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Mathematics for Physics: A Guided Tour for Graduate Students

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Overview

An engagingly-written account of mathematical tools and ideas, this book provides a graduate-level introduction to the mathematics used in research in physics. The first half of the book focuses on the traditional mathematical methods of physics – differential and integral equations, Fourier series and the calculus of variations. The second half contains an introduction to more advanced subjects, including differential geometry, topology and complex variables. The authors' exposition avoids excess rigor whilst explaining subtle but important points often glossed over in more elementary texts. The topics are illustrated at every stage by carefully chosen examples, exercises and problems drawn from realistic physics settings. These make it useful both as a textbook in advanced courses and for self-study.

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Editorial Reviews

From the Publisher
"The many features that make the book valuable to students and teachers also represent a substantial step toward making modern mathematics a part of the working arsenal of practicing physics. I strongly recommend it to those who feel the need to upgrade their mathematics repertoire."
David Khmelnitskii, Physics Today
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Product Details

  • ISBN-13: 9780521854030
  • Publisher: Cambridge University Press
  • Publication date: 8/31/2009
  • Edition description: New Edition
  • Pages: 820
  • Product dimensions: 7.00 (w) x 9.80 (h) x 1.80 (d)

Meet the Author

Michael Stone is a Professor in the Department of Physics at the University of Illinois at Urbana-Champaign. He has worked on quantum field theory, superconductivity, the quantum Hall effect and quantum computing.

Paul Goldbart is a Professor in the Department of Physics at the University of Illinois at Urbana-Champaign, where he directs the Institute for Condensed Matter Theory. His research ranges widely over the field of condensed matter physics, including soft matter, disordered systems, nanoscience and superconductivity.

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Table of Contents

Preface; 1. Calculus of variations; 2. Function spaces; 3. Linear ordinary differential equations; 4. Linear differential operators; 5. Green functions; 6. Partial differential equations; 7. The mathematics of real waves; 8. Special functions; 9. Integral equations; 10. Vectors and tensors; 11. Differential calculus on manifolds; 12. Integration on manifolds; 13. An introduction to differential topology; 14. Group and group representations; 15. Lie groups; 16. The geometry of fibre bundles; 17. Complex analysis I; 18. Applications of complex variables; 19. Special functions and complex variables; Appendixes; Reference; Index.

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