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# Multivariable calculus

## A brief introduction to multivariable calculus

In multivariable calculus, we progress from working with numbers on a line to points in space. It gives us the tools to break free from the constraints of one-dimension, using functions to describe space, and space to describe 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 functionsPartial derivatives of vector-valued functions: Derivatives of multivariable functions

Differentiating 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 functionsReview practice: Derivatives of multivariable functions

Line integrals for scalar functions (videos): Integrating multivariable functionsLine integrals for scalar functions (articles): Integrating multivariable functionsLine integrals in vector fields (videos): Integrating multivariable functionsLine integrals in vector fields (articles): Integrating multivariable functionsDouble integrals (videos): Integrating multivariable functionsDouble integrals (articles): Integrating multivariable functions

Triple integrals (videos): Integrating multivariable functionsTriple integrals (articles): Integrating multivariable functionsSurface integral preliminaries (videos): Integrating multivariable functionsSurface integrals (videos): Integrating multivariable functionsSurface integrals (articles): Integrating multivariable functionsFlux in 3D (videos): Integrating multivariable functionsFlux in 3D (articles): Integrating multivariable functions

Formal definitions of div and curl (optional reading): Green's, Stokes', and the divergence theoremsGreen's theorem (videos): 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 (videos): Green's, Stokes', and the divergence theorems

Stokes' theorem (articles): Green's, Stokes', and the divergence theorems3D divergence theorem (videos): 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