**Pure and Applied Undergraduate Texts**

Volume: 14;
2011;
409 pp;
Hardcover

MSC: Primary 34;

Print ISBN: 978-0-8218-5271-2

Product Code: AMSTEXT/14

List Price: $77.00

AMS Member Price: $61.60

MAA Member Price: $69.30

**Electronic ISBN: 978-1-4704-1127-5
Product Code: AMSTEXT/14.E**

List Price: $77.00

AMS Member Price: $61.60

MAA Member Price: $69.30

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#### Supplemental Materials

# Introduction to Differential Equations

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*Michael E. Taylor*

The mathematical formulations of problems in physics, economics,
biology, and other sciences are usually embodied in differential
equations. The analysis of the resulting equations then provides new
insight into the original problems. This book describes the tools for
performing that analysis.

The first chapter treats single differential equations, emphasizing
linear and nonlinear first order equations, linear second order
equations, and a class of nonlinear second order equations arising from
Newton's laws. The first order linear theory starts with a
self-contained presentation of the exponential and trigonometric
functions, which plays a central role in the subsequent development of
this chapter. Chapter 2 provides a mini-course on linear algebra,
giving detailed treatments of linear transformations, determinants and
invertibility, eigenvalues and eigenvectors, and generalized
eigenvectors. This treatment is more detailed than that in most
differential equations texts, and provides a solid foundation for the
next two chapters. Chapter 3 studies linear systems of differential
equations. It starts with the matrix exponential, melding material from
Chapters 1 and 2, and uses this exponential as a key tool in the linear
theory. Chapter 4 deals with nonlinear systems of differential
equations. This uses all the material developed in the first three
chapters and moves it to a deeper level. The chapter includes
theoretical studies, such as the fundamental existence and uniqueness
theorem, but also has numerous examples, arising from Newtonian
physics, mathematical biology, electrical circuits, and geometrical
problems. These studies bring in variational methods, a fertile source
of nonlinear systems of differential equations. The reader who works
through this book will be well prepared for advanced studies in
dynamical systems, mathematical physics, and partial differential
equations.

#### Readership

Undergraduate students interested in ordinary differential equations.