Linear Algebra: A First Course with Applications to Differential Equations

0. REVIEW OF PREREQUISITES

Part 1. Pre-Calculus Prerequisites 1

Part 2.Calculus Prerequisites 14

1. Vector Algebra 25

2. Applications of Vector Algebra to Analytic Geometry 51

3. Linear Spaces 91

4. Linear Transformations and Matrices 119

5. Determinants 161

6. Eigenvalues and Eigenvectors 187

7. Eigenvalues of Operators Acting on Euclidean Spaces 217

8. Applications to Linear Differential Equations 247

9. Applications to Systems of Differential Equations 273

10. The Method of Successive Approximations 303

Answers to Exercises 321

Index 343