This book offers readers a primer on the theory and applications of Ordinary Differential Equations. The style used is simple, yet thoroughand rigorous. Each chapterends witha broad set of exercises thatrange fromthe routineto the more challenging and thought-provoking. Solutions to selected exercises can be found at the end of the book. The book contains many interestingexamples on topicssuch as electriccircuits, the pendulum equation, the logistic equation, the Lotka-Volterra system, the Laplace Transform, etc., which introduce students to a number of interestingaspects of the theory and applications. The work is mainly intended for students of Mathematics, Physics, Engineering, Computer Science and otherareas of the natural and social sciences that use ordinary differential equations, and who have a firm grasp of Calculus and a minimalunderstanding of the basic concepts used in Linear Algebra. It also studies a few more advanced topics, such as Stability Theory and Boundary Value Problems, which may be suitable for more advanced undergraduate or first-year graduate students. The second edition has been revised to correct minor errata, and features a number of carefully selected new exercises, together with more detailed explanations of some of the topics.
A complete Solutions Manual, containing solutions to all the exercises published in the book, is available. Instructors who wish to adopt the book may request the manual by writing directly to one of the authors.
About the Author
Prof. Shair Ahmad is a professor of Mathematics at the University of Texas, San Antonio.
Prof. Antonio Ambrosetti is full professor of Mathematical Analysis at SISSA, Trieste, Italy.
Table of Contents
1 First order linear differential equations.- 2 Theory of first order differential equations.- 3 First order nonlinear differential equations.- 4 Existence and uniqueness for systems and higher order equations.- 5 Second order equations.- 6 Higher order linear equations.- 7 Systems of first order equations.- 8 Qualitative analysis of 2x2 systems and nonlinear second order equations.- 9 Sturm Liouville eigenvalue theory.- 10 Solutions by infinite series and Bessel functions.- 11 Laplace transform.- 12 Stability theory.- 13 Boundary value problems.- 14 Appendix A. Numerical methods.- 15 Answers to selected exercises.