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ausgerichtet ist.",[566,2036,2037,2038,2177,2178,2181,2182,2297,2298,2327,2328,2392,2393,2529,2530,2840],{},"Ein Feld mit ",[574,2039,2041,2071],{"className":2040},[577],[574,2042,2044],{"className":2043},[581],[583,2045,2046],{"xmlns":585},[587,2047,2048,2068],{},[590,2049,2050,2052,2054,2060,2062],{},[597,2051,870],{"mathvariant":770},[601,2053,873],{},[593,2055,2056,2058],{"accent":595},[597,2057,599],{},[601,2059,603],{},[601,2061,882],{},[593,2063,2064,2066],{"accent":595},[702,2065,908],{},[601,2067,603],{},[605,2069,2070],{"encoding":607},"\\operatorname{rot} \\vec F = \\vec 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heißt ",[570,2179,2180],{},"wirbelfrei",". Jedes Gradientenfeld ist wirbelfrei: ",[574,2183,2185,2218],{"className":2184},[577],[574,2186,2188],{"className":2187},[581],[583,2189,2190],{"xmlns":585},[587,2191,2192,2215],{},[590,2193,2194,2196,2198,2200,2202,2205,2207,2209],{},[597,2195,870],{"mathvariant":770},[601,2197,873],{},[601,2199,892],{"stretchy":909},[597,2201,771],{"mathvariant":770},[597,2203,2204],{},"f",[601,2206,1035],{"stretchy":909},[601,2208,882],{},[593,2210,2211,2213],{"accent":595},[702,2212,908],{},[601,2214,603],{},[605,2216,2217],{"encoding":607},"\\operatorname{rot}(\\nabla f) = \\vec 0",[574,2219,2221,2256],{"className":2220,"ariaHidden":595},[612],[574,2222,2224,2228,2234,2237,2240,2244,2247,2250,2253],{"className":2223},[616],[574,2225],{"className":2226,"style":2227},[620],"height:1em;vertical-align:-0.25em;",[574,2229,2231],{"className":2230},[1051],[574,2232,870],{"className":2233},[625,1055],[574,2235,892],{"className":2236},[1126],[574,2238,771],{"className":2239},[625],[574,2241,2204],{"className":2242,"style":2243},[625,650],"margin-right:0.1076em;",[574,2245,1035],{"className":2246},[1370],[574,2248],{"className":2249,"style":1098},[800],[574,2251,882],{"className":2252},[1102],[574,2254],{"className":2255,"style":1098},[800],[574,2257,2259,2262],{"className":2258},[616],[574,2260],{"className":2261,"style":2139},[620],[574,2263,2265],{"className":2264},[625,626],[574,2266,2268],{"className":2267},[630],[574,2269,2271],{"className":2270},[634],[574,2272,2274,2282],{"className":2273,"style":2139},[638],[574,2275,2276,2279],{"style":641},[574,2277],{"className":2278,"style":646},[645],[574,2280,908],{"className":2281},[625],[574,2283,2284,2287],{"style":2162},[574,2285],{"className":2286,"style":646},[645],[574,2288,2290],{"className":2289,"style":2169},[661],[574,2291,2293],{"className":2292,"style":667},[666],[669,2294,2295],{"xmlns":671,"width":672,"height":673,"style":674,"viewBox":675,"preserveAspectRatio":676},[678,2296],{"d":680}," für zweimal stetig differenzierbares ",[574,2299,2301,2314],{"className":2300},[577],[574,2302,2304],{"className":2303},[581],[583,2305,2306],{"xmlns":585},[587,2307,2308,2312],{},[590,2309,2310],{},[597,2311,2204],{},[605,2313,2204],{"encoding":607},[574,2315,2317],{"className":2316,"ariaHidden":595},[612],[574,2318,2320,2324],{"className":2319},[616],[574,2321],{"className":2322,"style":2323},[620],"height:0.8889em;vertical-align:-0.1944em;",[574,2325,2204],{"className":2326,"style":2243},[625,650],". Auf einfach zusammenhängenden Gebieten gilt auch die Umkehrung, dann besitzt ",[574,2329,2331,2348],{"className":2330},[577],[574,2332,2334],{"className":2333},[581],[583,2335,2336],{"xmlns":585},[587,2337,2338,2346],{},[590,2339,2340],{},[593,2341,2342,2344],{"accent":595},[597,2343,599],{},[601,2345,603],{},[605,2347,608],{"encoding":607},[574,2349,2351],{"className":2350,"ariaHidden":595},[612],[574,2352,2354,2357],{"className":2353},[616],[574,2355],{"className":2356,"style":621},[620],[574,2358,2360],{"className":2359},[625,626],[574,2361,2363],{"className":2362},[630],[574,2364,2366],{"className":2365},[634],[574,2367,2369,2377],{"className":2368,"style":621},[638],[574,2370,2371,2374],{"style":641},[574,2372],{"className":2373,"style":646},[645],[574,2375,599],{"className":2376,"style":651},[625,650],[574,2378,2379,2382],{"style":654},[574,2380],{"className":2381,"style":646},[645],[574,2383,2385],{"className":2384,"style":662},[661],[574,2386,2388],{"className":2387,"style":667},[666],[669,2389,2390],{"xmlns":671,"width":672,"height":673,"style":674,"viewBox":675,"preserveAspectRatio":676},[678,2391],{"d":680}," ein Potential. Für ebene Felder ",[574,2394,2396,2427],{"className":2395},[577],[574,2397,2399],{"className":2398},[581],[583,2400,2401],{"xmlns":585},[587,2402,2403,2424],{},[590,2404,2405,2407,2413,2416,2422],{},[601,2406,892],{"stretchy":909},[911,2408,2409,2411],{},[597,2410,599],{},[702,2412,1011],{},[601,2414,2415],{"separator":595},",",[911,2417,2418,2420],{},[597,2419,599],{},[702,2421,1022],{},[601,2423,1035],{"stretchy":909},[605,2425,2426],{"encoding":607},"(F_1, F_2)",[574,2428,2430],{"className":2429,"ariaHidden":595},[612],[574,2431,2433,2436,2439,2479,2483,2486,2526],{"className":2432},[616],[574,2434],{"className":2435,"style":2227},[620],[574,2437,892],{"className":2438},[1126],[574,2440,2442,2445],{"className":2441},[625],[574,2443,599],{"className":2444,"style":651},[625,650],[574,2446,2448],{"className":2447},[728],[574,2449,2451,2471],{"className":2450},[630,1135],[574,2452,2454,2468],{"className":2453},[634],[574,2455,2457],{"className":2456,"style":1398},[638],[574,2458,2459,2462],{"style":1401},[574,2460],{"className":2461,"style":744},[645],[574,2463,2465],{"className":2464},[748,749,750,751],[574,2466,1011],{"className":2467},[625,751],[574,2469,1165],{"className":2470},[1164],[574,2472,2474],{"className":2473},[634],[574,2475,2477],{"className":2476,"style":1278},[638],[574,2478],{},[574,2480,2415],{"className":2481},[2482],"mpunct",[574,2484],{"className":2485,"style":1059},[800],[574,2487,2489,2492],{"className":2488},[625],[574,2490,599],{"className":2491,"style":651},[625,650],[574,2493,2495],{"className":2494},[728],[574,2496,2498,2518],{"className":2497},[630,1135],[574,2499,2501,2515],{"className":2500},[634],[574,2502,2504],{"className":2503,"style":1398},[638],[574,2505,2506,2509],{"style":1401},[574,2507],{"className":2508,"style":744},[645],[574,2510,2512],{"className":2511},[748,749,750,751],[574,2513,1022],{"className":2514},[625,751],[574,2516,1165],{"className":2517},[1164],[574,2519,2521],{"className":2520},[634],[574,2522,2524],{"className":2523,"style":1278},[638],[574,2525],{},[574,2527,1035],{"className":2528},[1370]," betrachtet man nur die dritte Komponente ",[574,2531,2533,2584],{"className":2532},[577],[574,2534,2536],{"className":2535},[581],[583,2537,2538],{"xmlns":585},[587,2539,2540,2581],{},[590,2541,2542,2560,2563],{},[960,2543,2544,2554],{},[590,2545,2546,2548],{},[597,2547,964],{"mathvariant":770},[911,2549,2550,2552],{},[597,2551,599],{},[702,2553,1022],{},[590,2555,2556,2558],{},[597,2557,964],{"mathvariant":770},[597,2559,922],{},[601,2561,2562],{},"−",[960,2564,2565,2575],{},[590,2566,2567,2569],{},[597,2568,964],{"mathvariant":770},[911,2570,2571,2573],{},[597,2572,599],{},[702,2574,1011],{},[590,2576,2577,2579],{},[597,2578,964],{"mathvariant":770},[597,2580,937],{},[605,2582,2583],{"encoding":607},"\\frac{\\partial