Description
CAMBRIDGE INDIA Ordinary Differential Equations 2017 Edition by NANDAKUMARAN
Written in a clear, logical and concise manner, this comprehensive resource allows students to quickly understand the key principles, techniques and applications of ordinary differential equations. Important topics including first and second order linear equations, initial value problems and qualitative theory are presented in separate chapters. The concepts of two point boundary value problems, physical models and first order partial differential equations are discussed in detail. The text uses tools of calculus and real analysis to get solutions in explicit form. While discussing first order linear systems, linear algebra techniques are used. The real-life applications are interspersed throughout the book to invoke reader's interest. The methods and tricks to solve numerous mathematical problems with sufficient derivations and explanation are provided. The proofs of theorems are explained for the benefit of the readers.Contains separate chapters on first and second order linear equations and qualitative theoryIncludes advanced topics such as qualitative analysis of linear and nonlinear systemsCovers many important results from variable real analysis and linear algebraIncludes plenty of real-world applications, solved examples and numerical problems.Table of ContentsList of tablesList of figuresPreface1. Introduction and examples: physical models2. Preliminaries3. First and second order linear equations4. General theory of initial value problems5. Linear systems and qualitative analysis6. Series solutions: Frobenius theory7. Regular Sturm–Liouville theory8. Qualitative theory9. Two point boundary value problems10. First order partial differential equations: method of characteristicsAppendix A. Poinca`e–Bendixon and Leinard's theoremsBibliographyIndex.