A. K. Nandakumaran

Partial Differential Equations (eBook, PDF)

Classical Theory with a Modern Touch

• Format: PDF

Produktbeschreibung

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.

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Produktdetails

• Verlag: Cambridge University Press
• Erscheinungstermin: 29. Oktober 2020
• Englisch
• ISBN-13: 9781108963497
• Artikelnr.: 66183836

Autorenporträt

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).

Inhaltsangabe

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.