F_2}{\\partial x} - \\frac{\\partial F_1}{\\partial y}",[574,2585,2587,2722],{"className":2586,"ariaHidden":595},[612],[574,2588,2590,2594,2713,2716,2719],{"className":2589},[616],[574,2591],{"className":2592,"style":2593},[620],"height:1.2412em;vertical-align:-0.345em;",[574,2595,2597,2600,2710],{"className":2596},[625],[574,2598],{"className":2599},[1126,1296],[574,2601,2603],{"className":2602},[960],[574,2604,2606,2702],{"className":2605},[630,1135],[574,2607,2609,2699],{"className":2608},[634],[574,2610,2613,2630,2638],{"className":2611,"style":2612},[638],"height:0.8962em;",[574,2614,2615,2618],{"style":1312},[574,2616],{"className":2617,"style":646},[645],[574,2619,2621],{"className":2620},[748,749,750,751],[574,2622,2624,2627],{"className":2623},[625,751],[574,2625,964],{"className":2626,"style":1325},[625,751],[574,2628,922],{"className":2629},[625,650,751],[574,2631,2632,2635],{"style":1331},[574,2633],{"className":2634,"style":646},[645],[574,2636],{"className":2637,"style":1339},[1338],[574,2639,2641,2644],{"style":2640},"top:-3.4101em;",[574,2642],{"className":2643,"style":646},[645],[574,2645,2647],{"className":2646},[748,749,750,751],[574,2648,2650,2653],{"className":2649},[625,751],[574,2651,964],{"className":2652,"style":1325},[625,751],[574,2654,2656,2659],{"className":2655},[625,751],[574,2657,599],{"className":2658,"style":651},[625,650,751],[574,2660,2662],{"className":2661},[728],[574,2663,2665,2690],{"className":2664},[630,1135],[574,2666,2668,2687],{"className":2667},[634],[574,2669,2672],{"className":2670,"style":2671},[638],"height:0.3173em;",[574,2673,2675,2679],{"style":2674},"top:-2.357em;margin-left:-0.1389em;margin-right:0.0714em;",[574,2676],{"className":2677,"style":2678},[645],"height:2.5em;",[574,2680,2684],{"className":2681},[748,2682,2683,751],"reset-size3","size1",[574,2685,1022],{"className":2686},[625,751],[574,2688,1165],{"className":2689},[1164],[574,2691,2693],{"className":2692},[634],[574,2694,2697],{"className":2695,"style":2696},[638],"height:0.143em;",[574,2698],{},[574,2700,1165],{"className":2701},[1164],[574,2703,2705],{"className":2704},[634],[574,2706,2708],{"className":2707,"style":1364},[638],[574,2709],{},[574,2711],{"className":2712},[1370,1296],[574,2714],{"className":2715,"style":801},[800],[574,2717,2562],{"className":2718},[805],[574,2720],{"className":2721,"style":801},[800],[574,2723,2725,2729],{"className":2724},[616],[574,2726],{"className":2727,"style":2728},[620],"height:1.3773em;vertical-align:-0.4811em;",[574,2730,2732,2735,2837],{"className":2731},[625],[574,2733],{"className":2734},[1126,1296],[574,2736,2738],{"className":2737},[960],[574,2739,2741,2829],{"className":2740},[630,1135],[574,2742,2744,2826],{"className":2743},[634],[574,2745,2747,2764,2772],{"className":2746,"style":2612},[638],[574,2748,2749,2752],{"style":1312},[574,2750],{"className":2751,"style":646},[645],[574,2753,2755],{"className":2754},[748,749,750,751],[574,2756,2758,2761],{"className":2757},[625,751],[574,2759,964],{"className":2760,"style":1325},[625,751],[574,2762,937],{"className":2763,"style":1523},[625,650,751],[574,2765,2766,2769],{"style":1331},[574,2767],{"className":2768,"style":646},[645],[574,2770],{"className":2771,"style":1339},[1338],[574,2773,2774,2777],{"style":2640},[574,2775],{"className":2776,"style":646},[645],[574,2778,2780],{"className":2779},[748,749,750,751],[574,2781,2783,2786],{"className":2782},[625,751],[574,2784,964],{"className":2785,"style":1325},[625,751],[574,2787,2789,2792],{"className":2788},[625,751],[574,2790,599],{"className":2791,"style":651},[625,650,751],[574,2793,2795],{"className":2794},[728],[574,2796,2798,2818],{"className":2797},[630,1135],[574,2799,2801,2815],{"className":2800},[634],[574,2802,2804],{"className":2803,"style":2671},[638],[574,2805,2806,2809],{"style":2674},[574,2807],{"className":2808,"style":2678},[645],[574,2810,2812],{"className":2811},[748,2682,2683,751],[574,2813,1011],{"className":2814},[625,751],[574,2816,1165],{"className":2817},[1164],[574,2819,2821],{"className":2820},[634],[574,2822,2824],{"className":2823,"style":2696},[638],[574,2825],{},[574,2827,1165],{"className":2828},[1164],[574,2830,2832],{"className":2831},[634],[574,2833,2835],{"className":2834,"style":1610},[638],[574,2836],{},[574,2838],{"className":2839},[1370,1296],".",[561,2842,2844],{"id":2843},"beispiele","Beispiele",[566,2846,2847,2848,3031],{},"Für ",[574,2849,2851,2902],{"className":2850},[577],[574,2852,2854],{"className":2853},[581],[583,2855,2856],{"xmlns":585},[587,2857,2858,2899],{},[590,2859,2860,2866,2868,2870,2872,2874,2876,2880,2882,2884,2886,2888,2890,2892],{},[593,2861,2862,2864],{"accent":595},[597,2863,599],{},[601,2865,603],{},[601,2867,882],{},[601,2869,892],{"stretchy":909},[597,2871,922],{},[597,2873,937],{},[601,2875,2415],{"separator":595},[2877,2878,2879],"mtext",{}," ",[597,2881,937],{},[597,2883,952],{},[601,2885,2415],{"separator":595},[2877,2887,2879],{},[597,2889,952],{},[597,2891,922],{},[695,2893,2894,2896],{},[601,2895,1035],{"stretchy":909},[597,2897,2898],{},"T",[605,2900,2901],{"encoding":607},"\\vec F = (xy,\\ yz,\\ zx)^T",[574,2903,2905,2955],{"className":2904,"ariaHidden":595},[612],[574,2906,2908,2911,2946,2949,2952],{"className":2907},[616],[574,2909],{"className":2910,"style":621},[620],[574,2912,2914],{"className":2913},[625,626],[574,2915,2917],{"className":2916},[630],[574,2918,2920],{"className":2919},[634],[574,2921,2923,2931],{"className":2922,"style":621},[638],[574,2924,2925,2928],{"style":641},[574,2926],{"className":2927,"style":646},[645],[574,2929,599],{"className":2930,"style":651},[625,650],[574,2932,2933,2936],{"style":654},[574,2934],{"className":2935,"style":646},[645],[574,2937,2939],{"className":2938,"style":662},[661],[574,2940,2942],{"className":2941,"style":667},[666],[669,2943,2944],{"xmlns":671,"width":672,"height":673,"style":674,"viewBox":675,"preserveAspectRatio":676},[678,2945],{"d":680},[574,2947],{"className":2948,"style":1098},[800],[574,2950,882],{"className":2951},[1102],[574,2953],{"className":2954,"style":1098},[800],[574,2956,2958,2962,2965,2968,2971,2974,2977,2980,2983,2986,2989,2992,2995,2998,3001],{"className":2957},[616],[574,2959],{"className":2960,"style":2961},[620],"height:1.0913em;vertical-align:-0.25em;",[574,2963,892],{"className":2964},[1126],[574,2966,922],{"className":2967},[625,650],[574,2969,937],{"className":2970,"style":1523},[625,650],[574,2972,2415],{"className":2973},[2482],[574,2975,2879],{"className":2976},[800],[574,2978],{"className":2979,"style":1059},[800],[574,2981,937],{"className":2982,"style":1523},[625,650],[574,2984,952],{"className":2985,"style":1762},[625,650],[574,2987,2415],{"className":2988},[2482],[574,2990,2879],{"className":2991},[800],[574,2993],{"className":2994,"style":1059},[800],[574,2996,952],{"className":2997,"style":1762},[625,650