},[573,883],{"className":884},[885,804],"mclose",[573,887,720],{"className":888},[889],"mpunct",[573,891],{"className":892,"style":893},[767],"margin-right:0.1667em;",[573,895,897,900,964],{"className":896},[624],[573,898],{"className":899},[790,804],[573,901,903],{"className":902},[706],[573,904,906,955],{"className":905},[629,811],[573,907,909,952],{"className":908},[633],[573,910,912,930,938],{"className":911,"style":818},[637],[573,913,914,917],{"style":821},[573,915],{"className":916,"style":645},[644],[573,918,920],{"className":919},[828,829,830,831],[573,921,923,926],{"className":922},[624,831],[573,924,710],{"className":925,"style":838},[624,831],[573,927,731],{"className":928,"style":929},[624,649,831],"margin-right:0.0359em;",[573,931,932,935],{"style":844},[573,933],{"className":934,"style":645},[644],[573,936],{"className":937,"style":852},[851],[573,939,940,943],{"style":855},[573,941],{"className":942,"style":645},[644],[573,944,946],{"className":945},[828,829,830,831],[573,947,949],{"className":948},[624,831],[573,950,710],{"className":951,"style":838},[624,831],[573,953,872],{"className":954},[871],[573,956,958],{"className":957},[633],[573,959,962],{"className":960,"style":961},[637],"height:0.4811em;",[573,963],{},[573,965],{"className":966},[885,804],[573,968,720],{"className":969},[889],[573,971],{"className":972,"style":893},[767],[573,974,976,979,1042],{"className":975},[624],[573,977],{"className":978},[790,804],[573,980,982],{"className":981},[706],[573,983,985,1034],{"className":984},[629,811],[573,986,988,1031],{"className":987},[633],[573,989,991,1009,1017],{"className":990,"style":818},[637],[573,992,993,996],{"style":821},[573,994],{"className":995,"style":645},[644],[573,997,999],{"className":998},[828,829,830,831],[573,1000,1002,1005],{"className":1001},[624,831],[573,1003,710],{"className":1004,"style":838},[624,831],[573,1006,744],{"className":1007,"style":1008},[624,649,831],"margin-right:0.044em;",[573,1010,1011,1014],{"style":844},[573,1012],{"className":1013,"style":645},[644],[573,1015],{"className":1016,"style":852},[851],[573,1018,1019,1022],{"style":855},[573,1020],{"className":1021,"style":645},[644],[573,1023,1025],{"className":1024},[828,829,830,831],[573,1026,1028],{"className":1027},[624,831],[573,1029,710],{"className":1030,"style":838},[624,831],[573,1032,872],{"className":1033},[871],[573,1035,1037],{"className":1036},[633],[573,1038,1040],{"className":1039,"style":879},[637],[573,1041],{},[573,1043],{"className":1044},[885,804],[573,1046,1048],{"className":1047,"style":792},[885,791],[573,1049,747],{"className":1050},[796,797]," mit ",[573,1053,1055,1072],{"className":1054},[576],[573,1056,1058],{"className":1057},[580],[582,1059,1060],{"xmlns":584},[586,1061,1062,1070],{},[589,1063,1064],{},[592,1065,1066,1068],{"accent":594},[596,1067,598],{},[600,1069,602],{},[604,1071,607],{"encoding":606},[573,1073,1075],{"className":1074,"ariaHidden":594},[611],[573,1076,1078,1081],{"className":1077},[615],[573,1079],{"className":1080,"style":620},[619],[573,1082,1084],{"className":1083},[624,625],[573,1085,1087],{"className":1086},[629],[573,1088,1090],{"className":1089},[633],[573,1091,1093,1101],{"className":1092,"style":620},[637],[573,1094,1095,1098],{"style":640},[573,1096],{"className":1097,"style":645},[644],[573,1099,598],{"className":1100,"style":650},[624,649],[573,1102,1103,1106],{"style":653},[573,1104],{"className":1105,"style":645},[644],[573,1107,1109],{"className":1108,"style":661},[660],[573,1110,1112],{"className":1111,"style":666},[665],[668,1113,1114],{"xmlns":670,"width":671,"height":672,"style":673,"viewBox":674,"preserveAspectRatio":675},[677,1115],{"d":679}," vorstellen. In der Ebene entfällt der dritte Summand, im ",[573,1118,1120,1142],{"className":1119},[576],[573,1121,1123],{"className":1122},[580],[582,1124,1125],{"xmlns":584},[586,1126,1127,1139],{},[589,1128,1129],{},[1130,1131,1132,1136],"msup",{},[596,1133,1135],{"mathvariant":1134},"double-struck","R",[596,1137,1138],{},"n",[604,1140,1141],{"encoding":606},"\\mathbb{R}^n",[573,1143,1145],{"className":1144,"ariaHidden":594},[611],[573,1146,1148,1152],{"className":1147},[615],[573,1149],{"className":1150,"style":1151},[619],"height:0.6889em;",[573,1153,1155,1159],{"className":1154},[624],[573,1156,1135],{"className":1157},[624,1158],"mathbb",[573,1160,1163],{"className":1161},[1162],"msupsub",[573,1164,1166],{"className":1165},[629],[573,1167,1169],{"className":1168},[633],[573,1170,1173],{"className":1171,"style":1172},[637],"height:0.6644em;",[573,1174,1176,1180],{"style":1175},"top:-3.063em;margin-right:0.05em;",[573,1177],{"className":1178,"style":1179},[644],"height:2.7em;",[573,1181,1183],{"className":1182},[828,829,830,831],[573,1184,1138],{"className":1185},[624,649,831]," kommen entsprechend mehr hinzu.",[565,1188,1189,1190,1193],{},"Anschaulich misst die Divergenz die ",[569,1191,1192],{},"Quelldichte"," einer Strömung:",[1195,1196,1197,1311,1415],"ul",{},[1198,1199,1200,1310],"li",{},[573,1201,1203,1234],{"className":1202},[576],[573,1204,1206],{"className":1205},[580],[582,1207,1208],{"xmlns":584},[586,1209,1210,1231],{},[589,1211,1212,1215,1218,1224,1227],{},[596,1213,1214],{"mathvariant":695},"div",[600,1216,1217],{},"⁡",[592,1219,1220,1222],{"accent":594},[596,1221,598],{},[600,1223,602],{},[600,1225,1226],{},">",[1228,1229,1230],"mn",{},"0",[604,1232,1233],{"encoding":606},"\\operatorname{div} \\vec F > 0",[573,1235,1237,1300],{"className":1236,"ariaHidden":594},[611],[573,1238,1240,1244,1253,1256,1291,1294,1297],{"className":1239},[615],[573,1241],{"className":1242,"style":1243},[619],"height:1.0054em;vertical-align:-0.0391em;",[573,1245,1248],{"className":1246},[1247],"mop",[573,1249,1214],{"className":1250,"style":1252},[624,1251],"mathrm","margin-right:0.0139em;",[573,1254],{"className":1255,"style":893},[767],[573,1257,1259],{"className":1258},[624,625],[573,1260,1262],{"className":1261},[629],[573,1263,1265],{"className":1264},[633],[573,1266,1268,1276],{"className":1267,"style":620},[637],[573,1269,1270,1273],{"style":640},[573,1271],{"className":1272,"style":645},[644],[573,1274,598],{"className":1275,"style":650},[624,649],[573,1277,1278,1281],{"style":653},[573,1279],{"className":1280,"style":645},[644],[573,1282,1284],{"className":1283,"style":661},[660],[573,1285,1287],{"className":1286,"style":666},[665],[668,1288,1289],{"xmlns":670,"width":671,"height":672,"style":673,"viewBox":674,"preserveAspectRatio":675},[677,1290],{"d":679},[573,1292],{"className":1293,"style":768},[767],[573,1295,1226],{"className":1296},[772],[573,1298],{"className":1299,"style":768},[767],[573,1301,1303,1307],{"className":1302},[615],[573,1304],{"className":1305,"style":1306},[619],"height:0.6444em;",[573,1308,1230],{"className":1309},[624],": In