This introductory text combines models from physics and biology with rigorous reasoning in describing the theory of ordinary differential equations along with applications and computer simulations with Maple. Offering a concise course in the theory of ordinary differential equations, it also enables the reader to enter the field of computer simulations. Thus, it is a valuable read for students in mathematics as well as in physics and engineering. It is also addressed to all those interested in mathematical modeling with ordinary differential equations and systems.

Contents
Part I: Theory

Chapter 1 First-Order Differential Equations

Chapter 2 Linear Differential Systems

Chapter 3 Second-Order Differential Equations

Chapter 4 Nonlinear Differential Equations

Chapter 5 Stability of Solutions

Chapter 6 Differential Systems with Control Parameters

Part II: Exercises

Seminar 1 Classes of First-Order Differential Equations

Seminar 2 Mathematical Modeling with Differential Equations

Seminar 3 Linear Differential Systems

Seminar 4 Second-Order Differential Equations

Seminar 5 Gronwall’s Inequality

Seminar 6 Method of Successive Approximations

Seminar 7 Stability of Solutions

Part III: Maple Code

Lab 1 Introduction to Maple

Lab 2 Differential Equations with Maple

Lab 3 Linear Differential Systems

Lab 4 Second-Order Differential Equations

Lab 5 Nonlinear Differential Systems

Lab 6 Numerical Computation of Solutions

Lab 7 Writing Custom Maple Programs

Lab 8 Differential Systems with Control Parameters