],[574,2999,922],{"className":3000},[625,650],[574,3002,3004,3007],{"className":3003},[1370],[574,3005,1035],{"className":3006},[1370],[574,3008,3010],{"className":3009},[728],[574,3011,3013],{"className":3012},[630],[574,3014,3016],{"className":3015},[634],[574,3017,3020],{"className":3018,"style":3019},[638],"height:0.8413em;",[574,3021,3022,3025],{"style":740},[574,3023],{"className":3024,"style":744},[645],[574,3026,3028],{"className":3027},[748,749,750,751],[574,3029,2898],{"className":3030,"style":651},[625,650,751],":",[574,3033,3035],{"className":3034},[854],[574,3036,3038,3159],{"className":3037},[577],[574,3039,3041],{"className":3040},[581],[583,3042,3043],{"xmlns":585,"display":863},[587,3044,3045,3156],{},[590,3046,3047,3049,3051,3057,3059,3110,3112],{},[597,3048,870],{"mathvariant":770},[601,3050,873],{},[593,3052,3053,3055],{"accent":595},[597,3054,599],{},[601,3056,603],{},[601,3058,882],{},[590,3060,3061,3063,3108],{},[601,3062,892],{"fence":595},[894,3064,3066,3080,3094],{"rowspacing":896,"columnalign":3065,"columnspacing":898},"center",[900,3067,3068],{},[903,3069,3070],{},[906,3071,3072],{"scriptlevel":908,"displaystyle":909},[590,3073,3074,3076,3078],{},[702,3075,908],{},[601,3077,2562],{},[597,3079,937],{},[900,3081,3082],{},[903,3083,3084],{},[906,3085,3086],{"scriptlevel":908,"displaystyle":909},[590,3087,3088,3090,3092],{},[702,3089,908],{},[601,3091,2562],{},[597,3093,952],{},[900,3095,3096],{},[903,3097,3098],{},[906,3099,3100],{"scriptlevel":908,"displaystyle":909},[590,3101,3102,3104,3106],{},[702,3103,908],{},[601,3105,2562],{},[597,3107,922],{},[601,3109,1035],{"fence":595},[601,3111,882],{},[590,3113,3114,3116,3154],{},[601,3115,892],{"fence":595},[894,3117,3118,3130,3142],{"rowspacing":896,"columnalign":3065,"columnspacing":898},[900,3119,3120],{},[903,3121,3122],{},[906,3123,3124],{"scriptlevel":908,"displaystyle":909},[590,3125,3126,3128],{},[601,3127,2562],{},[597,3129,937],{},[900,3131,3132],{},[903,3133,3134],{},[906,3135,3136],{"scriptlevel":908,"displaystyle":909},[590,3137,3138,3140],{},[601,3139,2562],{},[597,3141,952],{},[900,3143,3144],{},[903,3145,3146],{},[906,3147,3148],{"scriptlevel":908,"displaystyle":909},[590,3149,3150,3152],{},[601,3151,2562],{},[597,3153,922],{},[601,3155,1035],{"fence":595},[605,3157,3158],{"encoding":607},"\\operatorname{rot} \\vec F = \\begin{pmatrix} 0 - y \\\\ 0 - z \\\\ 0 - x \\end{pmatrix} = \\begin{pmatrix} -y \\\\ -z \\\\ -x \\end{pmatrix}",[574,3160,3162,3221,3415],{"className":3161,"ariaHidden":595},[612],[574,3163,3165,3168,3174,3177,3212,3215,3218],{"className":3164},[616],[574,3166],{"className":3167,"style":621},[620],[574,3169,3171],{"className":3170},[1051],[574,3172,870],{"className":3173},[625,1055],[574,3175],{"className":3176,"style":1059},[800],[574,3178,3180],{"className":3179},[625,626],[574,3181,3183],{"className":3182},[630],[574,3184,3186],{"className":3185},[634],[574,3187,3189,3197],{"className":3188,"style":621},[638],[574,3190,3191,3194],{"style":641},[574,3192],{"className":3193,"style":646},[645],[574,3195,599],{"className":3196,"style":651},[625,650],[574,3198,3199,3202],{"style":654},[574,3200],{"className":3201,"style":646},[645],[574,3203,3205],{"className":3204,"style":662},[661],[574,3206,3208],{"className":3207,"style":667},[666],[669,3209,3210],{"xmlns":671,"width":672,"height":673,"style":674,"viewBox":675,"preserveAspectRatio":676},[678,3211],{"d":680},[574,3213],{"className":3214,"style":1098},[800],[574,3216,882],{"className":3217},[1102],[574,3219],{"className":3220,"style":1098},[800],[574,3222,3224,3228,3406,3409,3412],{"className":3223},[616],[574,3225],{"className":3226,"style":3227},[620],"height:3.6em;vertical-align:-1.55em;",[574,3229,3231,3268,3369],{"className":3230},[1122],[574,3232,3234],{"className":3233},[1126],[574,3235,3237],{"className":3236},[1130,1131],[574,3238,3240,3260],{"className":3239},[630,1135],[574,3241,3243,3257],{"className":3242},[634],[574,3244,3246],{"className":3245,"style":1142},[638],[574,3247,3248,3251],{"style":1145},[574,3249],{"className":3250,"style":1149},[645],[574,3252,3253],{"style":1152},[669,3254,3255],{"xmlns":671,"width":1155,"height":1156,"viewBox":1157},[678,3256],{"d":1160},[574,3258,1165],{"className":3259},[1164],[574,3261,3263],{"className":3262},[634],[574,3264,3266],{"className":3265,"style":1172},[638],[574,3267],{},[574,3269,3271],{"className":3270},[625],[574,3272,3274],{"className":3273},[894],[574,3275,3277],{"className":3276},[1184],[574,3278,3280,3361],{"className":3279},[630,1135],[574,3281,3283,3358],{"className":3282},[634],[574,3284,3286,3310,3334],{"className":3285,"style":1142},[638],[574,3287,3289,3292],{"style":3288},"top:-4.21em;",[574,3290],{"className":3291,"style":646},[645],[574,3293,3295,3298,3301,3304,3307],{"className":3294},[625],[574,3296,908],{"className":3297},[625],[574,3299],{"className":3300,"style":801},[800],[574,3302,2562],{"className":3303},[805],[574,3305],{"className":3306,"style":801},[800],[574,3308,937],{"className":3309,"style":1523},[625,650],[574,3311,3313,3316],{"style":3312},"top:-3.01em;",[574,3314],{"className":3315,"style":646},[645],[574,3317,3319,3322,3325,3328,3331],{"className":3318},[625],[574,3320,908],{"className":3321},[625],[574,3323],{"className":3324,"style":801},[800],[574,3326,2562],{"className":3327},[805],[574,3329],{"className":3330,"style":801},[800],[574,3332,952],{"className":3333,"style":1762},[625,650],[574,3335,3337,3340],{"style":3336},"top:-1.81em;",[574,3338],{"className":3339,"style":646},[645],[574,3341,3343,3346,3349,3352,3355],{"className":3342},[625],[574,3344,908],{"className":3345},[625],[574,3347],{"className":3348,"style":801},[800],[574,3350,2562],{"className":3351},[805],[574,3353],{"className":3354,"style":801},[800],[574,3356,922],{"className":3357},[625,650],[574,3359,1165],{"className":3360},[1164],[574,3362,3364],{"className":3363},[634],[574,3365,3367],{"className":3366,"style":1172},[638],[574,3368],{},[574,3370,3372],{"className":3371},[1370],[574,3373,3375],{"className":3374},[1130,1131],[574,3376,3378,3398],{"className":3377},[630,1135],[574,3379,3381,3395],{"className":3380},[634],[574,3382,3384],{"className":3383,"style":1142},[638],[574,3385,3386,3389],{"style":1145},[574,3387],{"className":3388,"style":1149},[645],[574,3390,3391],{"style":1152},[669,3392,3393],{"xmlns":671,"width":1155,"height":1156,"viewBox":1157},[678,3394],{"d":1938},[574,3396,1165],{"className":3397},[1164],[574,3399,3401],{"className":3400},[634],[574,3402,3404],{"className":3403,"style":1172},[638],[574,3405],{},[574,3407],{"className":3408,"style":1098},[800],[574,3410,882],{"className":3411},[1102],[574,3413],{"className":3414,"style":1098},[800],[574,3416,3418,3421],{"className":3417},[616],[574,3419],{"className":3420,"style":3227},[620],[574,3422,3424,3461,3532],{"className":3423},[1122],[574,3425,3427],{"className":3426},[1126],[574,3428,3430],{"className":3429},[1130,1131],[574,3431,3433,3453],{"className":3432},[630,1135],[574,3434,3436,3450