AMS Chelsea Publishing 1977; 205 pp; hardcover Volume: 295 ISBN10: 0821846221 ISBN13: 9780821846223 List Price: US$32 Member Price: US$28.80 Order Code: CHEL/295.H
 In summary, the author has provided an elegant introduction to important topics in the theory of ordinary differential equations and integral equations. Mathematical Reviews This book is intended for a onesemester course in differential and integral equations for advanced undergraduates or beginning graduate students, with a view toward preparing the reader for graduatelevel courses on more advanced topics. There is some emphasis on existence, uniqueness, and the qualitative behavior of solutions. Students from applied mathematics, physics, and engineering will find much of value in this book. The first five chapters cover ordinary differential equations. Chapter 5 contains a good treatment of the stability of ODEs. The next four chapters cover integral equations, including applications to secondorder differential equations. Chapter 7 is a concise introduction to the important Fredholm theory of linear integral equations. The final chapter is a wellselected collection of fascinating miscellaneous facts about differential and integral equations. The prerequisites are a good course in advanced calculus, some preparation in linear algebra, and a reasonable acquaintance with elementary complex analysis. There are exercises throughout the text, with the more advanced of them providing good challenges to the student. Readership Undergraduate and graduate students interested in differential and integral equations. Table of Contents Introduction: Some Elementary Methods  The linear equation of the first order
 The equation with separable variables
 Exact differential equations
 The uniqueness problem: An example
 Some integral inequalities
 Problems
Existence Theory for Differential Equations  The firstorder equation
 Firstorder differential systems
 Equations and systems of higher order
 Peano existence theorem
 A uniqueness theorem
 Problems
Some Global Problems for Ordinary Differential Equations  Statement of the problems
 Global uniqueness
 Global existence and the behavior of saturated solutions
 Dependence of solutions on initial values
 Differential inequalities and the comparison method
 A criterion of global existence
 Problems
Some Special Classes of Differential Systems and Equations  Linear systems: Generalities
 Linear homogeneous systems
 Nonhomogeneous systems
 Linear equations of higher order
 Autonomous systems
 Linear systems and equations with constant coefficients
 Problems
Stability Theory of Ordinary Differential Systems  Definitions and examples
 Stability of linear systems
 Stability in the first approximation
 Stability theorems by comparison method
 Further stability results
 Stability of automatic control systems
 Problems
Volterra Integral Equations  Existence and uniqueness of solution
 An existence theorem
 The linear equation
 The firstkind linear equation
 Some problems on the halfaxis
 Problems
Fredholm Theory of Linear Integral Equations  The resolvent kernel
 The entire functions of Fredholm and their applications
 A glimpse of Hilbert space theory
 Eigenvalues, eigenfunctions and adjoint equations
 Problems
Theory of SelfAdjoint Integral Equations and Some Applications  Some properties of an integral operator
 The existence of eigenvalues
 The HilbertSchmidt expansion theorem
 Complete kernels and systems
 The SturmLiouville problem
 Reduction to an integral equation: The first case
 Reduction to an integral equation: The second case
 Problems
Miscellanea (Nice Things)  Maximum and minimum solutions of scalar differential equations
 A theorem of Massera
 An oscillation theorem
 A formula of Picone and its consequences
 Liénard's equation
 Differential systems without uniqueness
 Abel's integral equation
 References
 Index
