Textbook on Ordinary Differential Equations

This book offers readers a primer on the theory and applications of Ordinary Differential Equations. The style used is simple, yet thorough and rigorous. Each chapter ends with a broad set of exercises that range from the routine to the more challenging and thought-provoking. Solutions to selected exercises can be found at the end of the book. The book contains many interesting examples on topics such as electric circuits, the pendulum equation, the logistic equation, the Lotka-Volterra system, the Laplace Transform, etc., which introduce students to a number of interesting aspects of the theory and applications. The work is mainly intended for students of Mathematics, Physics, Engineering, Computer Science and other areas of the natural and social sciences that use ordinary differential equations, and who have a firm grasp of Calculus and a minimal understanding 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.

“This is the second edition of an undergraduate introduction to ordinary differential equations suitable for mathematicians and engineers. … The style is clean and concise with many examples and exercises. Basic results are proven, more involved results are only stated. The new edition features some new exercises and better explanations at various points. So if you are looking for an application oriented introduction which is still concise and rigorous, this book might be just right for you.” (G. Teschl, Monatshefte für Mathematik, 2016)

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.