An excellent toolkit for senior undergraduate and graduate students, this book presents the qualitative properties of solutions, beside the representation formulae, of the three important equations of mathematical physics - Laplace and Poisson equations, heat or diffusion equation, and wave equations in one and more space dimensions.
An excellent toolkit for senior undergraduate and graduate students, this book presents the qualitative properties of solutions, beside the representation formulae, of the three important equations of mathematical physics - Laplace and Poisson equations, heat or diffusion equation, and wave equations in one and more space dimensions.Hinweis: Dieser Artikel kann nur an eine deutsche Lieferadresse ausgeliefert werden.
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.