Table of Contents

#### Introduction

##### Vectors

- Vectors (Lecture)
- Dot Product (Lecture)
- Law of Cosines (Lecture)

##### Differentials and Derivatives

- Differentials I (Lecture)
- Differentials II (Lecture)
- Coordinates (Lecture)
- Vector Differentials (Lecture)
- Polar Coordinates (Lecture)

##### Surfaces

- Surfaces (SWBQ: 10 min)
- Representations of surfaces (Lecture)
- Surfaces (Lecture)
- Contour Maps (Lecture)

##### Gradient and Directional Derivatives

- Gradient (Lecture)
- Properties of the Gradient (Lecture)
- Directional Derivatives (Lecture)
- Vector Fields (Lecture)

##### Polar and Curvilinear Coordinates

- The Area of a Circle (SWBQ: 10 min)
- Integrals in Polar Coordinates (Lecture)
- Integrals in Curvilinear Coordinates (Lecture)

#### Line Integrals

##### Line Integrals

- Line Integrals I (Lecture)
- Line Integrals II (Lecture)
- Use What You Know (Lecture)
- Path Independence (Lecture)

##### Conservative Vector Fields

- Conservative Vector Fields (Lecture)
- Finding Potentials (Lecture)

#### Surface Integrals

##### Surfaces

- Cross Product (Lecture)
- Surfaces (Lecture)
- Surface Elements (Lecture)

##### Flux

- Flux (Lecture)
- Surface Integrals I (Lecture)
- Surface Integrals II (Lecture)

#### Vector Derivative Operators

##### Divergence and Curl

- Divergence (Lecture)
- Divergence (SGA) [divergence only]
- Divergence Thm (Lecture)
- Curl (Lecture)
- Curl and Divergence (Lecture)
- Other Coords (Lecture)

##### Theorems

- Stokes' Theorem (Lecture)
- Product Rules (Lecture)
- Stokes' Theorem (Lecture)

##### Applications

- Second Derivatives (Lecture)
- Change of Variables (Lecture)
- Change of Variables (SGA) [optional]