# Mathematical Physics: Applied Mathematics for Scientists and Engineers, 2nd Edition

# Mathematical Physics: Applied Mathematics for Scientists and Engineers, 2nd Edition

ISBN: 978-3-527-61814-9 January 2010 689 Pages

## Description

What sets this volume apart from other mathematics texts is its emphasis on mathematical tools commonly used by scientists and engineers to solve real-world problems. Using a unique approach, it covers intermediate and advanced material in a manner appropriate for undergraduate students. Based on author Bruce Kusse's course at the Department of Applied and Engineering Physics at Cornell University, Mathematical Physics begins with essentials such as vector and tensor algebra, curvilinear coordinate systems, complex variables, Fourier series, Fourier and Laplace transforms, differential and integral equations, and solutions to Laplace's equations. The book moves on to explain complex topics that often fall through the cracks in undergraduate programs, including the Dirac delta-function, multivalued complex functions using branch cuts, branch points and Riemann sheets, contravariant and covariant tensors, and an introduction to group theory. This expanded second edition contains a new appendix on the calculus of variation -- a valuable addition to the already superb collection of topics on offer.

This is an ideal text for upper-level undergraduates in physics, applied physics, physical chemistry, biophysics, and all areas of engineering. It allows physics professors to prepare students for a wide range of employment in science and engineering and makes an excellent reference for scientists and engineers in industry. Worked out examples appear throughout the book and exercises follow every chapter. Solutions to the odd-numbered exercises are available for lecturers at www.wiley-vch.de/textbooks/.

This is an ideal text for upper-level undergraduates in physics, applied physics, physical chemistry, biophysics, and all areas of engineering. It allows physics professors to prepare students for a wide range of employment in science and engineering and makes an excellent reference for scientists and engineers in industry. Worked out examples appear throughout the book and exercises follow every chapter. Solutions to the odd-numbered exercises are available for lecturers at www.wiley-vch.de/textbooks/.

## Table of contents

1. A Review of Vector and Matrix Algebra Using Subscript/Summation Conventions

2. Differential and Integral Operations on Vector and Scalar Fields

3. Curvilinear Coordinate Systems

4. Introduction to Tensors

5. The Dirac Delta-Function

6. Introduction to Complex Variables

7. Fourier Series

8. Fourier Transforms

9. Laplace Transforms

10. Differential Equations

11. Solutions to Laplace's Equation

12. Integral Equations

13. Advanced Topics in Complex Analysis

14. Tensors in Non-Orthogonal Coordinate Systems

15. Introduction to Group Theory

A. The Levi-Civita Identitiy

B. The Curvilinear Curl

C. The Double Integral Identity

D. Green's Function Solutions

E. Pseudovectors and the Mirror Test

F. Christoffel Symbols and Covariant Derivatives

NEW APPENDIX: The Calculus of Variation

2. Differential and Integral Operations on Vector and Scalar Fields

3. Curvilinear Coordinate Systems

4. Introduction to Tensors

5. The Dirac Delta-Function

6. Introduction to Complex Variables

7. Fourier Series

8. Fourier Transforms

9. Laplace Transforms

10. Differential Equations

11. Solutions to Laplace's Equation

12. Integral Equations

13. Advanced Topics in Complex Analysis

14. Tensors in Non-Orthogonal Coordinate Systems

15. Introduction to Group Theory

A. The Levi-Civita Identitiy

B. The Curvilinear Curl

C. The Double Integral Identity

D. Green's Function Solutions

E. Pseudovectors and the Mirror Test

F. Christoffel Symbols and Covariant Derivatives

NEW APPENDIX: The Calculus of Variation

## New To This Edition

* new appendix on Calculus of Variation

* carefully prepared errata sheet

* softcover rather than hardback

* carefully prepared errata sheet

* softcover rather than hardback

## Reviews

"Any lecturer on mathematical methods is also looking for worked examples and numerous exercises. This book passes these tests admirably. [...] In summary, a welcome addition to the good books in this area."

Australian PHYSICS

Australian PHYSICS

## Features

- Covers applications in all areas of engineering and physical sciences.
- Features numerous figures and worked-out examples throughout the text.
- Presents mathematically advanced material in a readable form with few formal proofs.
- Organizes topics pedagogically in the order they will be most easily understood.
- Provides end-of-chapter exercises and offers free solutions manual for lecturers (available from the publisher).
- New to this second edition is an appendix on the calculus of variations - a valuable addition to the excellent choice of topics.