],{"className":3435},[634],[574,3437,3439],{"className":3438,"style":1142},[638],[574,3440,3441,3444],{"style":1145},[574,3442],{"className":3443,"style":1149},[645],[574,3445,3446],{"style":1152},[669,3447,3448],{"xmlns":671,"width":1155,"height":1156,"viewBox":1157},[678,3449],{"d":1160},[574,3451,1165],{"className":3452},[1164],[574,3454,3456],{"className":3455},[634],[574,3457,3459],{"className":3458,"style":1172},[638],[574,3460],{},[574,3462,3464],{"className":3463},[625],[574,3465,3467],{"className":3466},[894],[574,3468,3470],{"className":3469},[1184],[574,3471,3473,3524],{"className":3472},[630,1135],[574,3474,3476,3521],{"className":3475},[634],[574,3477,3479,3493,3507],{"className":3478,"style":1142},[638],[574,3480,3481,3484],{"style":3288},[574,3482],{"className":3483,"style":646},[645],[574,3485,3487,3490],{"className":3486},[625],[574,3488,2562],{"className":3489},[625],[574,3491,937],{"className":3492,"style":1523},[625,650],[574,3494,3495,3498],{"style":3312},[574,3496],{"className":3497,"style":646},[645],[574,3499,3501,3504],{"className":3500},[625],[574,3502,2562],{"className":3503},[625],[574,3505,952],{"className":3506,"style":1762},[625,650],[574,3508,3509,3512],{"style":3336},[574,3510],{"className":3511,"style":646},[645],[574,3513,3515,3518],{"className":3514},[625],[574,3516,2562],{"className":3517},[625],[574,3519,922],{"className":3520},[625,650],[574,3522,1165],{"className":3523},[1164],[574,3525,3527],{"className":3526},[634],[574,3528,3530],{"className":3529,"style":1172},[638],[574,3531],{},[574,3533,3535],{"className":3534},[1370],[574,3536,3538],{"className":3537},[1130,1131],[574,3539,3541,3561],{"className":3540},[630,1135],[574,3542,3544,3558],{"className":3543},[634],[574,3545,3547],{"className":3546,"style":1142},[638],[574,3548,3549,3552],{"style":1145},[574,3550],{"className":3551,"style":1149},[645],[574,3553,3554],{"style":1152},[669,3555,3556],{"xmlns":671,"width":1155,"height":1156,"viewBox":1157},[678,3557],{"d":1938},[574,3559,1165],{"className":3560},[1164],[574,3562,3564],{"className":3563},[634],[574,3565,3567],{"className":3566,"style":1172},[638],[574,3568],{},[566,3570,3571,3572,3637,3638,3819,3820,3637,3900,3998],{},"Im Punkt ",[574,3573,3575,3601],{"className":3574},[577],[574,3576,3578],{"className":3577},[581],[583,3579,3580],{"xmlns":585},[587,3581,3582,3598],{},[590,3583,3584,3586,3588,3590,3592,3594,3596],{},[601,3585,892],{"stretchy":909},[702,3587,1011],{},[601,3589,2415],{"separator":595},[702,3591,1022],{},[601,3593,2415],{"separator":595},[702,3595,704],{},[601,3597,1035],{"stretchy":909},[605,3599,3600],{"encoding":607},"(1, 2, 3)",[574,3602,3604],{"className":3603,"ariaHidden":595},[612],[574,3605,3607,3610,3613,3616,3619,3622,3625,3628,3631,3634],{"className":3606},[616],[574,3608],{"className":3609,"style":2227},[620],[574,3611,892],{"className":3612},[1126],[574,3614,1011],{"className":3615},[625],[574,3617,2415],{"className":3618},[2482],[574,3620],{"className":3621,"style":1059},[800],[574,3623,1022],{"className":3624},[625],[574,3626,2415],{"className":3627},[2482],[574,3629],{"className":3630,"style":1059},[800],[574,3632,704],{"className":3633},[625],[574,3635,1035],{"className":3636},[1370]," ist ",[574,3639,3641,3689],{"className":3640},[577],[574,3642,3644],{"className":3643},[581],[583,3645,3646],{"xmlns":585},[587,3647,3648,3686],{},[590,3649,3650,3652,3654,3660,3662,3664,3666,3668,3670,3672,3674,3676,3678,3680],{},[597,3651,870],{"mathvariant":770},[601,3653,873],{},[593,3655,3656,3658],{"accent":595},[597,3657,599],{},[601,3659,603],{},[601,3661,882],{},[601,3663,892],{"stretchy":909},[601,3665,2562],{},[702,3667,1022],{},[601,3669,2415],{"separator":595},[601,3671,2562],{},[702,3673,704],{},[601,3675,2415],{"separator":595},[601,3677,2562],{},[702,3679,1011],{},[695,3681,3682,3684],{},[601,3683,1035],{"stretchy":909},[597,3685,2898],{},[605,3687,3688],{"encoding":607},"\\operatorname{rot} \\vec F = (-2, -3, -1)^T",[574,3690,3692,3751],{"className":3691,"ariaHidden":595},[612],[574,3693,3695,3698,3704,3707,3742,3745,3748],{"className":3694},[616],[574,3696],{"className":3697,"style":621},[620],[574,3699,3701],{"className":3700},[1051],[574,3702,870],{"className":3703},[625,1055],[574,3705],{"className":3706,"style":1059},[800],[574,3708,3710],{"className":3709},[625,626],[574,3711,3713],{"className":3712},[630],[574,3714,3716],{"className":3715},[634],[574,3717,3719,3727],{"className":3718,"style":621},[638],[574,3720,3721,3724],{"style":641},[574,3722],{"className":3723,"style":646},[645],[574,3725,599],{"className":3726,"style":651},[625,650],[574,3728,3729,3732],{"style":654},[574,3730],{"className":3731,"style":646},[645],[574,3733,3735],{"className":3734,"style":662},[661],[574,3736,3738],{"className":3737,"style":667},[666],[669,3739,3740],{"xmlns":671,"width":672,"height":673,"style":674,"viewBox":675,"preserveAspectRatio":676},[678,3741],{"d":680},[574,3743],{"className":3744,"style":1098},[800],[574,3746,882],{"className":3747},[1102],[574,3749],{"className":3750,"style":1098},[800],[574,3752,3754,3757,3760,3763,3766,3769,3772,3775,3778,3781,3784,3787,3790],{"className":3753},[616],[574,3755],{"className":3756,"style":2961},[620],[574,3758,892],{"className":3759},[1126],[574,3761,2562],{"className":3762},[625],[574,3764,1022],{"className":3765},[625],[574,3767,2415],{"className":3768},[2482],[574,3770],{"className":3771,"style":1059},[800],[574,3773,2562],{"className":3774},[625],[574,3776,704],{"className":3777},[625],[574,3779,2415],{"className":3780},[2482],[574,3782],{"className":3783,"style":1059},[800],[574,3785,2562],{"className":3786},[625],[574,3788,1011],{"className":3789},[625],[574,3791,3793,3796],{"className":3792},[1370],[574,3794,1035],{"className":3795},[1370],[574,3797,3799],{"className":3798},[728],[574,3800,3802],{"className":3801},[630],[574,3803,3805],{"className":3804},[634],[574,3806,3808],{"className":3807,"style":3019},[638],[574,3809,3810,3813],{"style":740},[574,3811],{"className":3812,"style":744},[645],[574,3814,3816],{"className":3815},[748,749,750,751],[574,3817,2898],{"className":3818,"style":651},[625,650,751],". Zur Kontrolle: Die Divergenz von ",[574,3821,3823,3855],{"className":3822},[577],[574,3824,3826],{"className":3825},[581],[583,3827,3828],{"xmlns":585},[587,3829,3830,3852],{},[590,3831,3832,3834,3836,3838,3840,3842,3844,3846,3848,3850],{},[601,3833,892],{"stretchy":909},[601,3835,2562],{},[597,3837,937],{},[601,3839,2415],{"separator":595},[601,3841,2562],{},[597,3843,952],{},[601,3845,2415],{"separator":595},[601,3847,2562],{},[597,3849,922],{},[601,3851,1035],{"stretchy":909},[605,3853,3854],{"encoding":607},"(-y, -z, -x)",[574,3856,3858],{"className":3857,"ariaHidden":595},[612],[574,3859,3861,3864,3867,3870,3873,3876,3879,3882,3885,3888,3891,3894,3897],{"className":3860},[616],[574,3862],{"className":3863,"style":2227},[620],[574,3865,892],{"className":3866},[1126],[574,3868,2562],{"className":3869},[625],[574,3871,937],{"className":3872,"style":1523},[625,650],[574,3874,2415],{"className":3875},[2482],[574,3877],{"className":3878,"style":1059},[800],[574,3880,2562],{"className":3881},[625],[574,3883,952],{"className":3884,"style":1762},[625,650],[574,3886,2415],{"className":3887},[2482],[574,3889],{"className":3890,"style":1059},[800],[574,3892,2562],{"className":3893},[625],[574,3895,922],{"className":3896},[625,650],[574,3898,1035],{"className":3899},[1370],[574,3901,3903,3930],{"className":3902},[577],[574,3904,3906],{"className":3905},[581],[583,3907,3908],{"xmlns":585},[587,3909,3910,3927],{},[590,3911,3912,3914,3917,3919,3921,3923,3925],{},[702,3913,908],{},[601,3915,3916],{},"+",[702,3918,908],{},[601,3920,3916],{},[702,3922,908],{},[601,3924,882],{},[702,3926,908],{},[605,3928,3929],{"encoding":607},"0 + 0 + 0 = 0",[574,3931,3933,3952,3970,3989],{"className":3932,"ariaHidden":595},[612],[574,3934,3936,3940,3943,3946,3949],{"className":3935},[616],[574,3937],{"className":3938,"style":3939},[620],"height:0.7278em;vertical-align:-0.0833em;",[574,3941,908],{"className":3942},[625],[574,3944],{"className":3945,"style":801},[800],[574,3947,3916],{"className":3948},[805],[574,3950],{"className":3951,"style":801},[800],[574,3953,3955,3958,3961,3964,3967],{"className":3954},[616],[574,3956],{"className":3957,"style":3939},[620],[574,3959,908],{"className":3960},[625],[574,3962],{"className":3963,"style":801},[800],[574,3965,3916],{"className":3966},[805],[574,3968],{"className":3969,"style":801},[800],[574,3971,3973,3977,3980,3983,3986],{"className":3972},[616],[574,3974],{"className":3975,"style":3976},[620],"height:0.6444em;",[574,3978,908],{"className":3979},[625],[574,3981],{"className":3982,"style":1098},[800],[574,3984,882],{"className":3985},[1102],[574,3987],{"className":3988,"style":1098},[800],[574,3990,3992,3995],{"className":3991},[616],[574,3993],{"className":3994,"style":3976},[620],[574,3996,908],{"className":3997},[625],", wie es für jede Rotation sein muss.",[566,4000,4001,4002,4170,4171,4200,4201,4435,4436,4464],{},"Das Wirbelfeld ",[574,4003,4005,4049],{"className":4004},[577],[574,4006,4008],{"className":4007},[581],[583,4009,4010],{"xmlns":585},[587,4011,4012,4046],{},[590,4013,4014,4020,4022,4024,4026,4028,4030,4032,4034,4036,4038,4040],{},[593,4015,4016,4018],{"accent":595},[597,4017,599],{},[601,4019,603],{},[601,4021,882],{},[601,4023,892],{"stretchy":909},[601,4025,2562],{},[597,4027,937],{},[601,4029,2415],{"separator":595},[2877,4031,2879],{},[597,4033,922],{},[601,4035,2415],{"separator":595},[2877,4037,2879],{},[702,4039,908],{},[695,4041,4042,4044],{},[601,4043,1035],{"stretchy":909},[597,4045,2898],{},[605,4047,4048],{"encoding":607},"\\vec F = (-y,\\ x,\\ 0)^T",[574,4050,4052,4102],{"className":4051,"ariaHidden":595},[612],[574,4053,4055,4058,4093,4096,4099],{"className":4054},[616],[574,4056],{"className":4057,"style":621},[620],[574,4059,4061],{"className":4060},[625,626],[574,4062,4064],{"className":4063},[630],[574,4065,4067],{"className":4066},[634],[574,4068,4070,4078],{"className":4069,"style":621},[638],[574,4071,4072,4075],{"style":641},[574,4073],{"className":4074,"style":646},[645],[574,4076,599],{"className":4077,"style":651},[625,650],[574,4079,4080,4083],{"style":654},[574,4081],{"className":4082,"style":646},[645],[574,4084,4086],{"className":4085,"style":662},[661],[574,4087,4089],{"className":4088,"style":667},[666],[669,4090,4091],{"xmlns":671,"width":672,"height":673,"style":674,"viewBox":675,"preserveAspectRatio":676},[678,4092],{"d":680},[574,4094],{"className":4095,"style":1098},[800],[574,4097,882],{"className":4098},[1102],[574,4100],{"className":4101,"style":1098},[800],[574,4103,4105,4108,4111,4114,4117,4120,4123,4126,4129,4132,4135,4138,4141],{"className":4104},[616],[574,4106],{"className":4107,"style":2961},[620],[574,4109,892],{"className":4110},[1126],[574,4112,2562],{"className":4113},[625],[574,4115,937],{"className":4116,"style":1523},[625,650],[574,4118,2415],{"className":4119},[2482],[574,4121,2879],{"className":4122},[800],[574,4124],{"className":4125,"style":1059},[800],[574,4127,922],{"className":4128},[625,650],[574,4130,2415],{"className":4131},[2482],[574,4133,2879],{"className":4134},[800],[574,4136],{"className":4137,"style":1059},[800],[574,4139,908],{"className":4140},[625],[574,4142,4144,4147],{"className":4143},[1370],[574,4145,1035],{"className":4146},[1370],[574,4148,4150],{"className":4149},[728],[574,4151,4153],{"className":4152},[630],[574,4154,4156],{"className":4155},[634],[574,4157,4159],{"className":4158,"style":3019},[638],[574,4160,4161,4164],{"style":740},[574,4162],{"className":4163,"style":744},[645],[574,4165,4167],{"className":4166},[748,749,750,751],[574,4168,2898],{"className":4169,"style":651},[625,650,751]," kreist gegen den Uhrzeigersinn um die ",[574,4172,4174,4187],{"className":4173},[577],[574,4175,4177],{"className":4176},[581],[583,4178,4179],{"xmlns":585},[587,4180,4181,4185],{},[590,4182,4183],{},[597,4184,952],{},[605,4186,952],{"encoding":607},[574,4188,4190],{"className":4189,"ariaHidden":595},[612],[574,4191,4193,4197],{"className":4192},[616],[574,4194],{"className":4195,"style":4196},[620],"height:0.4306em;",[574,4198,952],{"className":4199,"style":1762},[625,650],"-Achse. Seine Rotation ist ",[574,4202,4204,4270],{"className":4203},[577],[574,4205,4207],{"className":4206},[581],[583,4208,4209],{"xmlns":585},[587,4210,4211,4267],{},[590,4212,4213,4247,4249,4251,4253,4255,4257,4259,4261],{},[695,4214,4215,4245],{},[590,4216,4217,4219,4221,4223,4225,4227,4229,4231,4233,4235,4237,4239,4241,4243],{},[601,4218,892],{"fence":595},[702,4220,908],{},[601,4222,2415],{"separator":595},[2877,4224,2879],{},[702,4226,908],{},[601,4228,2415],{"separator":595},[2877,4230,2879],{},[702,4232,1011],{},[601,4234,2562],{},[601,4236,892],{"stretchy":909},[601,4238,2562],{},[702,4240,1011],{},[601,4242,1035],{"stretchy":909},[601,4244,1035],{"fence":595},[597,4246,2898],{},[601,4248,882],{},[601,4250,892],{"stretchy":909},[702,4252,908],{},[601,4254,2415],{"separator":595},[702,4256,908],{},[601,4258,2415],{"separator":595},[702,4260,1022],{},[695,4262,4263,4265],{},[601,4264,1035],{"stretchy":909},[597,4266,2898],{},[605,4268,4269],{"encoding":607},"\\left(0,\\ 0,\\ 1 - (-1)\\right)^T = (0, 0, 