Physical Mathematics

by Kevin Cahill

Overview

Unique in its clarity, examples and range, Physical Mathematics explains as simply as possible the mathematics that graduate students and professional physicists need in their courses and research. The author illustrates the mathematics with numerous physical examples drawn from contemporary research. In addition to basic subjects such as linear algebra, Fourier analysis, complex variables, differential equations and Bessel functions, this textbook covers topics such as the singular-value decomposition, Lie algebras, the tensors and forms of general relativity, the central limit theorem and Kolmogorov test of statistics, the Monte Carlo methods of experimental and theoretical physics, the renormalization group of condensed-matter physics and the functional derivatives and Feynman path integrals of quantum field theory.

Product Details

ISBN-13:	9781107301214
Publisher:	Cambridge University Press
Publication date:	03/14/2013
Sold by:	Barnes & Noble
Format:	eBook
File size:	55 MB
Note:	This product may take a few minutes to download.

About the Author

Kevin Cahill is Professor of Physics and Astronomy at the University of New Mexico. He has done research at NIST, Saclay, Ecole Polytechnique, Orsay, Harvard University, NIH, LBL and SLAC, and has worked in quantum optics, quantum field theory, lattice gauge theory and biophysics. Physical Mathematics is based on courses taught by the author at the University of New Mexico and at Fudan University in Shanghai.

Table of Contents

Preface; 1. Linear algebra; 2. Fourier series; 3. Fourier and Laplace transforms; 4. Infinite series; 5. Complex-variable theory; 6. Differential equations; 7. Integral equations; 8. Legendre functions; 9. Bessel functions; 10. Group theory; 11. Tensors and local symmetries; 12. Forms; 13. Probability and statistics; 14. Monte Carlo methods; 15. Functional derivatives; 16. Path integrals; 17. The renormalization group; 18. Chaos and fractals; 19. Strings; Index.

Editorial Reviews

'Cahill has given us a concise and mathematically clear text, one that adds many contemporary topics to a classic selection.' Roy J. Glauber, Harvard University, Massachusetts

'Kevin Cahill’s book collects and presents the mathematical methods of physics succinctly, and will be much welcomed by students and researchers alike.' A. Zee, University of California, Santa Barbara

'This book provides a comprehensive coverage of the mathematics necessary for advanced study in physics. The key notions are presented concisely and accurately with a wealth of beautiful examples borrowed from physics, biophysics, and probability theory. The inclusion of advanced topics such as differential forms and group theory makes this book a most useful resource for graduate students and researchers in theoretical physics.' Alain Comtet, Université Pierre et Marie Curie

'I am impressed by the extremely clear and direct style with which this book has been written … The author has distilled his experience and obvious enjoyment of the subject, and presented mathematics in a remarkably human and accessible form.' David Waxman, Fudan University, Shanghai

‘The book places itself as a reference for the undergraduate students, the graduate students and the researchers who need to refresh some topics. As the author indicates, the book covers all the mathematics needed for a physicist. Also, the instructor who gives a course on mathematical physics can find useful material in the book. The topics are explained with little stress on the physical meaning which is meant to come spontaneously progressing in the book. The completeness of topics is preferred to proofs and deep explanations … this book is indicated for the student who wants a solid and complete reference for mathematical tool in physics. The instructor can use the book as a reference for basic or advanced courses of mathematical physics, as well as for more theoretically based courses.’ Stefano Scali, Contemporary Physics

From the Publisher