Calculus/Multivariable Calculus

This is an example of using spherical coordinates in 3 dimensions to calculate the volume of a given shape

Introduction to Multivariable Calculus

7.1 Vectors

7.2 Curves and Surfaces in Space

7.3 Vector Functions

7.4 Introduction to multivariable calculus

Differentiation

7.5 Limits and Continuity

7.6 Partial Derivatives

7.7 The chain rule and Clairaut's theorem

7.8 Chain Rule

7.9 Directional derivatives and the gradient vector

• Multivariate optimisation: The Lagrangian
• Calculus on matrices

7.10 Derivatives of Multivariate Functions

7.11 Inverse Function Theorem, Implicit Function Theorem (optional)

Integration

7.12 Multiple integration

• Old: Double Integrals

7.13 Change of variables

Vector calculus

7.14 Vector Calculus

7.15 Vector Calculus Identities

7.16 Inverting Vector Calculus Operators

7.17 Points, Paths, Surfaces, and Volumes

7.18 Helmholtz Decomposition Theorem

7.19 Discrete Analog to Vector Calculus

7.20 Exercises