
Preface  Preview Material  Table of Contents  Supplementary Material 
Pure and Applied Undergraduate Texts 2011; 409 pp; hardcover Volume: 14 ISBN10: 082185271X ISBN13: 9780821852712 List Price: US$73 Member Price: US$58.40 Order Code: AMSTEXT/14 See also: Tools for PDE: Pseudodifferential Operators, Paradifferential Operators, and Layer Potentials  Michael E Taylor Noncommutative Harmonic Analysis  Michael E Taylor Measure Theory and Integration  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 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. Request an examination or desk copy. Readership Undergraduate students interested in ordinary differential equations. 


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