Ordinary Differential Equations
Ordinary Differential Equations
P. S. Datti, Tata Institute of Fundamental Research, Centre for Applicable Mathematics, Bangalore
Raju K. George, Indian Institute of Space Science and Technology, Thiruvanantpuram
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 theory
- Includes advanced topics such as qualitative analysis of linear and nonlinear systems
- Covers many important results from variable real analysis and linear algebra
- Includes plenty of real-world applications, solved examples and numerical problems
Reviews & endorsements
'The articles in the book are neatly presented, … written in academic style with long lists of references at the end.' David Hopkins, The Mathematical Gazette
Product details
January 2019Adobe eBook Reader
9781108344241
0 pages
This ISBN is for an eBook version which is distributed on our behalf by a third party.
Table of Contents
- List of tables
- List of figures
- Preface
- 1. Introduction and examples: physical models
- 2. Preliminaries
- 3. First and second order linear equations
- 4. General theory of initial value problems
- 5. Linear systems and qualitative analysis
- 6. Series solutions: Frobenius theory
- 7. Regular Sturm–Liouville theory
- 8. Qualitative theory
- 9. Two point boundary value problems
- 10. First order partial differential equations: method of characteristics
- Appendix A. Poinca`e–Bendixon and Leinard's theorems
- Bibliography
- Index.
