For courses in Differential Equations and Linear Algebra.

The right balance between concepts, visualisation, applications, and skills

Differential Equations and Linear Algebra provides the conceptual development and geometric visualisation of a modern differential equations and linear algebra course that is essential to science and engineering students. It balances traditional manual methods with the new, computer-based methods that illuminate qualitative phenomena - a comprehensive approach that makes accessible a wider range of more realistic applications.

The book combines core topics in elementary differential equations with concepts and methods of elementary linear algebra. It starts and ends with discussions of mathematical modeling of real-world phenomena, evident in figures, examples, problems, and applications throughout.

Table of Contents

CHAPTER 1 First-Order Differential Equations

CHAPTER 2 Mathematical Models and Numerical Methods

CHAPTER 3 Linear Systems and Matrices

CHAPTER 4 Vector Spaces

CHAPTER 5 Higher-Order Linear Differential Equations

CHAPTER 6 Eigenvalues and Eigenvectors

CHAPTER 7 Linear Systems of Differential Equations

CHAPTER 8 Matrix Exponential Methods

CHAPTER 9 Nonlinear Systems and Phenomena

CHAPTER 10 Laplace Transform Methods

CHAPTER 11 Power Series Methods

References for Further Study

Appendix A: Existence and Uniqueness of Solutions

Appendix B: Theory of Determinants

Answers to Selected Problems