Partial Differential Equations

Classical Theory with a Modern Touch

A. K. Nandakumaran, P. S. Datti

• Publisher: Cambridge University Press
• Year: 2020
• Print ISBN: 9781108839808
• eBook ISBN: 9781108963497
• Topic: Mathematics
• Subtopic: Mathematics General
• Index: Mathematics

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.

Table of contents

• Cover
• Partial Differential Equations
• Series
• Title
• Copyright
• Dedication
• Contents
• Illustrations
• Preface
• Acknowledgments
• Notations
• CHAPTER 1 Introduction
• CHAPTER 2 Preliminaries
• CHAPTER 3 First-Order Partial Differential Equations: Method of Characteristics
• CHAPTER 4 Hamilton–Jacobi Equation
• CHAPTER 5 Conservation Laws
• CHAPTER 6 Classification of Second-Order Equations
• CHAPTER 7 Laplace and Poisson Equations
• CHAPTER 8 Heat Equation
• CHAPTER 9 One-Dimensional Wave Equation
• CHAPTER 10 Wave Equation in Higher Dimensions
• CHAPTER 11 Cauchy–Kovalevsky Theorem and Its Generalization
• CHAPTER 12 A Peep into Weak Derivatives, Sobolev Spaces and Weak Formulation
• References
• Index