der Umgebung fließt mehr heraus als hinein (Quelle).",[1198,1312,1313,1414],{},[573,1314,1316,1343],{"className":1315},[576],[573,1317,1319],{"className":1318},[580],[582,1320,1321],{"xmlns":584},[586,1322,1323,1340],{},[589,1324,1325,1327,1329,1335,1338],{},[596,1326,1214],{"mathvariant":695},[600,1328,1217],{},[592,1330,1331,1333],{"accent":594},[596,1332,598],{},[600,1334,602],{},[600,1336,1337],{},"\u003C",[1228,1339,1230],{},[604,1341,1342],{"encoding":606},"\\operatorname{div} \\vec F \u003C 0",[573,1344,1346,1405],{"className":1345,"ariaHidden":594},[611],[573,1347,1349,1352,1358,1361,1396,1399,1402],{"className":1348},[615],[573,1350],{"className":1351,"style":1243},[619],[573,1353,1355],{"className":1354},[1247],[573,1356,1214],{"className":1357,"style":1252},[624,1251],[573,1359],{"className":1360,"style":893},[767],[573,1362,1364],{"className":1363},[624,625],[573,1365,1367],{"className":1366},[629],[573,1368,1370],{"className":1369},[633],[573,1371,1373,1381],{"className":1372,"style":620},[637],[573,1374,1375,1378],{"style":640},[573,1376],{"className":1377,"style":645},[644],[573,1379,598],{"className":1380,"style":650},[624,649],[573,1382,1383,1386],{"style":653},[573,1384],{"className":1385,"style":645},[644],[573,1387,1389],{"className":1388,"style":661},[660],[573,1390,1392],{"className":1391,"style":666},[665],[668,1393,1394],{"xmlns":670,"width":671,"height":672,"style":673,"viewBox":674,"preserveAspectRatio":675},[677,1395],{"d":679},[573,1397],{"className":1398,"style":768},[767],[573,1400,1337],{"className":1401},[772],[573,1403],{"className":1404,"style":768},[767],[573,1406,1408,1411],{"className":1407},[615],[573,1409],{"className":1410,"style":1306},[619],[573,1412,1230],{"className":1413},[624],": Es fließt mehr hinein als heraus (Senke).",[1198,1416,1417,1517,1518,1521],{},[573,1418,1420,1446],{"className":1419},[576],[573,1421,1423],{"className":1422},[580],[582,1424,1425],{"xmlns":584},[586,1426,1427,1443],{},[589,1428,1429,1431,1433,1439,1441],{},[596,1430,1214],{"mathvariant":695},[600,1432,1217],{},[592,1434,1435,1437],{"accent":594},[596,1436,598],{},[600,1438,602],{},[600,1440,699],{},[1228,1442,1230],{},[604,1444,1445],{"encoding":606},"\\operatorname{div} \\vec F = 0",[573,1447,1449,1508],{"className":1448,"ariaHidden":594},[611],[573,1450,1452,1455,1461,1464,1499,1502,1505],{"className":1451},[615],[573,1453],{"className":1454,"style":620},[619],[573,1456,1458],{"className":1457},[1247],[573,1459,1214],{"className":1460,"style":1252},[624,1251],[573,1462],{"className":1463,"style":893},[767],[573,1465,1467],{"className":1466},[624,625],[573,1468,1470],{"className":1469},[629],[573,1471,1473],{"className":1472},[633],[573,1474,1476,1484],{"className":1475,"style":620},[637],[573,1477,1478,1481],{"style":640},[573,1479],{"className":1480,"style":645},[644],[573,1482,598],{"className":1483,"style":650},[624,649],[573,1485,1486,1489],{"style":653},[573,1487],{"className":1488,"style":645},[644],[573,1490,1492],{"className":1491,"style":661},[660],[573,1493,1495],{"className":1494,"style":666},[665],[668,1496,1497],{"xmlns":670,"width":671,"height":672,"style":673,"viewBox":674,"preserveAspectRatio":675},[677,1498],{"d":679},[573,1500],{"className":1501,"style":768},[767],[573,1503,699],{"className":1504},[772],[573,1506],{"className":1507,"style":768},[767],[573,1509,1511,1514],{"className":1510},[615],[573,1512],{"className":1513,"style":1306},[619],[573,1515,1230],{"className":1516},[624]," überall: Das Feld heißt ",[569,1519,1520],{},"quellenfrei",", z.B. die Strömung einer inkompressiblen Flüssigkeit oder ein Magnetfeld.",[565,1523,1524,1525,1648],{},"Genauer ist die Divergenz der Grenzwert aus dem Fluss durch die Oberfläche eines kleinen Volumens, geteilt durch dieses Volumen, wenn das Volumen auf den Punkt zusammenschrumpft. Daraus entsteht der Satz von Gauß. Für jedes zweimal stetig differenzierbare Feld gilt außerdem ",[573,1526,1528,1564],{"className":1527},[576],[573,1529,1531],{"className":1530},[580],[582,1532,1533],{"xmlns":584},[586,1534,1535,1561],{},[589,1536,1537,1539,1541,1544,1547,1549,1555,1557,1559],{},[596,1538,1214],{"mathvariant":695},[600,1540,1217],{},[600,1542,704],{"stretchy":1543},"false",[596,1545,1546],{"mathvariant":695},"rot",[600,1548,1217],{},[592,1550,1551,1553],{"accent":594},[596,1552,598],{},[600,1554,602],{},[600,1556,747],{"stretchy":1543},[600,1558,699],{},[1228,1560,1230],{},[604,1562,1563],{"encoding":606},"\\operatorname{div}(\\operatorname{rot} \\vec F) = 0",[573,1565,1567,1639],{"className":1566,"ariaHidden":594},[611],[573,1568,1570,1574,1580,1583,1589,1592,1627,1630,1633,1636],{"className":1569},[615],[573,1571],{"className":1572,"style":1573},[619],"height:1.2163em;vertical-align:-0.25em;",[573,1575,1577],{"className":1576},[1247],[573,1578,1214],{"className":1579,"style":1252},[624,1251],[573,1581,704],{"className":1582},[790],[573,1584,1586],{"className":1585},[1247],[573,1587,1546],{"className":1588},[624,1251],[573,1590],{"className":1591,"style":893},[767],[573,1593,1595],{"className":1594},[624,625],[573,1596,1598],{"className":1597},[629],[573,1599,1601],{"className":1600},[633],[573,1602,1604,1612],{"className":1603,"style":620},[637],[573,1605,1606,1609],{"style":640},[573,1607],{"className":1608,"style":645},[644],[573,1610,598],{"className":1611,"style":650},[624,649],[573,1613,1614,1617],{"style":653},[573,1615],{"className":1616,"style":645},[644],[573,1618,1620],{"className":1619,"style":661},[660],[573,1621,1623],{"className":1622,"style":666},[665],[668,1624,1625],{"xmlns":670,"width":671,"height":672,"style":673,"viewBox":674,"preserveAspectRatio":675},[677,1626],{"d":679},[573,1628,747],{"className":1629},[885],[573,1631],{"className":1632,"style":768},[767],[573,1634,699],{"className":1635},[772],[573,1637],{"className":1638,"style":768},[767],[573,1640,1642,1645],{"className":1641},[615],[573,1643],{"className":1644,"style":1306},[619],[573,1646,1230],{"className":1647},[624],".",[560,1650,1652],{"id":1651},"beispiele","Beispiele",[565,1654,1655,1656,1901],{},"Für ",[573,1657,1659,1719],{"className":1658},[576],[573,1660,1662],{"className":1661},[580],[582,1663,1664],{"xmlns":584},[586,1665,1666,1716],{},[589,1667,1668,1674,1676,1678,1685,1687,1689,1693,1695,1697,1699,1701,1703,1709],{},[592,1669,1670,1672],{"accent":594},[596,1671,598],{},[600,1673,602],{},[600,1675,699],{},[600,1677,704],{"stretchy":1543},[1130,1679,1680,1682],{},[596,1681,717],{},[1228,1683,1684],{},"2",[596,1686,731],{},[600,1688,720],{"separator":594},[1690,1691,1692],"mtext",{}," ",[596,1694,731],{},[596,1696,744],{},[600,1698,720],{"separator":594},[1690,1700,1692],{},[596,1702,717],{},[1130,1704,1705,1707],{},[596,1706,744],{},[1228,1708,1684],{},[1130,1710,1711,1713],{},[600,1712,747],{"stretchy":1543},[596,1714,1715],{},"T",[604,1717,1718],{"encoding":606},"\\vec