Calculus/Multivariable Calculus

Introduction to Multivariable Calculus
Vectors

Curves and Surfaces in Space

Vector Functions

Introduction to multivariable calculus

Differentiation
Limits and Continuity

Partial Derivatives

The chain rule and Clairaut's theorem

Chain Rule

Directional derivatives and the gradient vector


 * Multivariate optimisation: The Lagrangian
 * Calculus on matrices

Derivatives of Multivariate Functions

Inverse Function Theorem, Implicit Function Theorem (optional)

Integration
Multiple integration
 * Old: Double Integrals

Change of variables

Vector calculus
Vector Calculus

Vector Calculus Identities

Inverting Vector Calculus Operators

Points, Paths, Surfaces, and Volumes

Helmholtz Decomposition Theorem

Discrete Analog to Vector Calculus

Exercises