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Multivariable calculus

Thinking about multivariable functions

Mastery unavailable
Introduction to multivariable calculus: Thinking about multivariable functionsVectors and matrices: Thinking about multivariable functionsVisualizing scalar-valued functions: Thinking about multivariable functions
Visualizing vector-valued functions: Thinking about multivariable functionsTransformations: Thinking about multivariable functionsVisualizing multivariable functions (articles): Thinking about multivariable functions

Derivatives of multivariable functions

Partial derivatives: Derivatives of multivariable functionsGradient and directional derivatives: Derivatives of multivariable functionsPartial derivative and gradient (articles): Derivatives of multivariable functionsDifferentiating parametric curves: Derivatives of multivariable functionsMultivariable chain rule: Derivatives of multivariable functionsCurvature: Derivatives of multivariable functions
Partial derivatives of vector-valued functions: Derivatives of multivariable functionsDifferentiating vector-valued functions (articles): Derivatives of multivariable functionsDivergence: Derivatives of multivariable functionsCurl: Derivatives of multivariable functionsDivergence and curl (articles): Derivatives of multivariable functionsLaplacian: Derivatives of multivariable functionsJacobian: Derivatives of multivariable functions

Applications of multivariable derivatives

Tangent planes and local linearization: Applications of multivariable derivativesQuadratic approximations: Applications of multivariable derivativesOptimizing multivariable functions: Applications of multivariable derivatives
Optimizing multivariable functions (articles): Applications of multivariable derivativesLagrange multipliers and constrained optimization: Applications of multivariable derivativesConstrained optimization (articles): Applications of multivariable derivatives

Integrating multivariable functions

Line integrals for scalar functions: Integrating multivariable functionsLine integrals for scalar functions (articles): Integrating multivariable functionsLine integrals in vector fields: Integrating multivariable functionsLine integrals in vector fields (articles): Integrating multivariable functionsDouble integrals: Integrating multivariable functionsDouble integrals (articles): Integrating multivariable functionsTriple integrals: Integrating multivariable functions
Change of variables: Integrating multivariable functionsPolar, spherical, and cylindrical coordinates: Integrating multivariable functionsSurface integral preliminaries: Integrating multivariable functionsSurface integrals: Integrating multivariable functionsSurface integrals (articles): Integrating multivariable functionsFlux in 3D: Integrating multivariable functionsFlux in 3D (articles): Integrating multivariable functions

Green's, Stokes', and the divergence theorems

Formal definitions of div and curl (optional reading): Green's, Stokes', and the divergence theoremsGreen's theorem: Green's, Stokes', and the divergence theoremsGreen's theorem (articles): Green's, Stokes', and the divergence theorems2D divergence theorem: Green's, Stokes', and the divergence theoremsStokes' theorem: Green's, Stokes', and the divergence theorems
Stokes' theorem (articles): Green's, Stokes', and the divergence theorems3D divergence theorem: Green's, Stokes', and the divergence theoremsDivergence theorem (articles): Green's, Stokes', and the divergence theoremsProof of Stokes' theorem: Green's, Stokes', and the divergence theoremsTypes of regions in three dimensions: Green's, Stokes', and the divergence theoremsDivergence theorem proof: Green's, Stokes', and the divergence theorems

Course challenge

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