F = (x^2 y,\\ yz,\\ xz^2)^T",[573,1720,1722,1772],{"className":1721,"ariaHidden":594},[611],[573,1723,1725,1728,1763,1766,1769],{"className":1724},[615],[573,1726],{"className":1727,"style":620},[619],[573,1729,1731],{"className":1730},[624,625],[573,1732,1734],{"className":1733},[629],[573,1735,1737],{"className":1736},[633],[573,1738,1740,1748],{"className":1739,"style":620},[637],[573,1741,1742,1745],{"style":640},[573,1743],{"className":1744,"style":645},[644],[573,1746,598],{"className":1747,"style":650},[624,649],[573,1749,1750,1753],{"style":653},[573,1751],{"className":1752,"style":645},[644],[573,1754,1756],{"className":1755,"style":661},[660],[573,1757,1759],{"className":1758,"style":666},[665],[668,1760,1761],{"xmlns":670,"width":671,"height":672,"style":673,"viewBox":674,"preserveAspectRatio":675},[677,1762],{"d":679},[573,1764],{"className":1765,"style":768},[767],[573,1767,699],{"className":1768},[772],[573,1770],{"className":1771,"style":768},[767],[573,1773,1775,1779,1782,1812,1815,1818,1821,1824,1827,1830,1833,1836,1839,1842,1871],{"className":1774},[615],[573,1776],{"className":1777,"style":1778},[619],"height:1.0913em;vertical-align:-0.25em;",[573,1780,704],{"className":1781},[790],[573,1783,1785,1788],{"className":1784},[624],[573,1786,717],{"className":1787},[624,649],[573,1789,1791],{"className":1790},[1162],[573,1792,1794],{"className":1793},[629],[573,1795,1797],{"className":1796},[633],[573,1798,1801],{"className":1799,"style":1800},[637],"height:0.8141em;",[573,1802,1803,1806],{"style":1175},[573,1804],{"className":1805,"style":1179},[644],[573,1807,1809],{"className":1808},[828,829,830,831],[573,1810,1684],{"className":1811},[624,831],[573,1813,731],{"className":1814,"style":929},[624,649],[573,1816,720],{"className":1817},[889],[573,1819,1692],{"className":1820},[767],[573,1822],{"className":1823,"style":893},[767],[573,1825,731],{"className":1826,"style":929},[624,649],[573,1828,744],{"className":1829,"style":1008},[624,649],[573,1831,720],{"className":1832},[889],[573,1834,1692],{"className":1835},[767],[573,1837],{"className":1838,"style":893},[767],[573,1840,717],{"className":1841},[624,649],[573,1843,1845,1848],{"className":1844},[624],[573,1846,744],{"className":1847,"style":1008},[624,649],[573,1849,1851],{"className":1850},[1162],[573,1852,1854],{"className":1853},[629],[573,1855,1857],{"className":1856},[633],[573,1858,1860],{"className":1859,"style":1800},[637],[573,1861,1862,1865],{"style":1175},[573,1863],{"className":1864,"style":1179},[644],[573,1866,1868],{"className":1867},[828,829,830,831],[573,1869,1684],{"className":1870},[624,831],[573,1872,1874,1877],{"className":1873},[885],[573,1875,747],{"className":1876},[885],[573,1878,1880],{"className":1879},[1162],[573,1881,1883],{"className":1882},[629],[573,1884,1886],{"className":1885},[633],[573,1887,1890],{"className":1888,"style":1889},[637],"height:0.8413em;",[573,1891,1892,1895],{"style":1175},[573,1893],{"className":1894,"style":1179},[644],[573,1896,1898],{"className":1897},[828,829,830,831],[573,1899,1715],{"className":1900,"style":650},[624,649,831]," ist",[573,1903,1906],{"className":1904},[1905],"katex-display",[573,1907,1909,1953],{"className":1908},[576],[573,1910,1912],{"className":1911},[580],[582,1913,1915],{"xmlns":584,"display":1914},"block",[586,1916,1917,1950],{},[589,1918,1919,1921,1923,1929,1931,1933,1935,1937,1940,1942,1944,1946,1948],{},[596,1920,1214],{"mathvariant":695},[600,1922,1217],{},[592,1924,1925,1927],{"accent":594},[596,1926,598],{},[600,1928,602],{},[600,1930,699],{},[1228,1932,1684],{},[596,1934,717],{},[596,1936,731],{},[600,1938,1939],{},"+",[596,1941,744],{},[600,1943,1939],{},[1228,1945,1684],{},[596,1947,717],{},[596,1949,744],{},[604,1951,1952],{"encoding":606},"\\operatorname{div} \\vec F = 2xy + z + 2xz",[573,1954,1956,2015,2042,2061],{"className":1955,"ariaHidden":594},[611],[573,1957,1959,1962,1968,1971,2006,2009,2012],{"className":1958},[615],[573,1960],{"className":1961,"style":620},[619],[573,1963,1965],{"className":1964},[1247],[573,1966,1214],{"className":1967,"style":1252},[624,1251],[573,1969],{"className":1970,"style":893},[767],[573,1972,1974],{"className":1973},[624,625],[573,1975,1977],{"className":1976},[629],[573,1978,1980],{"className":1979},[633],[573,1981,1983,1991],{"className":1982,"style":620},[637],[573,1984,1985,1988],{"style":640},[573,1986],{"className":1987,"style":645},[644],[573,1989,598],{"className":1990,"style":650},[624,649],[573,1992,1993,1996],{"style":653},[573,1994],{"className":1995,"style":645},[644],[573,1997,1999],{"className":1998,"style":661},[660],[573,2000,2002],{"className":2001,"style":666},[665],[668,2003,2004],{"xmlns":670,"width":671,"height":672,"style":673,"viewBox":674,"preserveAspectRatio":675},[677,2005],{"d":679},[573,2007],{"className":2008,"style":768},[767],[573,2010,699],{"className":2011},[772],[573,2013],{"className":2014,"style":768},[767],[573,2016,2018,2022,2025,2028,2031,2035,2039],{"className":2017},[615],[573,2019],{"className":2020,"style":2021},[619],"height:0.8389em;vertical-align:-0.1944em;",[573,2023,1684],{"className":2024},[624],[573,2026,717],{"className":2027},[624,649],[573,2029,731],{"className":2030,"style":929},[624,649],[573,2032],{"className":2033,"style":2034},[767],"margin-right:0.2222em;",[573,2036,1939],{"className":2037},[2038],"mbin",[573,2040],{"className":2041,"style":2034},[767],[573,2043,2045,2049,2052,2055,2058],{"className":2044},[615],[573,2046],{"className":2047,"style":2048},[619],"height:0.6667em;vertical-align:-0.0833em;",[573,2050,744],{"className":2051,"style":1008},[624,649],[573,2053],{"className":2054,"style":2034},[767],[573,2056,1939],{"className":2057},[2038],[573,2059],{"className":2060,"style":2034},[767],[573,2062,2064,2067,2070,2073],{"className":2063},[615],[573,2065],{"className":2066,"style":1306},[619],[573,2068,1684],{"className":2069},[624],[573,2071,717],{"className":2072},[624,649],[573,2074,744],{"className":2075,"style":1008},[624,649],[565,2077,2078,2079,2147,2148,2247],{},"Im Punkt ",[573,2080,2082,2110],{"className":2081},[576],[573,2083,2085],{"className":2084},[580],[582,2086,2087],{"xmlns":584},[586,2088,2089,2107],{},[589,2090,2091,2093,2096,2098,2100,2102,2105],{},[600,2092,704],{"stretchy":1543},[1228,2094,2095],{},"1",[600,2097,720],{"separator":594},[1228,2099,1684],{},[600,2101,720],{"separator":594},[1228,2103,2104],{},"3",[600,2106,747],{"stretchy":1543},[604,2108,2109],{"encoding":606},"(1, 