Partial Differential Equations and Applications

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.

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