Multivariable & Vector Calculus
A 24-module path through multivariable & vector calculus, in study order from foundations to the frontier.
Modules
- Euclidean Space and Norms
- Open and Closed Sets in R^n
- Compactness in R^n
- Limits and Continuity in Several Variables
- Partial Derivatives
- Differentiability and the Total Derivative
- Jacobian Matrix and Linear Approximation
- The Gradient and Directional Derivatives
- The Chain Rule in Several Variables
- Clairaut's Theorem on Mixed Partials
- Taylor's Theorem in Several Variables
- Critical Points and Extrema
- The Hessian and Second Derivative Test
- Lagrange Multipliers
- The Inverse Function Theorem
- The Implicit Function Theorem
- Multiple Integrals over Rectangles
- Fubini's Theorem
- Integrals over General Regions
- Change of Variables and the Jacobian
- Line Integrals
- Conservative Fields and Potentials
- Green's Theorem
- Stokes' and Divergence Theorems