Partial Differential Equations - Nandakumaran, A. K.

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

Biographie:
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).

Sommaire:
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.