The book is a primer of the theory of Ordinary Differential Equations. Each chapter is completed by a broad set of exercises; the reader will also find a set of solutions of selected exercises. The book contains many interesting examples as well (like the equations for the electric circuits, the pendium equation, the logistic equation, the Lotka-Volterra system, and many other) which introduce the reader to some interesting aspects of the theory and its applications. The work is mainly addressed to students of Mathematics, Physics, Engineering, Statistics, Computer Sciences, with knowledge of Calculus and Linear Algebra, and contains more advanced topics for further developments, such as Laplace transform; Stability theory and existence of solutions to Boundary Value problems. 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.

Autorentext

Prof. Shair Ahmad is a professor of Mathematics at the University of Texas at San Antonio.

Prof. Antonio Ambrosetti is full professor of Mathematical Analysis at SISSA, Trieste, Italy.

Inhalt

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 2×2 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.- Appendix A. Numerical methods.- Answers to Selected Exercises.