1 Introduction to Linear Algebra
1.1 Systems of Linear Equations - Row Reduction
1.2 Matrices and Vectors - Basic Properties
1.3 Inverses and Determinants
1.4 Vector Spaces: R2 and R3
1.5 Linear Independence, Span, Bases, Dimension
1.6 Change of Basis
1.7 Matrix Transformations
1.8 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 and Curves in Space
2.6 Planes in 3D
2.7 Collision Detection and Response: Lines and Planes
2.8 Polar, Cylindrical, and Spherical Coordinates

3 Vector-Valued Functions
3.1 Vector-Valued Functions and Curves in Space
3.2 Differentiation of Vector-Valued Functions: Position, Velocity, and Acceleration
3.3 Euler's Method

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 Space

5 Appendix A: Trigonometry Review
5.1 Triangle Trig
5.2 Unit-Circle Trig
5.3 Trig as a collection of periodic functions
5.4 Translations and Transformations of Trig Functions
5.5 Circles and Ellipses
5.6 The Tangent Function
5.7 Trigonometry Review - Problem Set

6 Appendix B: Quick Guide to MATLAB®
6.1 Introduction
6.2 Running MATLAB®
6.3 Creating your own functions
6.4 Graphing with MATLAB®
6.5 Input and Output to and from the Command Window or Graph
6.6 Assignment

Detailed Solutions to Summary Worksheets
Detailed Solutions to Selected Problems