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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• Paperback: 501 pages ; Dimensions (in inches): 1.15 x 9.33 x 6.37
• Publisher: Pearson Education POD; 2 edition (January 1, 1971)
• ISBN: 0805370021
  
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A Course of Modern Analysis (Cambridge Mathematical Library)
by E. T. Whittaker, G. N. Watson

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• ISBN: 0521588073
  
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A Treatise on the Theory of Bessel Functions (Cambridge Mathematical Library)
by G. N. Watson

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• Publisher: Cambridge University Press; 2 edition (August 25, 1995)
• ISBN: 0521483913
  
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Special Functions : An Introduction to the Classical Functions of Mathematical Physics
by Nico M. Temme

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• Hardcover: 392 pages ; Dimensions (in inches): 0.97 x 9.50 x 6.37
• Publisher: Wiley-Interscience; (March 1, 1996)
• ISBN: 0471113131
  
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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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• Hardcover: 640 pages ; Dimensions (in inches): 9.21 x 1.50 x 6.14
• Publisher: Kluwer Academic Publishers; (January 1, 1992)
• ISBN: 0792314662

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

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• Hardcover: 593 pages ; Dimensions (in inches): 1.29 x 9.52 x 6.41
• Publisher: Springer-Verlag; (November 1, 1999)
• ISBN: 0387989315
  
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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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• ISBN: 0471359424
  
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Nonlinear Partial Differential Equations for Scientists and Engineers
by Lokenath Debnath

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• Hardcover: 593 pages ; Dimensions (in inches): 1.33 x 9.56 x 6.38
• Publisher: Birkhauser Boston; (July 1, 1997)
• ISBN: 0817639020 | All Editions

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

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• Hardcover: 1112 pages ; Dimensions (in inches): 1.78 x 9.46 x 6.62
• Publisher: Academic Press; 5 edition (October 2000)
• ISBN: 0120598256
  
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Mathematics of Classical and Quantum Physics
by Frederick W. Byron, W. Fuller Robert

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• Paperback: 661 pages ; Dimensions (in inches): 1.24 x 9.19 x 6.12
• Publisher: Dover Publications; Reprint edition (August 20, 1992)
• ISBN: 048667164X
  
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Mathematics for Physicists (Dover Books on Mathematics)
by Philippe Dennery, Andre Krzywicki

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• Publisher: Dover Publications; Dover ed edition (August 1, 1996)
• ISBN: 0486691934
  
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---

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

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• Publisher: Cambridge University Press; 2 edition (August 15, 2002)
• ISBN: 0521890675
  
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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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• ISBN: 0387985794
  
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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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• Publisher: Springer-Verlag; Bk&CD-Rom edition (March 28, 2003)
• ISBN: 0387955232
  
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Mathematical Methods in Physics and Engineering with Mathematica
by Ferdinand F. Cap, Ferdinand Cap

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• Hardcover: 352 pages ; Dimensions (in inches): 0.94 x 9.74 x 6.16
• Publisher: CRC Press; (May 28, 2003)
• ISBN: 1584884029

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

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• Hardcover: 633 pages ; Dimensions (in inches): 1.44 x 10.12 x 7.28
• Publisher: Wiley-Interscience; Bk&CD-Rom edition (April 22, 2003)
• ISBN: 0471266108
  
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Advanced Mathematical Methods with Maple
by Derek Richards

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• Paperback: 878 pages ; Dimensions (in inches): 1.66 x 9.76 x 6.78
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• ISBN: 0521779812
  
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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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• Hardcover: 816 pages ; Dimensions (in inches): 1.42 x 9.50 x 6.24
• Publisher: Wiley Text Books; 2 edition (April 6, 1983)
• ISBN: 0471044091
  
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Mathematical Physics (Chicago Lectures in Physics (Paperback))
by Robert Geroch

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• Paperback: 352 pages ; Dimensions (in inches): 0.75 x 9.04 x 6.05
• Publisher: University of Chicago Press; (October 1, 1985)
• ISBN: 0226288625
  
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Schaum's Outline of Advanced Mathematics for Engineers and Scientists
by Murray R Spiegel

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• Paperback: 416 pages ; Dimensions (in inches): 0.81 x 10.96 x 8.18
• Publisher: McGraw-Hill; 1 edition (June 1, 1971)
• ISBN: 0070602166
  
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Special Functions and Their Applications
by N. N. Lebedev, NikolaÖI Nikolaevich, Mathematician. Lebedev, Richard A. Silverman

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• Paperback: 308 pages ; Dimensions (in inches): 0.64 x 8.47 x 5.43
• Publisher: Dover Publications; Rev. Engli edition (June 1, 1972)
• ISBN: 0486606244
  
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Partial Differential Equations for Scientists and Engineers (Dover Books on Advanced Mathematics)
by Stanley J. Farlow

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• Paperback: 414 pages ; Dimensions (in inches): 0.91 x 9.26 x 6.04
• Publisher: Dover Publications; Reprint edition (September 1, 1993)
• ISBN: 048667620X
  
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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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• Paperback: 160 pages ; Dimensions (in inches): 0.36 x 8.53 x 5.42
• Publisher: Dover Publications; (January 1, 1990)
• ISBN: 0486661709
  
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Calculus of Variations
by S. V. Fomin, I. M. Gelfand

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• Paperback: 240 pages ; Dimensions (in inches): 0.51 x 8.48 x 5.35
• Publisher: Dover Publications; (October 16, 2000)
• ISBN: 0486414485
  
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Tensors, Differential Forms, and Variational Principles
by David Lovelock, Hanno Rund

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• Paperback: 384 pages ; Dimensions (in inches): 0.73 x 8.51 x 5.40
• Publisher: Dover Publications; (April 1, 1989)
• ISBN: 0486658406
  
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A few books on geometry: 

Geometrical Methods of Mathematical Physics
by Bernard Schutz

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• Paperback: 264 pages ; Dimensions (in inches): 0.70 x 9.14 x 5.96
• Publisher: Cambridge University Press; (January 28, 1980)
• ISBN: 0521298873
  
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Tensor Analysis on Manifolds
by Richard L Bishop, Samuel I. Goldberg

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• Paperback: 280 pages ; Dimensions (in inches): 0.57 x 8.27 x 5.62
• Publisher: Dover Publications; (September 1, 1981)
• ISBN: 0486640396
  
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Calculus on Manifolds: A Modern Approach to Classical Theorems of Advanced Calculus
by Michael Spivak

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