# Mathematical Physics with Partial Differential Equations

## 2nd Edition

**Authors:**James Kirkwood

**Paperback ISBN:**9780128147597

**eBook ISBN:**9780128147603

**Imprint:**Academic Press

**Published Date:**28th February 2018

**Page Count:**492

## Description

*Mathematical Physics with Partial Differential Equations, Second Edition,* is designed for upper division undergraduate and beginning graduate students taking mathematical physics taught out by math departments. The new edition is based on the success of the first, with a continuing focus on clear presentation, detailed examples, mathematical rigor and a careful selection of topics. It presents the familiar classical topics and methods of mathematical physics with more extensive coverage of the three most important partial differential equations in the field of mathematical physics—the heat equation, the wave equation and Laplace’s equation.

The book presents the most common techniques of solving these equations, and their derivations are developed in detail for a deeper understanding of mathematical applications. Unlike many physics-leaning mathematical physics books on the market, this work is heavily rooted in math, making the book more appealing for students wanting to progress in mathematical physics, with particularly deep coverage of Green’s functions, the Fourier transform, and the Laplace transform. A salient characteristic is the focus on fewer topics but at a far more rigorous level of detail than comparable undergraduate-facing textbooks. The depth of some of these topics, such as the Dirac-delta distribution, is not matched elsewhere.

New features in this edition include: novel and illustrative examples from physics including the 1-dimensional quantum mechanical oscillator, the hydrogen atom and the rigid rotor model; chapter-length discussion of relevant functions, including the Hermite polynomials, Legendre polynomials, Laguerre polynomials and Bessel functions; and all-new focus on complex examples only solvable by multiple methods.

## Key Features

- Introduces and evaluates numerous physical and engineering concepts in a rigorous mathematical framework
- Provides extremely detailed mathematical derivations and solutions with extensive proofs and weighting for application potential
- Explores an array of detailed examples from physics that give direct application to rigorous mathematics
- Offers instructors useful resources for teaching, including an illustrated instructor's manual, PowerPoint presentations in each chapter and a solutions manual

## Readership

UG/Grad math students taking mathematical physics, engineering math, etc

## Table of Contents

1. Preliminaries

2. Vector Calculus

3. Green’s Function

4. Fourier Series

5. Three Important Equations

6. Sturm-Liouville Theory

7. Solving PDE’s in Cartesian Coordinates by Separation of Variables

8. Generating Functions

9. Solving PDE’s in Cylindrical Coordinates by Separation of Variables

10. Solving PDE’s in spherical coordinates w/Sep. of Variables

11. The Fourier Transform

12. The Laplace Transform

13. Solving PDE’s using Green’s Functions

## Details

- No. of pages:
- 492

- Language:
- English

- Copyright:
- © Academic Press 2018

- Published:
- 28th February 2018

- Imprint:
- Academic Press

- Paperback ISBN:
- 9780128147597

- eBook ISBN:
- 9780128147603

## About the Author

### James Kirkwood

Bringing over 25 years of teaching expertise, James Kirkwood is the author of ten mathematics books published in a range of areas from calculus to real analysis and mathematical biology. He has been awarded 4 awards for continuing research in the area of mathematical physics, including the 2016 ‘Outstanding Faculty Award of the State Council for Higher Education in Virginia’ – the highest award the state bestows.

### Affiliations and Expertise

Professor of Mathematical Sciences, Sweet Briar College, Sweet Briar, VA, USA

## Reviews

"This is an interesting book with, perhaps, a somewhat inaccurate title. I do not really see this book as any kind of text on physics, but rather as an introduction to partial differential equations or, perhaps, mathematical modeling. ...The author’s writing style is reasonably clear and quite detailed, and he provides numerous examples throughout the book. ...People teaching a course that is more narrowly focused on the “big three” PDEs of mathematical physics might, however, want to take a look at this text. In addition, the level of detail and rigor found in the book might also make it quite suitable as a reference." **--The Mathematical Gazette**