Calculus 3: Vector fields, divergence, and curl
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All Calculus 33D SpaceVector FunctionsDot and cross productEquations of lines and planesParametric curves, conic sectionsTangent vectors and arc lengthCylinders and quadric surfacesIntegrals of vector functionsArc length and curvatureMultivariable functionsSurface parameterizationPartial derivativesLinearization, chain rule, gradientTangent planes and linear approximationsOptimizationLagrange multipliersDouble integralsTriple integralsChanging coordinates for integrationSurface areaVector fields, divergence, and curlLine integralsGreen's TheoremFluxStokes' TheoremDivergence TheoremComplex numbers
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Consider the vector field . To get an idea of how this vector field looks, plug in a few coordinates and plot the resultant vectors.
Consider the vector field F = ⟨(x^2)y, -x/y, xyz⟩. To find the divergence, take del dot this expression.
Consider the vector field F = ⟨(x²)y, -x/y, xyz⟩. Find the curl by taking the determinant of the matrix with i, j, k; d/dx, d/dy, d/dz; (x²)y, -x/y, xyz.