Partial differential equation

Author: Zhou Shulin
Publisher:
Publish Date: 2005-08-01
Features: This textbook is written for undergraduate courses on "Partial Differential Equations" for majors in basic mathematics and computational mathematics. Its prerequisite is Mathematical Analysis or Advanced Mathematics. Readers only need to have some basic knowledge of multivariable calculus to understand the entire content of this book. The book is divided into four chapters, focusing on the fundamental theory and methods of the simplest potential equations, heat equations, and wave equations in partial differential equations. In each chapter, the solution methods for the initial value problems and mixed problems of these equations are introduced, along with some a priori estimates related to these problems, thereby addressing key issues such as the existence, uniqueness, and stability of their solutions. The basic idea of this book is to explain "Partial Differential Equations" using mathematical analysis. In terms of content selection, it adheres to the principle of being concise and selective, fully reflecting the core content of "Partial Differential Equations." In content presentation, it progresses from simple to complex and is systematic. In terms of expression, it is rigorous, concise, and clear, making it suitable for both teaching and self-study. To help readers understand and expand their knowledge, each chapter is equipped with many thought-provoking exercises, and hints are provided for the more challenging ones. This book can serve as a textbook or teaching reference for undergraduate students in majors such as basic mathematics, computational mathematics, applied mathematics, financial mathematics, statistics, physics, and related disciplines. It can also be used as a reference for researchers who need to apply fundamental knowledge of partial differential equations in their practical work.