To begin, we will probably review some material from PHY515 as presented in Professor Nearing's on-line notes.  (Available for free!  And a counterexample to the adage that you get what you paid.)  It would be a good idea for each student to look over those notes to see if the material is familiar.  If not, and if there is a strong consensus that this is the case, we will cover some of the unfamiliar material.

Beyond that, I have not yet decided on a single book to use for the official course text.  I recommend that you browse through the books in the lists that follow.  If you have limited resources, then I further recommend that you buy directly from amazon.com (see the link at the end of the first list) one or both of Byron and Fuller and/or Dennery and Krzywicki.  These are fine books for cost-effective self-study.  If you carefully read them, you should learn a great deal.  There are many other inexpensive Dover re-publications of classic texts (some listed below) which can also be used in this way. 

It is a shame that Mathews and Walker is not re-published by Dover.


Books I have previously used to learn and to teach math methods:

 
Mathematical Methods of Physics (2nd Edition) [FACSIMILE]
by Jon Mathews, Robert L. Walker


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A Course of Modern Analysis (Cambridge Mathematical Library)
by E. T. Whittaker, G. N. Watson


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A Treatise on the Theory of Bessel Functions (Cambridge Mathematical Library)
by G. N. Watson


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Special Functions : An Introduction to the Classical Functions of Mathematical Physics
by Nico M. Temme


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Representation of Lie Groups and Special Functions: Simplest Lie Groups, Special Functions and Integral Transforms (Mathematics and Its Applications)
by N.Ja. Vilenkin, A.U. Klimyk


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Advanced Mathematical Methods for Scientists and Engineers: Asymptotic
by Carl M. Bender, Steven A. Orszag, C.M. Bender


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Linear and Nonlinear Waves (Pure and Applied Mathematics: A Wiley-Interscience Series of Texts, Monographs and Tracts)
by G. B. Whitham


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Nonlinear Partial Differential Equations for Scientists and Engineers
by Lokenath Debnath


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Mathematical Methods for Physicists
by George B. Arfken, Hans Weber, Hans-Jurgen Weber


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Mathematics of Classical and Quantum Physics
by Frederick W. Byron, W. Fuller Robert


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Mathematics for Physicists (Dover Books on Mathematics)
by Philippe Dennery, Andre Krzywicki


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Better Together

Buy this book with Mathematics of Classical and Quantum Physics by Frederick W. Byron, W. Fuller Robert today!
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More recently published books:
 
Mathematical Methods of Physics and Engineering
by K. F. Riley, M. P. Hobson, S. J. Bence


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Modern Mathematical Methods for Physicists and Engineers
by C. D. Cantrell


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Special Functions
by George E. Andrews, Richard Askey, Ranjan Roy, G.-C. Rota (Editor)


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Mathematical Physics
by Sadri Hassani


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Mathematical Methods: For Students of Physics and Related Fields (Undergraduate Texts in Contemporary Physics)
by Sadri Hassani


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Mathematical Methods using Mathematica
by Sadri Hassani


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Mathematical Methods in Physics and Engineering with Mathematica
by Ferdinand F. Cap, Ferdinand Cap


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Numerical and Analytical Methods for Scientists and Engineers, Using Mathematica
by Daniel Dubin


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Advanced Mathematical Methods with Maple
by Derek Richards


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Other books I have not used:


Mathematical Methods in the Physical Sciences, 2nd Edition

by Mary L. Boas


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Mathematical Physics (Chicago Lectures in Physics (Paperback))
by Robert Geroch


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Schaum's Outline of Advanced Mathematics for Engineers and Scientists
by Murray R Spiegel


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Special Functions and Their Applications
by N. N. Lebedev, NikolaÖI Nikolaevich, Mathematician. Lebedev, Richard A. Silverman


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Partial Differential Equations for Scientists and Engineers (Dover Books on Advanced Mathematics)
by Stanley J. Farlow


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Variational Methods for Boundary Value Problems for Systems of Elliptic Equations (Dover Books on Advanced Mathematics)

by M.A. Lavrent'Ev


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Calculus of Variations
by S. V. Fomin, I. M. Gelfand


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Tensors, Differential Forms, and Variational Principles
by David Lovelock, Hanno Rund


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A few books on geometry: 

Geometrical Methods of Mathematical Physics
by Bernard Schutz


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Tensor Analysis on Manifolds

by Richard L Bishop, Samuel I. Goldberg


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Calculus on Manifolds: A Modern Approach to Classical Theorems of Advanced Calculus
by Michael Spivak


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