Partial Differential Equations
Classical Theory with a Modern Touch

A valuable guide covering the key principles of partial differential equations and their real world applications.

A. K. Nandakumaran (Author), P. S. Datti (Author)

9781108839808, Cambridge University Press

Hardback, published 29 October 2020

374 pages
24.6 x 19 x 2.2 cm, 0.74 kg

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.

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.

Subject Areas: Applied mathematics [PBW], Calculus & mathematical analysis [PBK]