This book is designed for senior undergraduate and graduate students pursuing courses in mathematics, physics, engineering and biology. The text begins with a study of ordinary differential equations. The concepts of first- and second-order equations are covered initially. It moves further to linear systems, series solutions, regular SturmLiouville theory, boundary value problems and qualitative theory. Thereafter, partial differential equations are explored. Topics such as first-order partial differential equations, classification of partial differential equations and Laplace and Poisson equations are also discussed in detail. The book concludes with heat equation, one-dimensional wave equation and wave equation in higher dimensions. It highlights the importance of analysis, linear algebra and geometry in the study of differential equations. It provides sufficient theoretical material at the beginning of each chapter, which will enable students to better understand the concepts and begin solving problems straightaway.
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Meant for senior undergraduates and graduates of mathematics, physics, engineering and biology, the text examines differential equations.
Acknowledgements; Preface; List of illustrations; PART I. ORDINARY
DIFFERENTIAL EQUATIONS:
1. First and Second Order ODE;
2. Linear Systems;
3.
Series Solutions: Frobenius Theory;
4. Regular Sturm-Liouville Theory and
Boundary Value Problems;
5. Qualitative Theory; PART II. PARTIAL DIFFERENTIAL
EQUATIONS:
6. First Order Partial Differential Equations;
7. Classification
of Partial Differential Equations;
8. Laplace and Poisson Equations;
9. Heat
Equation;
10. One Dimensional Wave Equation;
11. Wave Equation in Higher
Dimensions; References; Index.
A. K. Nandakumaran is Chairman & Professor, Department of Mathematics, Indian Institute of Science, Bangalore. He received Sir C. V. Raman Young Scientist State Award in Mathematics in 2003. P. S. Datti is Former Faculty, Tata Institute of Fundamental Research Centre for Applicable Mathematics, Bangalore.