2, 3)",[573,2111,2113],{"className":2112,"ariaHidden":594},[611],[573,2114,2116,2120,2123,2126,2129,2132,2135,2138,2141,2144],{"className":2115},[615],[573,2117],{"className":2118,"style":2119},[619],"height:1em;vertical-align:-0.25em;",[573,2121,704],{"className":2122},[790],[573,2124,2095],{"className":2125},[624],[573,2127,720],{"className":2128},[889],[573,2130],{"className":2131,"style":893},[767],[573,2133,1684],{"className":2134},[624],[573,2136,720],{"className":2137},[889],[573,2139],{"className":2140,"style":893},[767],[573,2142,2104],{"className":2143},[624],[573,2145,747],{"className":2146},[885]," ergibt das ",[573,2149,2151,2180],{"className":2150},[576],[573,2152,2154],{"className":2153},[580],[582,2155,2156],{"xmlns":584},[586,2157,2158,2177],{},[589,2159,2160,2163,2165,2167,2169,2172,2174],{},[1228,2161,2162],{},"4",[600,2164,1939],{},[1228,2166,2104],{},[600,2168,1939],{},[1228,2170,2171],{},"6",[600,2173,699],{},[1228,2175,2176],{},"13",[604,2178,2179],{"encoding":606},"4 + 3 + 6 = 13",[573,2181,2183,2202,2220,2238],{"className":2182,"ariaHidden":594},[611],[573,2184,2186,2190,2193,2196,2199],{"className":2185},[615],[573,2187],{"className":2188,"style":2189},[619],"height:0.7278em;vertical-align:-0.0833em;",[573,2191,2162],{"className":2192},[624],[573,2194],{"className":2195,"style":2034},[767],[573,2197,1939],{"className":2198},[2038],[573,2200],{"className":2201,"style":2034},[767],[573,2203,2205,2208,2211,2214,2217],{"className":2204},[615],[573,2206],{"className":2207,"style":2189},[619],[573,2209,2104],{"className":2210},[624],[573,2212],{"className":2213,"style":2034},[767],[573,2215,1939],{"className":2216},[2038],[573,2218],{"className":2219,"style":2034},[767],[573,2221,2223,2226,2229,2232,2235],{"className":2222},[615],[573,2224],{"className":2225,"style":1306},[619],[573,2227,2171],{"className":2228},[624],[573,2230],{"className":2231,"style":768},[767],[573,2233,699],{"className":2234},[772],[573,2236],{"className":2237,"style":768},[767],[573,2239,2241,2244],{"className":2240},[615],[573,2242],{"className":2243,"style":1306},[619],[573,2245,2176],{"className":2246},[624],", dort liegt also eine Quelle.",[565,2249,2250,2251,2404,2405,1648],{},"Das radiale Feld ",[573,2252,2254,2292],{"className":2253},[576],[573,2255,2257],{"className":2256},[580],[582,2258,2259],{"xmlns":584},[586,2260,2261,2289],{},[589,2262,2263,2269,2271,2273,2275,2277,2279,2281,2283],{},[592,2264,2265,2267],{"accent":594},[596,2266,598],{},[600,2268,602],{},[600,2270,699],{},[600,2272,704],{"stretchy":1543},[596,2274,717],{},[600,2276,720],{"separator":594},[596,2278,731],{},[600,2280,720],{"separator":594},[596,2282,744],{},[1130,2284,2285,2287],{},[600,2286,747],{"stretchy":1543},[596,2288,1715],{},[604,2290,2291],{"encoding":606},"\\vec F = (x, y, z)^T",[573,2293,2295,2345],{"className":2294,"ariaHidden":594},[611],[573,2296,2298,2301,2336,2339,2342],{"className":2297},[615],[573,2299],{"className":2300,"style":620},[619],[573,2302,2304],{"className":2303},[624,625],[573,2305,2307],{"className":2306},[629],[573,2308,2310],{"className":2309},[633],[573,2311,2313,2321],{"className":2312,"style":620},[637],[573,2314,2315,2318],{"style":640},[573,2316],{"className":2317,"style":645},[644],[573,2319,598],{"className":2320,"style":650},[624,649],[573,2322,2323,2326],{"style":653},[573,2324],{"className":2325,"style":645},[644],[573,2327,2329],{"className":2328,"style":661},[660],[573,2330,2332],{"className":2331,"style":666},[665],[668,2333,2334],{"xmlns":670,"width":671,"height":672,"style":673,"viewBox":674,"preserveAspectRatio":675},[677,2335],{"d":679},[573,2337],{"className":2338,"style":768},[767],[573,2340,699],{"className":2341},[772],[573,2343],{"className":2344,"style":768},[767],[573,2346,2348,2351,2354,2357,2360,2363,2366,2369,2372,2375],{"className":2347},[615],[573,2349],{"className":2350,"style":1778},[619],[573,2352,704],{"className":2353},[790],[573,2355,717],{"className":2356},[624,649],[573,2358,720],{"className":2359},[889],[573,2361],{"className":2362,"style":893},[767],[573,2364,731],{"className":2365,"style":929},[624,649],[573,2367,720],{"className":2368},[889],[573,2370],{"className":2371,"style":893},[767],[573,2373,744],{"className":2374,"style":1008},[624,649],[573,2376,2378,2381],{"className":2377},[885],[573,2379,747],{"className":2380},[885],[573,2382,2384],{"className":2383},[1162],[573,2385,2387],{"className":2386},[629],[573,2388,2390],{"className":2389},[633],[573,2391,2393],{"className":2392,"style":1889},[637],[573,2394,2395,2398],{"style":1175},[573,2396],{"className":2397,"style":1179},[644],[573,2399,2401],{"className":2400},[828,829,830,831],[573,2402,1715],{"className":2403,"style":650},[624,649,831]," zeigt überall vom Ursprung weg und hat die konstante Divergenz ",[573,2406,2408,2434],{"className":2407},[576],[573,2409,2411],{"className":2410},[580],[582,2412,2413],{"xmlns":584},[586,2414,2415,2431],{},[589,2416,2417,2419,2421,2423,2425,2427,2429],{},[1228,2418,2095],{},[600,2420,1939],{},[1228,2422,2095],{},[600,2424,1939],{},[1228,2426,2095],{},[600,2428,699],{},[1228,2430,2104],{},[604,2432,2433],{"encoding":606},"1 + 1 + 1 = 3",[573,2435,2437,2455,2473,2491],{"className":2436,"ariaHidden":594},[611],[573,2438,2440,2443,2446,2449,2452],{"className":2439},[615],[573,2441],{"className":2442,"style":2189},[619],[573,2444,2095],{"className":2445},[624],[573,2447],{"className":2448,"style":2034},[767],[573,2450,1939],{"className":2451},[2038],[573,2453],{"className":2454,"style":2034},[767],[573,2456,2458,2461,2464,2467,2470],{"className":2457},[615],[573,2459],{"className":2460,"style":2189},[619],[573,2462,2095],{"className":2463},[624],[573,2465],{"className":2466,"style":2034},[767],[573,2468,1939],{"className":2469},[2038],[573,2471],{"className":2472,"style":2034},[767],[573,2474,2476,2479,2482,2485,2488],{"className":2475},[615],[573,2477],{"className":2478,"style":1306},[619],[573,2480,2095],{"className":2481},[624],[573,2483],{"className":2484,"style":768},[767],[573,2486,699],{"className":2487},[772],[573,2489],{"className":2490,"style":768},[767],[573,2492,2494,2497],{"className":2493},[615],[573,2495],{"className":2496,"style":1306},[619],[573,2498,2104],{"className":2499},[624],[565,2501,2502,2503,2672,2673,2702,2703,1648],{},"Das Wirbelfeld ",[573,2504,2506,2551],{"className":2505},[576],[573,2507,2509],{"className":2508},[580],[582,2510,2511],{"xmlns":584},[586,2512,2513,2548],{},[589,2514,2515,2521,2523,2525,2528,2530,2532,2534,2536,2538,2540,2542],{},[592,2516,2517,2519],{"accent":594},[596,2518,598],{},[600,2520,602],{},[600,2522,699],{},[600,2524,704],{"stretchy":1543},[600,2526,2527],{},"−",[596,2529,731],{},[600,2531,720],{"separator":594},[1690,2533,1692],{},[596,2535,717],{},[600,2537,720],{"separator":594},[1690,2539,1692],{},[1228,2541,1230],{},[1130,2543,2544,2546],{},[600,2545,747],{"stretchy":1543},[596,2547,1715],{},[604,2549,2550],{"encoding":606},"\\vec F = (-y,\\ x,\\ 0)^T",[573,2552,2554,2604],{"className":2553,"ariaHidden":594},[611],[573,2555,2557,2560,2595,2598,2601],{"className":2556},[615],[573,2558],{"className":2559,"style":620},[619],[573,2561,2563],{"className":2562},[624,625],[573,2564,2566],{"className":2565},[629],[573,2567,2569],{"className":2568},[633],[573,2570,2572,2580],{"className":2571,"style":620},[637],[573,2573,2574,2577],{"style":640},[573,2575],{"className":2576,"style":645},[644],[573,2578,598],{"className":2579,"style":650},[624,649],[573,2581,2582,2585],{"style":653},[573,2583],{"className":2584,"style":645},[644],[573,2586,2588],{"className":2587,"style":661},[660],[573,2589,2591],{"className":2590,"style":666},[665],[668,2592,2593],{"xmlns":670,"width":671,"height":672,"style":673,"viewBox":674,"preserveAspectRatio":675},[677,2594],{"d":679},[573,2596],{"className":2597,"style":768},[767],[573,2599,699],{"className":2600},[772],[573,2602],{"className":2603,"style":768},[767],[573,2605,2607,2610,2613,2616,2619,2622,2625,2628,2631,2634,2637,2640,2643],{"className":2606},[615],[573,2608],{"className":2609,"style":1778},[619],[573,2611,704],{"className":2612},[790],[573,2614,2527],{"className":2615},[624],[573,2617,731],{"className":2618,"style":929},[624,649],[573,2620,720],{"className":2621},[889],[573,2623,1692],{"className":2624},[767],[573,2626],{"className":2627,"style":893},[767],[573,2629,717],{"className":2630},[624,649],[573,2632,720],{"className":2633},[889],[573,2635,1692],{"className":2636},[767],[573,2638],{"className":2639,"style":893},[767],[573,2641,1230],{"className":2642},[624],[573,2644,2646,2649],{"className":2645},[885],[573,2647,747],{"className":2648},[885],[573,2650,2652],{"className":2651},[1162],[573,2653,2655],{"className":2654},[629],[573,2656,2658],{"className":2657},[633],[573,2659,2661],{"className":2660,"style":1889},[637],[573,2662,2663,2666],{"style":1175},[573,2664],{"className":2665,"style":1179},[644],[573,2667,2669],{"className":2668},[828,829,830,831],[573,2670,1715],{"className":2671,"style":650},[624,649,831]," kreist um die ",[573,2674,2676,2689],{"className":2675},[576],[573,2677,2679],{"className":2678},[580],[582,2680,2681],{"xmlns":584},[586,2682,2683,2687],{},[589,2684,2685],{},[596,2686,744],{},[604,2688,744],{"encoding":606},[573,2690,2692],{"className":2691,"ariaHidden":594},[611],[573,2693,2695,2699],{"className":2694},[615],[573,2696],{"className":2697,"style":2698},[619],"height:0.4306em;",[573,2700,744],{"className":2701,"style":1008},[624,649],"-Achse. Es ist quellenfrei, denn ",[573,2704,2706,2762],{"className":2705},[576],[573,2707,2709],{"className":2708},[580],[582,2710,2711],{"xmlns":584},[586,2712,2713,2759],{},[589,2714,2715,2735,2737,2751,2753,2755,2757],{},[706,2716,2717,2729],{},[589,2718,2719,2721,2723,2725,2727],{},[596,2720,710],{"mathvariant":695},[600,2722,704],{"stretchy":1543},[600,2724,2527],{},[596,2726,731],{},[600,2728,747],{"stretchy":1543},[589,2730,2731,2733],{},[596,2732,710],{"mathvariant":695},[596,2734,717],{},[600,2736,1939],{},[706,2738,2739,2745],{},[589,2740,2741,2743],{},[596,2742,710],{"mathvariant":695},[596,2744,717],{},[589,2746,2747,2749],{},[596,2748,710],{"mathvariant":695},[596,2750,731],{},[600,2752,1939],{},[1228,2754,1230],{},[600,2756,699],{},[1228,2758,1230],{},[604,2760,2761],{"encoding":606},"\\frac{\\partial(-y)}{\\partial x} + \\frac{\\partial x}{\\partial y} + 0 = 0",[573,2763,2765,2866,2956,2974],{"className":2764,"ariaHidden":594},[611],[573,2766,2768,2772,2857,2860,2863],{"className":2767},[615],[573,2769],{"className":2770,"style":2771},[619],"height:1.355em;vertical-align:-0.345em;",[573,2773,2775,2778,2854],{"className":2774},[624],[573,2776],{"className":2777},[790,804],[573,2779,2781],{"className":2780},[706],[573,2782,2784,2846],{"className":2783},[629,811],[573,2785,2787,2843],{"className":2786},[633],[573,2788,2791,2808,2816],{"className":2789,"style":2790},[637],"height:1.01em;",[573,2792,2793,2796],{"style":821},[573,2794],{"className":2795,"style":645},[644],[573,2797,2799],{"className":2798},[828,829,830,831],[573,2800,2802,2805],{"className":2801},[624,831],[573,2803,710],{"className":2804,"style":838},[624,831],[573,2806,717],{"className":2807},[624,649,831],[573,2809,2810,2813],{"style":844},[573,2811],{"className":2812,"style":645},[644],[573,2814],{"className":2815,"style":852},[851],[573,2817,2819,2822],{"style":2818},"top:-3.485em;",[573,2820],{"className":2821,"style":645},[644],[573,2823,2825],{"className":2824},[828,829,830,831],[573,2826,2828,2831,2834,2837,2840],{"className":2827},[624,831],[573,2829,710],{"className":2830,"style":838},[624,831],[573,2832,704],{"className":2833},[790,831],[573,2835,2527],{"className":2836},[624,831],[573,2838,731],{"className":2839,"style":929},[624,649,831],[573,2841,747],{"className":2842},[885,831],[573,2844,872],{"className":2845},[871],[573,2847,2849],{"className":2848},[633],[573,2850,2852],{"className":2851,"style":879},[637],[573,2853],{},[573,2855],{"className":2856},[885,804],[573,2858],{"className":2859,"style":2034},[767],[573,2861,1939],{"className":2862},[2038],[573,2864],{"className":2865,"style":2034},[767],[573,2867,2869,2873,2947,2950,2953],{"className":2868},[615],[573,2870],{"className":2871,"style":2872},[619],"height:1.3612em;vertical-align:-0.4811em;",[573,2874,2876,2879,2944],{"className":2875},[624],[573,2877],{"className":2878},[790,804],[573,2880,2882],{"className":2881},[706],[573,2883,2885,2936],{"className":2884},[629,811],[573,2886,2888,2933],{"className":2887},[633],[573,2889,2891,2908,2916],{"className":2890,"style":818},[637],[573,2892,2893,2896],{"style":821},[573,2894],{"className":2895,"style":645},[644],[573,2897,2899],{"className":2898},[828,829,830,831],[573,2900,2902,2905],{"className":2901},[624,831],[573,2903,710],{"className":2904,"style":838},[624,831],[573,2906,731],{"className":2907,"style":929},[624,649,831],[573,2909,2910,2913],{"style":844},[573,2911],{"className":2912,"style":645},[644],[573,2914],{"className":2915,"style":852},[851],[573,2917,2918,2921],{"style":855},[573,2919],{"className":2920,"style":645},[644],[573,2922,2924],{"className":2923},[828,829,830,831],[573,2925,2927,2930],{"className":2926},[624,831],[573,2928,710],{"className":2929,"style":838},[624,831],[573,2931,717],{"className":2932},[624,649,831],[573,2934,872],{"className":2935},[871],[573,2937,2939],{"className":2938},[633],[573,2940,2942],{"className":2941,"style":961},[637],[573,2943],{},[573,2945],{"className":2946},[885,804],[573,2948],{"className":2949,"style":2034},[767],[573,2951,1939],{"className":2952},[2038],[573,2954],{"className":2955,"style":2034},[767],[573,2957,2959,2962,2965,2968,2971],{"className":2958},[615],[573,2960],{"className":2961,"style":1306},[619],[573,2963,1230],{"className":2964},[624],[573,2966],{"className":2967,"style":768},[767],[573,2969,699],{"className":2970},[772],[573,2972],{"className":2973,"style":768},[767],[573,2975,2977,2980],{"className":2976},[615],[573,2978],{"className":2979,"style":1306},[619],[573,2981,1230],{"className":2982},[624],[560,2984,2986],{"id":2985},"typische-fehler","Typische