Physical Mathematics

Kevin Cahill

• Publisher: Cambridge University Press
• Year: 2013
• Print ISBN:
  9781107005211
• eBook ISBN:
  9781107302303
• Topic: Physical Sciences
• Subtopic: Mathematical & Computational Physics

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.

Table of contents

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