Study Guide and Exercise Tutorial for Mathematical and Physical Methods

Author: Liu Jijun
Publisher:
Publish Date: 2006-05-01
Features: This book is a learning aid material for undergraduate students taking the course of Mathematical Methods in Physics and Engineering, covering topics such as Fourier series and ordinary differential equations. It attempts to explain the fundamental theories and methods of mathematical physics by integrating the knowledge background of engineering students, offering a fresh perspective to assist students in their learning. This book is suitable for undergraduate and graduate students in engineering, applied mathematics, and related fields, as well as researchers and engineering professionals in relevant disciplines.
Chapter 1 first provides a systematic summary and review of the essential knowledge from advanced mathematics that will be used in this course (e.g., Fourier series, ordinary differential equations), facilitating student use. In the following chapters, we take the method of separation of variables as the main thread to systematically introduce the fundamental content and methods of this course. Chapter 2 discusses the method of separation of variables on finite intervals, Chapter 3 covers integral transformations (still unified within the framework of separation of variables). Chapter 4 introduces the method of traveling waves, which is unique to wave equations on unbounded domains, and establishes its connection with solutions on bounded domains. Chapter 5 presents the Green function method, which has significant engineering applications, discussing both the engineering context and mathematical foundations. Chapter 6 introduces the theory and methods of special functions through the separation of variables in specific physical problems. Chapter 7 provides selected typical examples with solutions and evaluations.
This book is a learning aid material for undergraduate students taking the course of Mathematical Methods in Physics and Engineering. Chapter 1 first provides a systematic summary and review of the essential knowledge from advanced mathematics that will be used in this course (e.g., Fourier series, ordinary differential equations), facilitating student use. In the following chapters, we take the method of separation of variables as the main thread to systematically introduce the fundamental content and methods of this course. Chapter 2 discusses the method of separation of variables on finite intervals, Chapter 3 covers integral transformations (still unified within the framework of separation of variables). Chapter 4 introduces the method of traveling waves, which is unique to wave equations on unbounded domains, and establishes its connection with solutions on bounded domains. Chapter 5 presents the Green function method, which has significant engineering applications, discussing both the engineering context and mathematical foundations. Chapter 6 introduces the theory and methods of special functions through the separation of variables in specific physical problems. Chapter 7 provides selected typical examples with solutions and evaluations.
This book attempts to explain the fundamental theories and methods of mathematical physics by integrating the knowledge background of engineering students, offering a fresh perspective to assist students in their learning. It is suitable for undergraduate and graduate students in engineering, applied mathematics, and related fields, as well as researchers and engineering professionals in relevant disciplines.