Fehler",[1195,2988,2989,3394,3397],{},[1198,2990,2991,2992,3067,3068,3097,3098,3167,3168,3196,3197,3167,3267,3295,3296,3167,3366,1648],{},"Jede Komponente nach der falschen Variablen ableiten, z.B. ",[573,2993,2995,3014],{"className":2994},[576],[573,2996,2998],{"className":2997},[580],[582,2999,3000],{"xmlns":584},[586,3001,3002,3011],{},[589,3003,3004],{},[3005,3006,3007,3009],"msub",{},[596,3008,598],{},[1228,3010,2095],{},[604,3012,3013],{"encoding":606},"F_1",[573,3015,3017],{"className":3016,"ariaHidden":594},[611],[573,3018,3020,3024],{"className":3019},[615],[573,3021],{"className":3022,"style":3023},[619],"height:0.8333em;vertical-align:-0.15em;",[573,3025,3027,3030],{"className":3026},[624],[573,3028,598],{"className":3029,"style":650},[624,649],[573,3031,3033],{"className":3032},[1162],[573,3034,3036,3058],{"className":3035},[629,811],[573,3037,3039,3055],{"className":3038},[633],[573,3040,3043],{"className":3041,"style":3042},[637],"height:0.3011em;",[573,3044,3046,3049],{"style":3045},"top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;",[573,3047],{"className":3048,"style":1179},[644],[573,3050,3052],{"className":3051},[828,829,830,831],[573,3053,2095],{"className":3054},[624,831],[573,3056,872],{"className":3057},[871],[573,3059,3061],{"className":3060},[633],[573,3062,3065],{"className":3063,"style":3064},[637],"height:0.15em;",[573,3066],{}," nach ",[573,3069,3071,3084],{"className":3070},[576],[573,3072,3074],{"className":3073},[580],[582,3075,3076],{"xmlns":584},[586,3077,3078,3082],{},[589,3079,3080],{},[596,3081,731],{},[604,3083,731],{"encoding":606},[573,3085,3087],{"className":3086,"ariaHidden":594},[611],[573,3088,3090,3094],{"className":3089},[615],[573,3091],{"className":3092,"style":3093},[619],"height:0.625em;vertical-align:-0.1944em;",[573,3095,731],{"className":3096,"style":929},[624,649],". Es gehören immer ",[573,3099,3101,3118],{"className":3100},[576],[573,3102,3104],{"className":3103},[580],[582,3105,3106],{"xmlns":584},[586,3107,3108,3116],{},[589,3109,3110],{},[3005,3111,3112,3114],{},[596,3113,598],{},[1228,3115,2095],{},[604,3117,3013],{"encoding":606},[573,3119,3121],{"className":3120,"ariaHidden":594},[611],[573,3122,3124,3127],{"className":3123},[615],[573,3125],{"className":3126,"style":3023},[619],[573,3128,3130,3133],{"className":3129},[624],[573,3131,598],{"className":3132,"style":650},[624,649],[573,3134,3136],{"className":3135},[1162],[573,3137,3139,3159],{"className":3138},[629,811],[573,3140,3142,3156],{"className":3141},[633],[573,3143,3145],{"className":3144,"style":3042},[637],[573,3146,3147,3150],{"style":3045},[573,3148],{"className":3149,"style":1179},[644],[573,3151,3153],{"className":3152},[828,829,830,831],[573,3154,2095],{"className":3155},[624,831],[573,3157,872],{"className":3158},[871],[573,3160,3162],{"className":3161},[633],[573,3163,3165],{"className":3164,"style":3064},[637],[573,3166],{}," zu ",[573,3169,3171,3184],{"className":3170},[576],[573,3172,3174],{"className":3173},[580],[582,3175,3176],{"xmlns":584},[586,3177,3178,3182],{},[589,3179,3180],{},[596,3181,717],{},[604,3183,717],{"encoding":606},[573,3185,3187],{"className":3186,"ariaHidden":594},[611],[573,3188,3190,3193],{"className":3189},[615],[573,3191],{"className":3192,"style":2698},[619],[573,3194,717],{"className":3195},[624,649],", ",[573,3198,3200,3218],{"className":3199},[576],[573,3201,3203],{"className":3202},[580],[582,3204,3205],{"xmlns":584},[586,3206,3207,3215],{},[589,3208,3209],{},[3005,3210,3211,3213],{},[596,3212,598],{},[1228,3214,1684],{},[604,3216,3217],{"encoding":606},"F_2",[573,3219,3221],{"className":3220,"ariaHidden":594},[611],[573,3222,3224,3227],{"className":3223},[615],[573,3225],{"className":3226,"style":3023},[619],[573,3228,3230,3233],{"className":3229},[624],[573,3231,598],{"className":3232,"style":650},[624,649],[573,3234,3236],{"className":3235},[1162],[573,3237,3239,3259],{"className":3238},[629,811],[573,3240,3242,3256],{"className":3241},[633],[573,3243,3245],{"className":3244,"style":3042},[637],[573,3246,3247,3250],{"style":3045},[573,3248],{"className":3249,"style":1179},[644],[573,3251,3253],{"className":3252},[828,829,830,831],[573,3254,1684],{"className":3255},[624,831],[573,3257,872],{"className":3258},[871],[573,3260,3262],{"className":3261},[633],[573,3263,3265],{"className":3264,"style":3064},[637],[573,3266],{},[573,3268,3270,3283],{"className":3269},[576],[573,3271,3273],{"className":3272},[580],[582,3274,3275],{"xmlns":584},[586,3276,3277,3281],{},[589,3278,3279],{},[596,3280,731],{},[604,3282,731],{"encoding":606},[573,3284,3286],{"className":3285,"ariaHidden":594},[611],[573,3287,3289,3292],{"className":3288},[615],[573,3290],{"className":3291,"style":3093},[619],[573,3293,731],{"className":3294,"style":929},[624,649]," und ",[573,3297,3299,3317],{"className":3298},[576],[573,3300,3302],{"className":3301},[580],[582,3303,3304],{"xmlns":584},[586,3305,3306,3314],{},[589,3307,3308],{},[3005,3309,3310,3312],{},[596,3311,598],{},[1228,3313,2104],{},[604,3315,3316],{"encoding":606},"F_3",[573,3318,3320],{"className":3319,"ariaHidden":594},[611],[573,3321,3323,3326],{"className":3322},[615],[573,3324],{"className":3325,"style":3023},[619],[573,3327,3329,3332],{"className":3328},[624],[573,3330,598],{"className":3331,"style":650},[624,649],[573,3333,3335],{"className":3334},[1162],[573,3336,3338,3358],{"className":3337},[629,811],[573,3339,3341,3355],{"className":3340},[633],[573,3342,3344],{"className":3343,"style":3042},[637],[573,3345,3346,3349],{"style":3045},[573,3347],{"className":3348,"style":1179},[644],[573,3350,3352],{"className":3351},[828,829,830,831],[573,3353,2104],{"className":3354},[624,831],[573,3356,872],{"className":3357},[871],[573,3359,3361],{"className":3360},[633],[573,3362,3364],{"className":3363,"style":3064},[637],[573,3365],{},[573,3367,3369,3382],{"className":3368},[576],[573,3370,3372],{"className":3371},[580],[582,3373,3374],{"xmlns":584},[586,3375,3376,3380],{},[589,3377,3378],{},[596,3379,744],{},[604,3381,744],{"encoding":606},[573,3383,3385],{"className":3384,"ariaHidden":594},[611],[573,3386,3388,3391],{"className":3387},[615],[573,3389],{"className":3390,"style":2698},[619],[573,3392,744],{"className":3393,"style":1008},[624,649],[1198,3395,3396],{},"Das