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