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Look Inside Ordinary Differential Equations

Ordinary Differential Equations
Principles and Applications

Part of Cambridge IISc Series

Authors:
A. K. Nandakumaran, Indian Institute of Science, Bangalore
P. S. Datti, Tata Institute of Fundamental Research, Centre for Applicable Mathematics, Bangalore
Raju K. George, Indian Institute of Space Science and Technology, Thiruvanantpuram

Date Published: May 2017
availability: In stock
format: Hardback
isbn: 9781108416412

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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
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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

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Product details
- Date Published: May 2017
- format: Hardback
- isbn: 9781108416412
- length: 344 pages
- dimensions: 235 x 156 x 20 mm
- weight: 0.53kg
- availability: In stock
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.
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Authors
A. K. Nandakumaran, Indian Institute of Science, Bangalore
A. K. Nandakumaran received his Ph.D. from Tata Institute of Fundamental Research, Mumbai, India (TIFR). He served in TIFR for a brief period and later joined the Department of Mathematics, Indian Institute of Science as Assistant Professor, where he is currently serving as Professor. His areas of interest are partial differential equations, control and controllability problems, inverse problems and computations. He received the Sir C. V. Raman Young Scientist State Award in Mathematics in 2003.
P. S. Datti, Tata Institute of Fundamental Research, Centre for Applicable Mathematics, Bangalore
P. S. Datti obtained his Ph.D. from Courant Institute of Mathematical Sciences, New York in 1985 under the supervision of Sergiu Klainerman. His main areas of research interest include nonlinear hyperbolic equations, hyperbolic conservations, ordinary differential equations, evolution equations and boundary layer phenomena. He has written Tata Institute of Fundamental Research (TIFR) Lecture Notes for the lectures delivered by G. B. Whitham (CalTech) and Cathleen Morawetz (Courant Institute). After serving in TIFR Centre for Applicable Mathematics for over 35 years, he retired in December 2016.
Raju K. George, Indian Institute of Space Science and Technology, Thiruvanantpuram
Raju K. George joined the University of Baroda as a faculty after completing his Ph.D. from Indian Institute of Technology Bombay. He served there for twelve years and later joined the Indian Institute of Space Science and Technology (IIST), Thiruvananthapuram, as Professor and Head of Mathematics. He was a visiting Professor at the University of Delaware 2002–2004. His research area includes functional analysis, mathematical control theory, soft computing and industrial mathematics.