Ergebnis als Vektor angeben. Die Divergenz ist eine Zahl bzw. ein Skalarfeld.",[1198,3398,3399],{},"Divergenz und Gradient verwechseln. Der Gradient wirkt auf ein Skalarfeld und liefert ein Vektorfeld, die Divergenz umgekehrt.",{"title":3401,"searchDepth":3402,"depth":3402,"links":3403},"",2,[3404,3405,3406],{"id":562,"depth":3402,"text":563},{"id":1651,"depth":3402,"text":1652},{"id":2985,"depth":3402,"text":2986},[3408,3410,3415,3417],{"lhs":3409,"rhs":1230},"round(((x + 1e-5)^2*y - (x - 1e-5)^2*y) \u002F (2e-5) + ((y + 1e-5)*z - (y - 1e-5)*z) \u002F (2e-5) + (x*(z + 1e-5)^2 - x*(z - 1e-5)^2) \u002F (2e-5) - (2*x*y + z + 2*x*z), 6)",{"lhs":3411,"rhs":2176,"where":3412},"2*x*y + z + 2*x*z",{"x":3413,"y":3402,"z":3414},1,3,{"lhs":3416,"rhs":2104},"round(((x + 1e-5) - (x - 1e-5)) \u002F (2e-5) + ((y + 1e-5) - (y - 1e-5)) \u002F (2e-5) + ((z + 1e-5) - (z - 1e-5)) \u002F (2e-5), 6)",{"lhs":3418,"rhs":1230},"round((-y - (-y)) \u002F (2e-5) + (x - x) \u002F (2e-5), 6)","\\vec{F} = (F_1, F_2, F_3)^{T} \\text{ partiell differenzierbares Vektorfeld auf } D \\subseteq \\mathbb{R}^3","\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>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmsub>\u003Cmi>F\u003C\u002Fmi>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmsub>\u003Cmi>F\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmsub>\u003Cmi>F\u003C\u002Fmi>\u003Cmn>3\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmsup>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmi>T\u003C\u002Fmi>\u003C\u002Fmsup>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\vec{F} = (F_1, F_2, F_3)^{T}\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>\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:1.0913em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.1389em;\">F\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3011em;\">\u003Cspan style=\"top:-2.55em;margin-left:-0.1389em;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>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.1389em;\">F\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3011em;\">\u003Cspan style=\"top:-2.55em;margin-left:-0.1389em;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\">2\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:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.1389em;\">F\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3011em;\">\u003Cspan style=\"top:-2.55em;margin-left:-0.1389em;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\">3\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:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose\">\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8413em;\">\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\">\u003Cspan class=\"mord mathnormal mtight\" style=\"margin-right:0.1389em;\">T\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">partiell differenzierbares Vektorfeld auf\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>D\u003C\u002Fmi>\u003Cmo>⊆\u003C\u002Fmo>\u003Cmsup>\u003Cmi mathvariant=\"double-struck\">R\u003C\u002Fmi>\u003Cmn>3\u003C\u002Fmn>\u003C\u002Fmsup>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">D \\subseteq \\mathbb{R}^3\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:0.8193em;vertical-align:-0.136em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0278em;\">D\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:0.8141em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathbb\">R\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\">3\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",null,"md","divergence","\\operatorname{div} \\vec{F} = \\nabla \\cdot \\vec{F} = \\frac{\\partial F_1}{\\partial x} + \\frac{\\partial F_2}{\\partial y} + \\frac{\\partial F_3}{\\partial z}","\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>\u003Cmi mathvariant=\"normal\">div\u003C\u002Fmi>\u003Cmo>⁡\u003C\u002Fmo>\u003Cmover accent=\"true\">\u003Cmi>F\u003C\u002Fmi>\u003Cmo>⃗\u003C\u002Fmo>\u003C\u002Fmover>\u003Cmo>=\u003C\u002Fmo>\u003Cmi mathvariant=\"normal\">∇\u003C\u002Fmi>\u003Cmo>⋅\u003C\u002Fmo>\u003Cmover accent=\"true\">\u003Cmi>F\u003C\u002Fmi>\u003Cmo>⃗\u003C\u002Fmo>\u003C\u002Fmover>\u003Cmo>=\u003C\u002Fmo>\u003Cmfrac>\u003Cmrow>\u003Cmi mathvariant=\"normal\">∂\u003C\u002Fmi>\u003Cmsub>\u003Cmi>F\u003C\u002Fmi>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmsub>\u003C\u002Fmrow>\u003Cmrow>\u003Cmi mathvariant=\"normal\">∂\u003C\u002Fmi>\u003Cmi>x\u003C\u002Fmi>\u003C\u002Fmrow>\u003C\u002Fmfrac>\u003Cmo>+\u003C\u002Fmo>\u003Cmfrac>\u003Cmrow>\u003Cmi mathvariant=\"normal\">∂\u003C\u002Fmi>\u003Cmsub>\u003Cmi>F\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsub>\u003C\u002Fmrow>\u003Cmrow>\u003Cmi mathvariant=\"normal\">∂\u003C\u002Fmi>\u003Cmi>y\u003C\u002Fmi>\u003C\u002Fmrow>\u003C\u002Fmfrac>\u003Cmo>+\u003C\u002Fmo>\u003Cmfrac>\u003Cmrow>\u003Cmi mathvariant=\"normal\">∂\u003C\u002Fmi>\u003Cmsub>\u003Cmi>F\u003C\u002Fmi>\u003Cmn>3\u003C\u002Fmn>\u003C\u002Fmsub>\u003C\u002Fmrow>\u003Cmrow>\u003Cmi mathvariant=\"normal\">∂\u003C\u002Fmi>\u003Cmi>z\u003C\u002Fmi>\u003C\u002Fmrow>\u003C\u002Fmfrac>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\operatorname{div} \\vec{F} = \\nabla \\cdot \\vec{F} = \\frac{\\partial F_1}{\\partial x} + \\frac{\\partial F_2}{\\partial y} + \\frac{\\partial F_3}{\\partial z}\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\" style=\"margin-right:0.0139em;\">div\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:0.2778em;\">\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:0.6833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">∇\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:0.9663em;\">\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>\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:2.0574em;vertical-align:-0.686em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mopen nulldelimiter\">\u003C\u002Fspan>\u003Cspan class=\"mfrac\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.3714em;\">\u003Cspan