Table of Contents

#### Introduction

##### Warmup

- Introduction
- Pretest and/or Skills Test (Pretest: 15 min)

##### Representations of Multivariable Functions

- Pizza and Cola (SWBQ: 10 min)
- Surfaces (SWBQ: 10 min)
- Representations of surfaces (Lecture)
- Surfaces (Lecture)
- Contour Maps (Lecture)
- The Heater (SGA: 30–45 min)

#### Multiple Integrals

##### Review of Single Variable Integration

- The Cylinder (SGA: 30 min)
- Integration (SWBQ)
- Activity: chop (single integrals)
- Wrap up: chop (double integrals)
- Chop, Multiply, and Add (Lecture)
- Single Integrals (Lecture)
- Chocolate (Lecture)

##### Double Integrals

- Double Integrals (Lecture)
- Constant limits (SWBQ: ConcepTest)
- Order of Integration (Lecture)
- Match region to limits (SWBQ: ConcepTest)
- Non-constant limits (Lecture)
- Example: Computation
- Activity: Chop (Mass)
- Triple Integrals (Lecture)
- Mass (Lecture)
- Questions for integrals (Lecture)

##### Polar and Curvilinear Coordinates

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

#### Partial Derivatives I

##### Review of Differentiation

- Derivatives? (SWBQ)
- Representations of Derivatives (Lecture)
- Differentiate (SWBQ: 10 min)
- Skills test (15 min)
- Derivative Rules (SWBQ)

##### Differentials and Derivatives

- Derivative Rules from Differentials (Lecture: ?? min)
- Derivative and Integration rules (Lecture: ?? min)
- Differentials (Lecture)

##### Partial Derivatives

- Partial Derivatives? (SWBQ)
- Representations of Partial Derivatives (Lecture)
- Thick Derivatives (Lecture)
- Computing Partial Derivatives (Lecture)
- Second-Order Partial Derivatives (Lecture)

##### Chain Rule

- Chain Rule (SWBQ)
- Chain Rule (Lecture)
- Tree Diagrams (Lecture)
- Summary and Examples (Lecture)

#### Vectors I

##### Introduction

##### Dot Product

- The Dot Product (SWBQ)
- The Dot Product (Lecture)
- Geometry and Algebra (Lecture)

#### Partial Derivatives II

##### Gradient and Directional Derivatives

- The Master Formula (Lecture)
- The Gradient (Lecture)
- Properties of the Gradient (Lecture)
- Directional Derivatives (Lecture)

##### Optimization

- Maxima and Minima (SQBQ)
- The Second-Derivative Test (SWBQ)
- Max/min (Lecture)
- Second-Derivative Test (Lecture)
- Lagrange multipliers (Lecture)

#### Vectors II

##### Applications

- The Cross Product (Lecture)
- Curves (Lecture)
- Parametric Curves (Lecture)
- Arclength (Lecture)
- Change of Variables (Lecture)

#### Extra

- Differentiation (SWBQ: 10 min)