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# Multivariable calculus

## Updates coming!

Practice content is coming! We will update this course in late July with about 50 new exercises and some new articles as well. The course will also be mastery enabled, so you will be able to track your progress. And you will keep your progress in any of the videos or articles where you’ve already worked.

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