Ordinary Differential Equations: Principles and Applications(Cambridge IISc Series)

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.

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.

About the Author :
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 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 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.

Review :
'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