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Equations and Analytical Tools in Mathematical Physics

A Concise Introduction

  • Book
  • © 2021

Overview

Authors:
  1. Yichao Zhu

    1. Department of Engineering Mechanics, Dalian University of Technology, Dalian, China

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  • Introduces second-order partial differential equations and special functions
  • Provides easily understandable knowledge maps
  • Includes prerequisite calculus and linear algebra for new learners

  • 7516 Accesses

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Table of contents (7 chapters)

  1. Front Matter

    Pages i-xii
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  2. Second-Order Linear Partial Differential Equations

    1. Front Matter

      Pages 1-1
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    2. The Wave Equation

      • Yichao Zhu
      Pages 3-55

    3. The Heat Equation

      • Yichao Zhu
      Pages 57-98

    4. Poisson’s Equation

      • Yichao Zhu
      Pages 99-139

    5. Summary over Second-Order Linear Partial Differential Equation

      • Yichao Zhu
      Pages 141-162

  3. Special Functions

    1. Front Matter

      Pages 163-163
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    2. Bessel Functions

      • Yichao Zhu
      Pages 165-197

    3. Legendre Polynomial

      • Yichao Zhu
      Pages 199-229

    4. Introduction of Hypergeometric Function

      • Yichao Zhu
      Pages 231-245

  4. Back Matter

    Pages 247-252
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Keywords

About this book

​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.

Authors and Affiliations

  • Department of Engineering Mechanics, Dalian University of Technology, Dalian, China

    Yichao Zhu

About the author

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.


Bibliographic Information

  • Book Title: Equations and Analytical Tools in Mathematical Physics

  • Book Subtitle: A Concise Introduction

  • Authors: Yichao Zhu

  • DOI: https://doi.org/10.1007/978-981-16-5441-1

  • Publisher: Springer Singapore

  • eBook Packages: Physics and Astronomy, Physics and Astronomy (R0)

  • Copyright Information: Science Press 2021

  • Hardcover ISBN: 978-981-16-5440-4Published: 05 October 2021

  • Softcover ISBN: 978-981-16-5443-5Published: 06 October 2022

  • eBook ISBN: 978-981-16-5441-1Published: 04 October 2021

  • Edition Number: 1

  • Number of Pages: XII, 252

  • Number of Illustrations: 8 b/w illustrations, 29 illustrations in colour

  • Topics: Mathematical Methods in Physics, Applications of Mathematics, Mathematical Physics, Analysis

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