Contents

**1 Introduction to Linear Algebra**

1.1 Systems of Linear Equations - Row Reduction

1.2 Matrices and Vectors

1.3 Inverses and Determinants

1.4 Vector Spaces: R2 and R3

1.5 Linear Independence, Span, Basis, Dimension

1.6 Change of Basis

1.7 Matrix Transformations

Chapter 1 Project: Real-Time Collision Detection

**2 Vectors and the Geometry of Space**

2.1 Vectors in the Plane

2.2 Vectors in Space

2.3 The Dot Product

2.4 The Cross Product

2.5 Lines in 2D and 3D

2.6 Planes

2.7 Collision Detection and Response: Lines and Planes

Chapter 2 Project: The Separating Axis Theorem

**3 Vector-Valued Functions **

3.1 Vector-Valued Functions and Curves

3.2 Dierentiation of Vector-Valued Functions

3.3 Projectiles

3.4 Euler's Method

3.5 Bouncing Around in 2D

Chapter 3 Project: Projectile Game in 2D

**4 Multi-Variable Functions and Surfaces **

4.1 Surfaces: z = f(x; y)

4.2 Partial Derivatives, Gradients, and Normal Vectors

4.3 Bouncing Around in 3D

Chapter 4 Project: Projectile Game in 3D

**CONTENTS ii**

A Trigonometry Review

A.1 Triangle Trigonometry

A.2 Unit-Circle Trigonometry

A.3 Trigonometry as a Collection of Periodic Functions

A.4 Translations and Transformations of Trig Functions

A.5 Circles and Ellipses

A.6 The Tangent Function

A.7 Trigonometry Review - Problem Set

B Review of Dierentiation Rules

C A Quick Guide to MATLAB®

C.1 Running MATLAB®

C.2 Creating your own functions

C.3 Graphing with MATLAB®

C.4 Input and Output with the Command Window

C.5 Input and Output with a Figure

C.6 Assignment

Detailed Solutions to Worksheets

Detailed Solutions to Selected Problems

Index