(chap:ODE)=
# Ordinary Differential Equations
**Learning Objectives**:
- To review basic methods for solving some differential equations.
- To apply the theory to simple mathematical models.
- To introduce an existence and uniqueness theorem.
On completion of this chapter the reader should be able to
- solve certain first- and second-order differential equations;
- apply the theory to chemical kinetics and electric circuits;
- interpret the solutions in physical terms;
- understand the existence and uniqueness theorem and its implications.
The basic theory of ordinary differential equations (ODEs) and analytical methods for solving some types of ODEs are reviewed. This chapter is not intended to be a comprehensive study on differential equations, but more an introduction to the theory that will be used in later chapters. Most of the material will be covered in first- and second-year undergraduate mathematics courses. The differential equations are applied to all kinds of models, but this
chapter concentrates on chemical kinetics and electric circuits in particular.
The chapter ends with the existence and uniqueness theorem and some analysis.
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