Mathematical Physics with Partial Differential Equations book cover

Mathematical Physics with Partial Differential Equations

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.

Audience

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

Hardbound, 432 Pages

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


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

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