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### Introduction to Vectors

In this module, you will learn about cross products, dot products, vectors in two and three dimensions, and three-dimensional rectangular coordinate system.

Lesson 1.1: Vectors in Two Dimensions
Lesson 1.2: Three-dimensional Rectangular Coordinate System
Lesson 1.3: Vectors in Three Dimensions
Lesson 1.4: Dot Products
Lesson 1.5: Cross Products

### Vector-Valued Functions

In this module, you will study the calculus of vector-valued functions, lines and curves in space, and parametric curves.

Lesson 2.1: Parametric Curves
Lesson 2.2: Lines and Curves in Space
Lesson 2.3: Calculus of Vector-Valued Functions

### Some Applications of Vector-Valued Functions

In this module, you will study motion in space, arc length, and analysis of space curves.

Lesson 3.1: Motion in Space
Lesson 3.2: Arc Length
Lesson 3.3: Curvature and Normal Vectors

### Planes and Surfaces

In this module, you will learn about the applications of differentiation.

Lesson 4.1: Planes
Lesson 4.2: Surfaces
Lesson 4.3: Graphs and Level Surfaces

### Functions of Several Variables

In this module, you will learn about the Chain Rule, partial derivatives, limits and continuity, and polar coordinates.

Lesson 5.1: Polar Coordinates
Lesson 5.2: Limits and Continuity
Lesson 5.3: Partial Derivatives
Lesson 5.4: The Chain Rule

### Applications of Derivatives

In this module, you will study derivatives and its related applications.

Lesson 6.1: Directional Derivatives and the Gradient
Lesson 6.2: Tangent Planes and Linear Approximation
Lesson 6.3: Maximum/minimum Problems

Lesson 6.4: Lagrange Multiples