Equations and Analytical Tools in Mathematical Physics

This book highlights a concise and readable introduction to typical treatments of partial differential equations in mathematical physics. Mathematical physics is regarded by many as a profound discipline. In conventional textbooks of mathematical physics, the known and the new pieces of knowledge often intertwine with each other. The book aims to ease readers' struggle by facilitating a smooth transition to new knowledge. To achieve so, the author designs knowledge maps before each chapter and provides comparative summaries in each chapter whenever appropriate. Through these unique ways, readers can clarify the underlying structures among different equations and extend one's vision to the big picture. The book also emphasizes applications of the knowledge by providing practical examples. The book is intended for all those interested in mathematical physics, enabling them to develop a solid command in using partial differential equations to solve physics and engineering problems in a not-so-painful learning experience.

Autorentext
Dr. Yichao Zhu received his Ph.D. in applied mathematics from the University of Oxford in 2012. He is Associate Professor at the Department of Engineering Mechanics, Dalian University of Technology, China. His research interests include modeling and simulations of physical processes involving multiple temporal and spatial scales, especially the applications of mathematical tools in developing quantitative insights over problems in material sciences and engineering-related subjects.

Inhalt
Part I Second-order Linear Partial Differential Equations Chapter 1 Wave Equation

Chapter 2 Heat Equation

Chapter 3 Poisson's Equation

Chapter 4 Discussion on Second-order Linear Partial Differential Equations

Part II Special Functions

Chapter 5 Bessel Function

Chapter 6 Legendre Polynomial

Chapter 7 Special Functions through Hypergeometric Function