Partial Differential Equations

Classical Theory with a Modern Touch

Series:

Author:

A. K. Nandakumaran, Indian Institute of Science, Bangalore
P. S. Datti, Tata Institute of Fundamental Research, Centre for Applicable Mathematics, Bangalore

Published:

October 2020

Format:

Hardback

ISBN:

9781108839808

£59.99

GBP

Hardback

$79.99 USD

eBook

Description

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.

Highlights the importance of studying the equations outside the realm of classical solutions
Separate chapters on advanced topics such as the Hamilton-Jacobi equation and conservation laws
Explains the interplay between geometry and analysis in the existence and uniqueness of solutions in the treatment of first order equations

Product details

Published: March 2021
Format: Adobe eBook Reader
ISBN: 9781108963497
Length: 0 pages
Availability: This ISBN is for an eBook version which is distributed on our behalf by a third party.

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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.

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About the authors

Authors

A. K. Nandakumaran , Indian Institute of Science, Bangalore
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 , Tata Institute of Fundamental Research, Centre for Applicable Mathematics, Bangalore
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).

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