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, 2015.
• Edition: Second Edition.
• Series: UNITEXT, 88
• Subjects: Mathematics.; Differential equations.; Applied mathematics.; Engineering mathematics.; Numerical analysis.; Ordinary Differential Equations.; Numerical Analysis.; Applications of Mathematics.

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 e...

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.