2)^T",[574,4271,4273,4376],{"className":4272,"ariaHidden":595},[612],[574,4274,4276,4280,4367,4370,4373],{"className":4275},[616],[574,4277],{"className":4278,"style":4279},[620],"height:1.2312em;vertical-align:-0.25em;",[574,4281,4283,4342],{"className":4282},[1122],[574,4284,4286,4291,4294,4297,4300,4303,4306,4309,4312,4315,4318,4321,4324,4327,4330,4333,4336,4339],{"className":4285},[1122],[574,4287,892],{"className":4288,"style":4290},[1126,4289],"delimcenter","top:0em;",[574,4292,908],{"className":4293},[625],[574,4295,2415],{"className":4296},[2482],[574,4298,2879],{"className":4299},[800],[574,4301],{"className":4302,"style":1059},[800],[574,4304,908],{"className":4305},[625],[574,4307,2415],{"className":4308},[2482],[574,4310,2879],{"className":4311},[800],[574,4313],{"className":4314,"style":1059},[800],[574,4316,1011],{"className":4317},[625],[574,4319],{"className":4320,"style":801},[800],[574,4322,2562],{"className":4323},[805],[574,4325],{"className":4326,"style":801},[800],[574,4328,892],{"className":4329},[1126],[574,4331,2562],{"className":4332},[625],[574,4334,1011],{"className":4335},[625],[574,4337,1035],{"className":4338},[1370],[574,4340,1035],{"className":4341,"style":4290},[1370,4289],[574,4343,4345],{"className":4344},[728],[574,4346,4348],{"className":4347},[630],[574,4349,4351],{"className":4350},[634],[574,4352,4355],{"className":4353,"style":4354},[638],"height:0.9812em;",[574,4356,4358,4361],{"style":4357},"top:-3.2029em;margin-right:0.05em;",[574,4359],{"className":4360,"style":744},[645],[574,4362,4364],{"className":4363},[748,749,750,751],[574,4365,2898],{"className":4366,"style":651},[625,650,751],[574,4368],{"className":4369,"style":1098},[800],[574,4371,882],{"className":4372},[1102],[574,4374],{"className":4375,"style":1098},[800],[574,4377,4379,4382,4385,4388,4391,4394,4397,4400,4403,4406],{"className":4378},[616],[574,4380],{"className":4381,"style":2961},[620],[574,4383,892],{"className":4384},[1126],[574,4386,908],{"className":4387},[625],[574,4389,2415],{"className":4390},[2482],[574,4392],{"className":4393,"style":1059},[800],[574,4395,908],{"className":4396},[625],[574,4398,2415],{"className":4399},[2482],[574,4401],{"className":4402,"style":1059},[800],[574,4404,1022],{"className":4405},[625],[574,4407,4409,4412],{"className":4408},[1370],[574,4410,1035],{"className":4411},[1370],[574,4413,4415],{"className":4414},[728],[574,4416,4418],{"className":4417},[630],[574,4419,4421],{"className":4420},[634],[574,4422,4424],{"className":4423,"style":3019},[638],[574,4425,4426,4429],{"style":740},[574,4427],{"className":4428,"style":744},[645],[574,4430,4432],{"className":4431},[748,749,750,751],[574,4433,2898],{"className":4434,"style":651},[625,650,751],", also überall gleich: Jedes kleine Schaufelrad dreht sich gleich schnell um die ",[574,4437,4439,4452],{"className":4438},[577],[574,4440,4442],{"className":4441},[581],[583,4443,4444],{"xmlns":585},[587,4445,4446,4450],{},[590,4447,4448],{},[597,4449,952],{},[605,4451,952],{"encoding":607},[574,4453,4455],{"className":4454,"ariaHidden":595},[612],[574,4456,4458,4461],{"className":4457},[616],[574,4459],{"className":4460,"style":4196},[620],[574,4462,952],{"className":4463,"style":1762},[625,650],"-Richtung.",[561,4466,4468],{"id":4467},"typische-fehler","Typische Fehler",[4470,4471,4472,4776,4779],"ul",{},[4473,4474,4475,4476,4775],"li",{},"Vorzeichen in der zweiten Komponente vertauschen. Es heißt ",[574,4477,4479,4529],{"className":4478},[577],[574,4480,4482],{"className":4481},[581],[583,4483,4484],{"xmlns":585},[587,4485,4486,4526],{},[590,4487,4488,4506,4508],{},[960,4489,4490,4500],{},[590,4491,4492,4494],{},[597,4493,964],{"mathvariant":770},[911,4495,4496,4498],{},[597,4497,599],{},[702,4499,1011],{},[590,4501,4502,4504],{},[597,4503,964],{"mathvariant":770},[597,4505,952],{},[601,4507,2562],{},[960,4509,4510,4520],{},[590,4511,4512,4514],{},[597,4513,964],{"mathvariant":770},[911,4515,4516,4518],{},[597,4517,599],{},[702,4519,704],{},[590,4521,4522,4524],{},[597,4523,964],{"mathvariant":770},[597,4525,922],{},[605,4527,4528],{"encoding":607},"\\frac{\\partial F_1}{\\partial z} - \\frac{\\partial F_3}{\\partial x}",[574,4530,4532,4658],{"className":4531,"ariaHidden":595},[612],[574,4533,4535,4538,4649,4652,4655],{"className":4534},[616],[574,4536],{"className":4537,"style":2593},[620],[574,4539,4541,4544,4646],{"className":4540},[625],[574,4542],{"className":4543},[1126,1296],[574,4545,4547],{"className":4546},[960],[574,4548,4550,4638],{"className":4549},[630,1135],[574,4551,4553,4635],{"className":4552},[634],[574,4554,4556,4573,4581],{"className":4555,"style":2612},[638],[574,4557,4558,4561],{"style":1312},[574,4559],{"className":4560,"style":646},[645],[574,4562,4564],{"className":4563},[748,749,750,751],[574,4565,4567,4570],{"className":4566},[625,751],[574,4568,964],{"className":4569,"style":1325},[625,751],[574,4571,952],{"className":4572,"style":1762},[625,650,751],[574,4574,4575,4578],{"style":1331},[574,4576],{"className":4577,"style":646},[645],[574,4579],{"className":4580,"style":1339},[1338],[574,4582,4583,4586],{"style":2640},[574,4584],{"className":4585,"style":646},[645],[574,4587,4589],{"className":4588},[748,749,750,751],[574,4590,4592,4595],{"className":4591},[625,751],[574,4593,964],{"className":4594,"style":1325},[625,751],[574,4596,4598,4601],{"className":4597},[625,751],[574,4599,599],{"className":4600,"style":651},[625,650,751],[574,4602,4604],{"className":4603},[728],[574,4605,4607,4627],{"className":4606},[630,1135],[574,4608,4610,4624],{"className":4609},[634],[574,4611,4613],{"className":4612,"style":2671},[638],[574,4614,4615,4618],{"style":2674},[574,4616],{"className":4617,"style":2678},[645],[574,4619,4621],{"className":4620},[748,2682,2683,751],[574,4622,1011],{"className":4623},[625,751],[574,4625,1165],{"className":4626},[1164],[574,4628,4630],{"className":4629},[634],[574,4631,4633],{"className":4632,"style":2696},[638],[574,4634],{},[574,4636,1165],{"className":4637},[1164],[574,4639,4641],{"className":4640},[634],[574,4642,4644],{"className":4643,"style":1364},[638],[574,4645],{},[574,4647],{"className":4648},[1370,1296],[574,4650],{"className":4651,"style":801},[800],[574,4653,2562],{"className":4654},[805],[574,4656],{"className":4657,"style":801},[800],[574,4659,4661,4664],{"className":4660},[616],[574,4662],{"className":4663,"style":2593},[620],[574,4665,4667,4670,4772],{"className":4666},[625],[574,4668],{"className":4669},[1126,1296],[574,4671,4673],{"className":4672},[960],[574,4674,4676,4764],{"className":4675},[630,1135],[574,4677,4679,4761],{"className":4678},[634],[574,4680,4682,4699,4707],{"className":4681,"style":2612},[638],[574,4683,4684,4687],{"style":1312},[574,4685],{"className":4686,"style":646},[645],[574,4688,4690],{"className":4689},[748,749,750,751],[574,4691,4693,4696],{"className":4692},[625,751],[574,4694,964],{"className":4695,"style":1325},[625,751],[574,4697,922],{"className":4698},[625,650,751],[574,4700,4701,4704],{"style":1331},[574,4702],{"className":4703,"style":646},[645],[574,4705],{"className":4706,"style":1339},[1338],[574,4708,4709,4712],{"style":2640},[574,4710],{"className":4711,"style":646},[645],[574,4713,4715],{"className":4714},[748,749,750,751],[574,4716,4718,4721],{"className":4717},[625,751],[574,4719,964],{"className":4720,"style":1325},[625,751],[574,4722,4724,4727],{"className":4723},[625,751],[574,4725,599],{"className":4726,"style":651},[625,650,751],[574,4728,4730],{"className":4729},[728],[574,4731,4733,4753],{"className":4732},[630,1135],[574,4734,4736,4750],{"className":4735},[634],[574,4737,4739],{"className":4738,"style":2671},[638],[574,4740,4741,4744],{"style":2674},[574,4742],{"className":4743,"style":2678},[645],[574,4745,4747],{"className":4746},[748,2682,2683,751],[574,4748,704],{"className":4749},[625,751],[574,4751,1165],{"className":4752},[1164],[574,4754,4756],{"className":4755},[634],[574,4757,4759],{"className":4758,"style":2696},[638],[574,4760],{},[574,4762,1165],{"className":4763},[1164],[574,4765,4767],{"className":4766},[634],[574,4768,4770],{"className":4769,"style":1364},[638],[574,4771],{},[574,4773],{"className":4774},[1370,1296],", die