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, Greens representation, Schauders 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.
- Class tested over multiple years with advanced undergraduate and graduate courses
- Features many concrete examples and chapter exercises
- Appropriate for advanced undergraduate and graduate courses geared to math and engineering students
- Requires minimal background beyond advanced calculus and differential equations
Recenzijas
"The book under review is concerned with partial differential equations, and its main target audience are mathematically interested applied scientists as well as mathematicians at the beginning of their study of partial differential equation. The book consists of nine chapters and two appendices. All chapters also contain exercises illustrating the course material; a notes section referring to some further reading or putting the material in a broader context for each individual chapter is provided just before the exercises section.... The author made a successful effort to focus on the more applied aspects of the theory whilst not completely ignoring mathematical rigour and rationale. For this strategy to work, as a rule, modelling and the discussion of examples are set as a primary instance before the individual models are discussed mathematically." --Marcus Waurick, zbMATHOpen
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 Greens representation
CHAPTER 9 Systems of first-order partial differential equations
APPENDIX A Some essential results in ordinary differential equations
APPENDIX B Sobolev spaces
Dr. Hong-Ming Yin is currently a Professor in the Department of Mathematics, Washington State University. He has held positions at the University of Toronto and the University of Notre Dame, as well as visiting positions at the University of California at Berkeley and the Chinese University of Hong Kong. His research is focused on mathematical models and analysis by using partial differential equations. He has published more than 100 peer-reviewed research papers in various mathematics journals, including top-rated journals such as Transactions of the American Mathematical Society and Comm. In PDEs, he has taught related courses to advanced undergraduate students and graduate students for over 30 years.
