Partial Differential Equations
Classical Theory with a Modern Touch
$79.99 USD
Part of Cambridge IISc Series
- Authors:
- A. K. Nandakumaran, Indian Institute of Science, Bangalore
- P. S. Datti, Tata Institute of Fundamental Research, Centre for Applicable Mathematics, Bangalore
- Date Published: March 2021
- availability: This ISBN is for an eBook version which is distributed on our behalf by a third party.
- format: Adobe eBook Reader
- isbn: 9781108963497
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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.
Read more- 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
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×Product details
- Date Published: March 2021
- format: Adobe eBook Reader
- isbn: 9781108963497
- availability: This ISBN is for an eBook version which is distributed on our behalf by a third party.
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.
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