Reihenfolge folgt dem Muster des Kreuzprodukts.",[4473,4777,4778],{},"Rotation und Divergenz verwechseln. Die Rotation ist ein Vektor, die Divergenz eine Zahl.",[4473,4780,4781,4782,4917,4918,5138,5139,5167],{},"Aus ",[574,4783,4785,4814],{"className":4784},[577],[574,4786,4788],{"className":4787},[581],[583,4789,4790],{"xmlns":585},[587,4791,4792,4812],{},[590,4793,4794,4796,4798,4804,4806],{},[597,4795,870],{"mathvariant":770},[601,4797,873],{},[593,4799,4800,4802],{"accent":595},[597,4801,599],{},[601,4803,603],{},[601,4805,882],{},[593,4807,4808,4810],{"accent":595},[702,4809,908],{},[601,4811,603],{},[605,4813,2070],{"encoding":607},[574,4815,4817,4876],{"className":4816,"ariaHidden":595},[612],[574,4818,4820,4823,4829,4832,4867,4870,4873],{"className":4819},[616],[574,4821],{"className":4822,"style":621},[620],[574,4824,4826],{"className":4825},[1051],[574,4827,870],{"className":4828},[625,1055],[574,4830],{"className":4831,"style":1059},[800],[574,4833,4835],{"className":4834},[625,626],[574,4836,4838],{"className":4837},[630],[574,4839,4841],{"className":4840},[634],[574,4842,4844,4852],{"className":4843,"style":621},[638],[574,4845,4846,4849],{"style":641},[574,4847],{"className":4848,"style":646},[645],[574,4850,599],{"className":4851,"style":651},[625,650],[574,4853,4854,4857],{"style":654},[574,4855],{"className":4856,"style":646},[645],[574,4858,4860],{"className":4859,"style":662},[661],[574,4861,4863],{"className":4862,"style":667},[666],[669,4864,4865],{"xmlns":671,"width":672,"height":673,"style":674,"viewBox":675,"preserveAspectRatio":676},[678,4866],{"d":680},[574,4868],{"className":4869,"style":1098},[800],[574,4871,882],{"className":4872},[1102],[574,4874],{"className":4875,"style":1098},[800],[574,4877,4879,4882],{"className":4878},[616],[574,4880],{"className":4881,"style":2139},[620],[574,4883,4885],{"className":4884},[625,626],[574,4886,4888],{"className":4887},[630],[574,4889,4891],{"className":4890},[634],[574,4892,4894,4902],{"className":4893,"style":2139},[638],[574,4895,4896,4899],{"style":641},[574,4897],{"className":4898,"style":646},[645],[574,4900,908],{"className":4901},[625],[574,4903,4904,4907],{"style":2162},[574,4905],{"className":4906,"style":646},[645],[574,4908,4910],{"className":4909,"style":2169},[661],[574,4911,4913],{"className":4912,"style":667},[666],[669,4914,4915],{"xmlns":671,"width":672,"height":673,"style":674,"viewBox":675,"preserveAspectRatio":676},[678,4916],{"d":680}," auf ein Potential schließen, obwohl das Gebiet Löcher hat. Das Feld ",[574,4919,4921,4969],{"className":4920},[577],[574,4922,4924],{"className":4923},[581],[583,4925,4926],{"xmlns":585},[587,4927,4928,4966],{},[590,4929,4930,4950,4952,4954,4956,4958,4960,4962,4964],{},[960,4931,4932,4934],{},[702,4933,1011],{},[590,4935,4936,4942,4944],{},[695,4937,4938,4940],{},[597,4939,922],{},[702,4941,1022],{},[601,4943,3916],{},[695,4945,4946,4948],{},[597,4947,937],{},[702,4949,1022],{},[601,4951,892],{"stretchy":909},[601,4953,2562],{},[597,4955,937],{},[601,4957,2415],{"separator":595},[597,4959,922],{},[601,4961,2415],{"separator":595},[702,4963,908],{},[601,4965,1035],{"stretchy":909},[605,4967,4968],{"encoding":607},"\\frac{1}{x^2 + y^2}(-y, x, 0)",[574,4970,4972],{"className":4971,"ariaHidden":595},[612],[574,4973,4975,4979,5108,5111,5114,5117,5120,5123,5126,5129,5132,5135],{"className":4974},[616],[574,4976],{"className":4977,"style":4978},[620],"height:1.3262em;vertical-align:-0.4811em;",[574,4980,4982,4985,5105],{"className":4981},[625],[574,4983],{"className":4984},[1126,1296],[574,4986,4988],{"className":4987},[960],[574,4989,4991,5097],{"className":4990},[630,1135],[574,4992,4994,5094],{"className":4993},[634],[574,4995,4998,5072,5080],{"className":4996,"style":4997},[638],"height:0.8451em;",[574,4999,5000,5003],{"style":1312},[574,5001],{"className":5002,"style":646},[645],[574,5004,5006],{"className":5005},[748,749,750,751],[574,5007,5009,5040,5043],{"className":5008},[625,751],[574,5010,5012,5015],{"className":5011},[625,751],[574,5013,922],{"className":5014},[625,650,751],[574,5016,5018],{"className":5017},[728],[574,5019,5021],{"className":5020},[630],[574,5022,5024],{"className":5023},[634],[574,5025,5028],{"className":5026,"style":5027},[638],"height:0.7463em;",[574,5029,5031,5034],{"style":5030},"top:-2.786em;margin-right:0.0714em;",[574,5032],{"className":5033,"style":2678},[645],[574,5035,5037],{"className":5036},[748,2682,2683,751],[574,5038,1022],{"className":5039},[625,751],[574,5041,3916],{"className":5042},[805,751],[574,5044,5046,5049],{"className":5045},[625,751],[574,5047,937],{"className":5048,"style":1523},[625,650,751],[574,5050,5052],{"className":5051},[728],[574,5053,5055],{"className":5054},[630],[574,5056,5058],{"className":5057},[634],[574,5059,5061],{"className":5060,"style":5027},[638],[574,5062,5063,5066],{"style":5030},[574,5064],{"className":5065,"style":2678},[645],[574,5067,5069],{"className":5068},[748,2682,2683,751],[574,5070,1022],{"className":5071},[625,751],[574,5073,5074,5077],{"style":1331},[574,5075],{"className":5076,"style":646},[645],[574,5078],{"className":5079,"style":1339},[1338],[574,5081,5082,5085],{"style":1342},[574,5083],{"className":5084,"style":646},[645],[574,5086,5088],{"className":5087},[748,749,750,751],[574,5089,5091],{"className":5090},[625,751],[574,5092,1011],{"className":5093},[625,751],[574,5095,1165],{"className":5096},[1164],[574,5098,5100],{"className":5099},[634],[574,5101,5103],{"className":5102,"style":1610},[638],[574,5104],{},[574,5106],{"className":5107},[1370,1296],[574,5109,892],{"className":5110},[1126],[574,5112,2562],{"className":5113},[625],[574,5115,937],{"className":5116,"style":1523},[625,650],[574,5118,2415],{"className":5119},[2482],[574,5121],{"className":5122,"style":1059},[800],[574,5124,922],{"className":5125},[625,650],[574,5127,2415],{"className":5128},[2482],[574,5130],{"className":5131,"style":1059},[800],[574,5133,908],{"className":5134},[625],[574,5136,1035],{"className":5137},[1370]," ist außerhalb der ",[574,5140,5142,5155],{"className":5141},[577],[574,5143,5145],{"className":5144},[581],[583,5146,5147],{"xmlns":585},[587,5148,5149,5153],{},[590,5150,5151],{},[597,5152,952],{},[605,5154,952],{"encoding":607},[574,5156,5158],{"className":5157,"ariaHidden":595},[612],[574,5159,5161,5164],{"className":5160},[616],[574,5162],{"className":5163,"style":4196},[620],[574,5165,952],{"className":5166,"style":1762},[625,650],"-Achse wirbelfrei, hat dort aber kein