**What you will learn from this course?**

Thinking about multivariable functions

– Introduction to multivariable calculus

– Visualizing scalar-valued functions

– Visualizing vector-valued functions

– Transformations

– Visualizing multivariable functions (articles)

– Review practice

Derivatives of multivariable functions

– Partial derivatives

– Gradient and directional derivatives

– Partial derivative and gradient (articles)

– Differentiating parametric curves

– Multivariable chain rule

– Curvature

– Partial derivatives of vector-valued functions

– Differentiating vector-valued functions (articles)

– Divergence

– Curl

– Divergence and curl (articles)

– Laplacian

– Jacobia

– Review practice

Applications of multivariable derivatives

– Tangent planes and local linearization

– Quadratic approximations

– Optimizing multivariable functions

– Optimizing multivariable functions (articles)

– Lagrange multipliers and constrained optimization

– Constrained optimization (articles)

Integrating multivariable functions

– Line integrals for scalar functions (videos)

– Line integrals for scalar functions (articles)

– Line integrals in vector fields (videos)

– Line integrals in vector fields (articles)

– Double integrals (videos)

– Double integrals (articles)

– Triple integrals (videos)

– Triple integrals (articles)

– Surface integral preliminaries (videos)

– Surface integrals (videos)

– Surface integrals (articles)

– Flux in 3D (videos)

– Flux in 3D (articles)

Green’s, Stokes’, and the divergence theorems

– Formal definitions of div and curl (optional reading)

– Green’s theorem (videos)

– Green’s theorem (articles)

– 2D divergence theorem

– Stokes’ theorem (videos)

– Stokes’ theorem (articles)

– 3D divergence theorem (videos)

– Divergence theorem (articles)

– Proof of Stokes’ theorem

– Types of regions in three dimensions

– Divergence theorem proof

**Certification :**No

**Time to complete :**1 month

**Cost :**Free

**Course Level :**Intermediate

**Language :**English