Calculus/Multivariable Calculus


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

7.10 Derivatives of Multivariate Functions

7.11 Inverse Function Theorem, Implicit Function Theorem (optional)

Integration

7.12 Multiple integration

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

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