Potential.",{"title":5169,"searchDepth":5170,"depth":5170,"links":5171},"",2,[5172,5173,5174],{"id":563,"depth":5170,"text":564},{"id":2843,"depth":5170,"text":2844},{"id":4467,"depth":5170,"text":4468},[5176,5178,5180,5182,5186,5191,5196,5198,5200],{"lhs":5177,"rhs":908},"round(0 - (y*(z + 1e-5) - y*(z - 1e-5)) \u002F (2e-5) - (-y), 6)",{"lhs":5179,"rhs":908},"round(0 - (z*(x + 1e-5) - z*(x - 1e-5)) \u002F (2e-5) - (-z), 6)",{"lhs":5181,"rhs":908},"round(0 - (x*(y + 1e-5) - x*(y - 1e-5)) \u002F (2e-5) - (-x), 6)",{"lhs":5183,"rhs":5184,"where":5185},"-y","-2",{"y":5170},{"lhs":5187,"rhs":5188,"where":5189},"-z","-3",{"z":5190},3,{"lhs":5192,"rhs":5193,"where":5194},"-x","-1",{"x":5195},1,{"lhs":5197,"rhs":908},"0 + 0 + 0",{"lhs":5199,"rhs":1022},"1 - (-1)",{"lhs":5201,"rhs":908},"round((3*x^2*(y + 1e-5)*z^2 - 3*x^2*(y - 1e-5)*z^2) \u002F (2e-5) - (x^2*(z + 1e-5)^3 - x^2*(z - 1e-5)^3) \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","\\operatorname{rot} \\vec{F} = \\nabla \\times \\vec{F} = \\begin{pmatrix} \\frac{\\partial F_3}{\\partial y} - \\frac{\\partial F_2}{\\partial z} \\\\[4pt] \\frac{\\partial F_1}{\\partial z} - \\frac{\\partial F_3}{\\partial x} \\\\[4pt] \\frac{\\partial F_2}{\\partial x} - \\frac{\\partial F_1}{\\partial y} \\end{pmatrix}","\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\">rot\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>\u003Cmrow>\u003Cmo fence=\"true\">(\u003C\u002Fmo>\u003Cmtable rowspacing=\"0.16em\" columnalign=\"center\" columnspacing=\"1em\">\u003Cmtr>\u003Cmtd>\u003Cmstyle scriptlevel=\"0\" displaystyle=\"false\">\u003Cmrow>\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>y\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>z\u003C\u002Fmi>\u003C\u002Fmrow>\u003C\u002Fmfrac>\u003C\u002Fmrow>\u003C\u002Fmstyle>\u003C\u002Fmtd>\u003C\u002Fmtr>\u003Cmtr>\u003Cmtd>\u003Cmstyle scriptlevel=\"0\" displaystyle=\"false\">\u003Cmrow>\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>z\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>x\u003C\u002Fmi>\u003C\u002Fmrow>\u003C\u002Fmfrac>\u003C\u002Fmrow>\u003C\u002Fmstyle>\u003C\u002Fmtd>\u003C\u002Fmtr>\u003Cmtr>\u003Cmtd>\u003Cmstyle scriptlevel=\"0\" displaystyle=\"false\">\u003Cmrow>\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>x\u003C\u002Fmi>\u003C\u002Fmrow>\u003C\u002Fmfrac>\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>y\u003C\u002Fmi>\u003C\u002Fmrow>\u003C\u002Fmfrac>\u003C\u002Fmrow>\u003C\u002Fmstyle>\u003C\u002Fmtd>\u003C\u002Fmtr>\u003C\u002Fmtable>\u003Cmo fence=\"true\">)\u003C\u002Fmo>\u003C\u002Fmrow>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\operatorname{rot} \\vec{F} = \\nabla \\times \\vec{F} = \\begin{pmatrix} \\frac{\\partial F_3}{\\partial y} - \\frac{\\partial F_2}{\\partial z} \\\\[4pt] \\frac{\\partial F_1}{\\partial z} - \\frac{\\partial F_3}{\\partial x} \\\\[4pt] \\frac{\\partial F_2}{\\partial x} - \\frac{\\partial F_1}{\\partial y} \\end{pmatrix}\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>\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:0.7667em;vertical-align:-0.0833em;\">\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:4.8em;vertical-align:-2.15em;\">\u003C\u002Fspan>\u003Cspan class=\"minner\">\u003Cspan class=\"mopen\">\u003Cspan class=\"delimsizing mult\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:2.65em;\">\u003Cspan style=\"top:-4.65em;\">\u003Cspan class=\"pstrut\" style=\"height:6.8em;\">\u003C\u002Fspan>\u003Cspan style=\"width:0.875em;height:4.8em;\">\u003Csvg xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" width=\"0.875em\" height=\"4.8em\" viewBox=\"0 0 875 4800\">\u003Cpath d=\"M863,9c0,-2,-2,-5,-6,-9c0,0,-17,0,-17,0c-12.7,0,-19.3,0.3,-20,1\nc-5.3,5.3,-10.3,11,-15,17c-242.7,294.7,-395.3,682,-458,1162c-21.3,163.3,-33.3,349,\n-36,557 l0,1284c0.2,6,0,26,0,60c2,159.3,10,310.7,24,454c53.3,528,210,\n949.7,470,1265c4.7,6,9.7,11.7,15,17c0.7,0.7,7,1,19,1c0,0,18,0,18,0c4,-4,6,-7,6,-9\nc0,-2.7,-3.3,-8.7,-10,-18c-135.3,-192.7,-235.5,-414.3,-300.5,-665c-65,-250.7,-102.5,\n-544.7,-112.5,-882c-2,-104,-3,-167,-3,-189\nl0,-1292c0,-162.7,5.7,-314,17,-454c20.7,-272,63.7,-513,129,-723c65.3,\n-210,155.3,-396.3,270,-559c6.7,-9.3,10,-15.3,10,-18z\"\u002F>\u003C\u002Fsvg>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:2.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mtable\">\u003Cspan class=\"col-align-c\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:2.5949em;\">\u003Cspan style=\"top:-4.6987em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\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:0.8962em;\">\u003Cspan style=\"top:-2.655em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\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:0.0359em;\">y\u003C\u002Fspan>\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:-3.4101em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\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 mtight\">\u003Cspan class=\"mord mathnormal mtight\" 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:0.3173em;\">\u003Cspan style=\"top:-2.357em;margin-left:-0.1389em;margin-right:0.0714em;\">\u003Cspan class=\"pstrut\" style=\"height:2.5em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size3 size1 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:0.143em;\">\u003Cspan>\u003C\u002Fspan>\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:0.4811em;\">\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>\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:0.8962em;\">\u003Cspan style=\"top:-2.655em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\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:0.044em;\">z\u003C\u002Fspan>\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:-3.4101em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\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 mtight\">\u003Cspan class=\"mord mathnormal mtight\" 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:0.3173em;\">\u003Cspan style=\"top:-2.357em;margin-left:-0.1389em;margin-right:0.0714em;\">\u003Cspan class=\"pstrut\" style=\"height:2.5em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size3 size1 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:0.143em;\">\u003Cspan>\u003C\u002Fspan>\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:0.345em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose nulldelimiter\">\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.0424em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\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:0.8962em;\">\u003Cspan style=\"top:-2.655em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\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:0.044em;\">z\u003C\u002Fspan>\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:-3.4101em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\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 mtight\">\u003Cspan class=\"mord mathnormal mtight\" style=\"margin-right:0.1389em;\">F\u003C\u002Fspan>\u003Cspan 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