Introduction to differential equations
 Responsibility
 Michael E. Taylor.
 Language
 English.
 Imprint
 Providence, R.I. : American Mathematical Society, c2011.
 Physical description
 xii, 409 p. : ill. ; 27 cm.
 Series
 Pure and applied undergraduate texts ; 14.
 Sally series (Providence, R.I.)
Access
Available online
Math & Statistics Library
Stacks
Call number  Status 

QA372 .T39 2011  Unknown 
More options
Creators/Contributors
 Author/Creator
 Taylor, Michael Eugene, 1946
Contents/Summary
 Bibliography
 Includes bibliographical references (p. 403405) and index.
 Contents

 * Single differential equations * Linear algebra * Linear systems of differential equations * Nonlinear systems of differential equations * Bibliography * Index.
 (source: Nielsen Book Data)
 Publisher's Summary
 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 selfcontained presentation of the exponential and trigonometric functions, which plays a central role in the subsequent development of this chapter. Chapter 2 provides a minicourse 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.
(source: Nielsen Book Data)
Subjects
Bibliographic information
 Publication date
 2011
 Series
 Pure and applied undergraduate texts ; 14
 The Sally series
 ISBN
 9780821852712 (acidfree paper)
 082185271X (acidfree paper)