style=\"top:-2.314em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\" style=\"margin-right:0.0556em;\">∂\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.23em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"frac-line\" style=\"border-bottom-width:0.04em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.677em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\" style=\"margin-right:0.0556em;\">∂\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.1389em;\">F\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3011em;\">\u003Cspan style=\"top:-2.55em;margin-left:-0.1389em;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>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\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:0.686em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose nulldelimiter\">\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:2.2519em;vertical-align:-0.8804em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mopen nulldelimiter\">\u003C\u002Fspan>\u003Cspan class=\"mfrac\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.3714em;\">\u003Cspan style=\"top:-2.314em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\" style=\"margin-right:0.0556em;\">∂\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0359em;\">y\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.23em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"frac-line\" style=\"border-bottom-width:0.04em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.677em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\" style=\"margin-right:0.0556em;\">∂\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.1389em;\">F\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3011em;\">\u003Cspan style=\"top:-2.55em;margin-left:-0.1389em;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\">2\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:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\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:0.8804em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose nulldelimiter\">\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:2.0574em;vertical-align:-0.686em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mopen nulldelimiter\">\u003C\u002Fspan>\u003Cspan class=\"mfrac\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.3714em;\">\u003Cspan style=\"top:-2.314em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\" style=\"margin-right:0.0556em;\">∂\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.044em;\">z\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.23em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"frac-line\" style=\"border-bottom-width:0.04em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.677em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\" style=\"margin-right:0.0556em;\">∂\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.1389em;\">F\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3011em;\">\u003Cspan style=\"top:-2.55em;margin-left:-0.1389em;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\">3\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:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\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:0.686em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose nulldelimiter\">\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","university",{},true,"\u002Fde\u002Fformulas\u002Fmath\u002Fmultivariable-calculus\u002Fdivergenz",[],[3432,3433,3434,3435],"curl","gradient","divergence-theorem","laplace-operator",{"title":548,"description":3401},"de\u002Fformulas\u002Fmath\u002Fmultivariable-calculus\u002Fdivergenz","Die Divergenz eines Vektorfelds ist die Summe der partiellen Ableitungen seiner Komponenten und misst die Quellstärke.",[3440,3441,3442,3443,3444],"divergenz","vektorfeld","quellendichte","nabla","vektoranalysis",[3446,3450,3454,3458],{"symbol":3447,"meaning":3448,"symbolHtml":3449},"\\vec{F}","Vektorfeld, z.B. ein Strömungs- oder Kraftfeld","\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":3451,"meaning":3452,"symbolHtml":3453},"F_1, F_2, F_3","Komponenten des Vektorfelds in x-, y- und z-Richtung","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmsub>\u003Cmi>F\u003C\u002Fmi>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmsub>\u003Cmi>F\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmsub>\u003Cmi>F\u003C\u002Fmi>\u003Cmn>3\u003C\u002Fmn>\u003C\u002Fmsub>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">F_1, F_2, F_3\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:0.8778em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.1389em;\">F\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3011em;\">\u003Cspan style=\"top:-2.55em;margin-left:-0.1389em;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>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.1389em;\">F\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3011em;\">\u003Cspan style=\"top:-2.55em;margin-left:-0.1389em;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\">2\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:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.1389em;\">F\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3011em;\">\u003Cspan style=\"top:-2.55em;margin-left:-0.1389em;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\">3\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:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":3455,"meaning":3456,"symbolHtml":3457},"\\nabla","Nabla-Operator, der Vektor der partiellen Ableitungen","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi mathvariant=\"normal\">∇\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\nabla\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\">∇\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":3459,"meaning":3460,"symbolHtml":3461},"\\operatorname{div} \\vec{F}","Divergenz, ein Skalarfeld","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi mathvariant=\"normal\">div\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{div} \\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\" style=\"margin-right:0.0139em;\">div\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>","eKAFTfAW9qW1aKMkf3XV-F71gfCP5oq359Ek7TjO9Qw",[3464,3467,3470,3473],{"stem":3465,"title":3466,"category":368},"de\u002Fformulas\u002Fmath\u002Fmultivariable-calculus\u002Fgradient","Gradient",{"stem":3468,"title":3469,"category":368},"de\u002Fformulas\u002Fmath\u002Fmultivariable-calculus\u002Flaplace-operator","Laplace-Operator",{"stem":3471,"title":3472,"category":368},"de\u002Fformulas\u002Fmath\u002Fmultivariable-calculus\u002Frotation","Rotation",{"stem":3474,"title":3475,"category":368},"de\u002Fformulas\u002Fmath\u002Fmultivariable-calculus\u002Fsatz-von-gauss","Satz von Gauß",1793824266811]