A Textbook on Ordinary Differential Equations

• Main Authors: Ahmad, Shair (Author), Ambrosetti, Antonio (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2014.
• Series: UNITEXT, 73
• Subjects: Mathematics.; Mathematical analysis.; Analysis (Mathematics).; Differential equations.; Applied mathematics.; Engineering mathematics.; Numerical analysis.; Ordinary Differential Equations.; Analysis.; Numerical Analysis.; Applications of Mathematics.

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 pen...

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 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.