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

Autorentext

Radu Precup, Babe -Bolyai University, Romania.