Physical Mathematics

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Cambridge University Press, Mar 14, 2013 - Science
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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.
 

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Contents

Fourier series
75
Fourier and Laplace transforms
108
Infinite series
136
Complexvariable theory
160
9
175
Differential equations
223
Integral equations
296
Legendre functions
305
20
403
Forms
479
Probability and statistics
502
Monte Carlo methods
563
Functional derivatives
578
Path integrals
586
Chaos and fractals
635
Strings
643

Bessel functions
325
Tensors and local symmetries
400
References
651
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About the author (2013)

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.

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