Partial Differential Equations and Applications

A Bridge for Students and Researchers in Applied Sciences
Erscheinungsjahr 2023
ISBN: 978-0-443-18705-6
Verlag: Elsevier Science

Buch, Englisch, 330 Seiten, Format (B × H): 236 mm x 190 mm, Gewicht: 680 g

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.

Autoren/Hrsg.

Yin, Hong-Ming

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen

Inhaltsverzeichnis

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

Über Autor(innen)

Yin, Hong-Ming
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.