Partial Differential Equations and Applications: A Bridge for Students and Researchers in Applied Sciences offers a unique approach to this key subject by connecting mathematical principles to the latest research advances in select topics. Beginning with very elementary PDEs, such as classical heat equations, wave equations and Laplace equations, the book focuses on concrete examples. It gives students basic skills and techniques to find explicit solutions for partial differential equations.
As it progresses, the book covers more advanced topics such as the maximum principle and applications, Green's representation, Schauder's theory, finite-time blowup, and shock waves. By exploring these topics, students gain the necessary tools to deal with research topics in their own fields, whether proceeding in math or engineering areas.
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Table of Contents
Preface CHAPTER 1 Basics of partial differential equations CHAPTER 2 Function spaces and the Fredholm Alternative CHAPTER 3 Eigenvalue problems and eigenfunction expansions CHAPTER 4 The heat equation CHAPTER 5 The wave equation CHAPTER 6 The Laplace equation CHAPTER 7 The Fourier transform and applications CHAPTER 8 The fundamental solution and Green's representation CHAPTER 9 Systems of first-order partial differential equations APPENDIX A Some essential results in ordinary differential equations APPENDIX B Sobolev spaces
