Mathematical Physics with Partial Differential Equations

By

  • James Kirkwood, Professor of Mathematical Sciences, Sweet Briar College, Sweet Briar, VA, USA

Mathematical Physics with Partial Differential Equations is for advanced undergraduate and beginning graduate students taking a course on mathematical physics taught out of math departments. The text presents some of the most important topics and methods of mathematical physics. The premise is to study in detail the three most important partial differential equations in the field - the heat equation, the wave equation, and Laplace’s equation. The most common techniques of solving such equations are developed in this book, including Green’s functions, the Fourier transform, and the Laplace transform, which all have applications in mathematics and physics far beyond solving the above equations. The book’s focus is on both the equations and their methods of solution. Ordinary differential equations and PDEs are solved including Bessel Functions, making the book useful as a graduate level textbook. The book’s rigor supports the vital sophistication for someone wanting to continue further in areas of mathematical physics.
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Audience

Advanced Undergraduate and Graduate Students, Instructors, Academic Researchers in University Mathematics Departments

 

Book information

  • Published: January 2012
  • Imprint: ACADEMIC PRESS
  • ISBN: 978-0-12-386911-1

Reviews

"The text presents some of the most important topics and methods of mathematical physics…The book’s rigor is appropriate for readers wanting to continue their study of further areas of mathematical physics."--Zentralblatt MATH 2012-1235-35002




Table of Contents

Chapter 1 Prelimininaries
Chapter 2 Vector Calculus
Chapter 3 Green’s Functions
Chapter 4 Fourier Series
Chapter 5 Three Important Equations
Chapter 6 Sturm-Liouville Theory
Chapter 7 Solving PDE’s in Cartesian Coordinates by Separation of Variables
Chapter 8 Solving PDE’s in Cylindrical Coordinates by Separation of Variables
Chapter 9 Solving PDE’s in Spherical Coordinates w/ Sep. of Variables
Chapter 10 The Fourier Transform
Chapter 11 The Laplace Transform
Chapter 12 Solving PDE’s Using Green’s Functions
Appendix
Bibliography