Partial Differential Equations: Classical Theory with a Modern Touch

by A. K. Nandakumaran, P. S. Datti

Overview

Suitable for both senior undergraduate and graduate students, this is a self-contained book dealing with the classical theory of the partial differential equations through a modern approach; requiring minimal previous knowledge. It represents the solutions to three important equations of mathematical physics – Laplace and Poisson equations, Heat or diffusion equation, and wave equations in one and more space dimensions. Keen readers will benefit from more advanced topics and many references cited at the end of each chapter. In addition, the book covers advanced topics such as Conservation Laws and Hamilton-Jacobi Equation. Numerous real-life applications are interspersed throughout the book to retain readers' interest.

Product Details

ISBN-13:	9781108839808
Publisher:	Cambridge University Press
Publication date:	10/29/2020
Series:	Cambridge IISc Series
Pages:	374
Product dimensions:	7.48(w) x 9.69(h) x 0.87(d)

About the Author

A. K. Nandakumaran is a Professor in the Department of Mathematics, Indian Institute of Science, Bengaluru. He obtained his Masters degree from Calicut University, Kerala and then worked for his Ph.D. in Tata Institute of Fundamental Research and Indian Institute of Science. His general area of research includes partial differential equations and special areas include homogenization, control and controllability problems, inverse problems and computations. His work also includes tomographic reconstruction problems. He is a Press author of the book Ordinary Differential Equations: Principles and Applications (2017). He is a Fellow of National Academy of Sciences India (NASI) and convener of Kishore Vaigyanik Prothsahan Yojana (KVPY).

P. S. Datti is a Former Professor at TIFR Centre for Applicable Mathematics, Bengaluru. After obtaining M.Sc. in 1976 from Karnatak University, Dharawad, he joined the then TIFR-IISc Joint Programme in Applications of Mathematics as a research student. He then moved to the Courant Institute of Mathematical Sciences for his Ph.D. His main areas of research interest include nonlinear hyperbolic equations, hyperbolic conservation laws, ordinary differential equations, evolution equations and boundary layer phenomenon. He has written TIFR Lecture Notes for the lectures delivered by G.B. Whitham (CalTech) and Cathleen Morawetz (Courant Institute). He is a Press author of the book Ordinary Differential Equations: Principles and Applications (2017).

Table of Contents

List of illustrations; Preface; Acknowledgements; Notations; 1. Introduction; 2. Preliminaries; 3. First-order partial differential equations: method of characteristics; 4. Hamilton–Jacobi equation; 5. Conservation laws; 6. Classification of second-order equations; 7. Laplace and Poisson equations; 8. Heat equation; 9. One-dimensional wave equation; 10. Wave equation in higher dimensions; 11. Cauchy–Kovalevsky theorem and its generalization; 12. A peep into weak derivatives, Sobolev spaces and weak formulation; References; Index.