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Physics 7701 home page!
URL: https://www.asc.ohiostate.edu/physics/ntg/7701/7701.php
The course information is available here plus lots of supplementary
info. Please check this page regularly.
The Lea references will be closest to the lectures. Look at the others according to what text you have (note that Arfken 6th edition is a library ebook).
Reading Due  Reading  Topic 

21Aug2013  Lea, chapter 1 excerpt  review of vector calculus and matrices 
23Aug2013  Lea, chapter 2 excerpt  survey of complex analysis 
23Aug2013  Cahill, sections 5.1, 5.4, 5.6, 5.10  derivatives of complex functions, CauchyRiemann, Laurent expansion 
23Aug2013  Arfken 6th, sections 6.16.6  introduction to complex analysis 
23Aug2013  Arfken 7th, sections 1.8, 11.111.2, 11.5  complex numbers and functions, CauchyRiemann, Laurent expansion 
26Aug2013  Cahill, chapter 5  complexvariable theory 
26Aug2013  Arfken 6th, sections 7.1 and 7.2  evaluating contour integrals; dispersion relations 
26Aug2013  Arfken 7th, chapter 11  introduction to complex analysis 
06Sep2013  Cahill, sections 6.16.3, 6.19  Differential equations and Frobenius method 
06Sep2013  Arfken 6th, sections 9.4 and 9.5  Singular points of a differential equation and series solutions (Frobenius' method) 
06Sep2013  Arfken 7th, chapter 7 (sections 7.4 and 7.5)  Singular points of a differential equation and series solutions (Frobenius' method) 
06Sep2013  Lea, chapter 3 excerpt  differential equations (particularly Frobenius method and asymptotic solutions) 
11Sep2013  Cahill, chapter 2  Fourier series 
11Sep2013  Lea, chapter 4 excerpt  Fourier series 
11Sep2013  Arfken 6th, chapter 14  Fourier series 
11Sep2013  Arfken 7th, chapter 19  Fourier series 
25Sep2013  Lea, chapter 6 excerpt  Generalized functions in physics 
25Sep2013  Cahill, section 2.10  Delta function and Fourier series 
25Sep2013  Arfken 6th, section 1.15  Delta function 
25Sep2013  Arfken 7th, section 1.11  Delta function 
04Oct2013  Lea, chapter 7 excerpt  Fourier transforms 
04Oct2013  Cahill, chapter 3  Fourier transforms 
04Oct2013  Arfken 6th, sections 15.115.7  Fourier transforms 
04Oct2013  Arfken 7th, sections 20.120.6  Fourier transforms 
16Oct2013  Lea, chapter 1 excerpt  review of vector calculus 
16Oct2013  Arfken 7th, chapter 3  summary of vector calculus 
16Oct2013  Arfken 6th, chapter 1 plus 2.12.5  summary of vector calculus 
18Oct2013  Jackson 1.1 to 1.4; Zangwill 3.1 to 3.4  Coulomb's law, electric field, scalar potential, Gauss's law 
21Oct2013  Jackson 1.5 to 1.7; Zangwill 7.1, 8.1  Poisson and Laplace equations, electrostatic work 
23Oct2013  Jackson 1.11; Zangwill 3.5 to 3.6, 5.4 to 5.6  Electrostatic energy, capacitance 
28Oct2013  Jackson 1.8 to 1.10; Zangwill 7.2 to 7.3, 8.2 to 8.5  Green's theorem, Green functions 
01Nov2013  Jackson 2.1 to 2.8; Zangwill 7.4 to 7.8  Method of images, boundary value problems in electrostatics, expansions 
08Nov2013  Lea, Appendix C excerpt  Green's functions 
08Nov2013  Arfken 6th, Sections 9.7 and 10.5  Green's functions 
08Nov2013  Arfken 7th, Chapter 10  Green's functions 
20Nov2013  Lea, chapter 8 excerpt  SturmLiouville theory 
20Nov2013  Arfken 6th, chapter 10  SturmLiouville theory 
20Nov2013  Arfken 7th, chapter 8  SturmLiouville theory 
20Nov2013  Jackson chapter 3 (except 3.4,3.13) and 4.1,4.2; Zangwill 4, 7, 8.18.5  Boundary value problems in electrostatics (spherical and cylindrical) and basics of multipole expansions 
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Click on the problem set number to get a pdf copy of the assignment.
Due Date  Assignment  Comments  Solutions 

27Aug2013  #1  Hints, suggestions, etc.  solutions and notebook 
04Sep2013  #2  Hints, suggestions, etc.  solutions and notebook 
10Sep2013  #3  Hints, suggestions, etc.  solutions and notebook 
18Sep2013  #4  Hints, suggestions, etc.  solutions and notebook 
03Oct2013  #5  Hints, suggestions, etc.  solutions and notebook 
15Oct2013  #6  Hints, suggestions, etc.  solutions and notebook 
23Oct2013  #7  Hints, suggestions, etc.  solutions and notebook 
31Oct2013  #8  Hints, suggestions, etc.  solutions 
14Nov2013  #9  Hints, suggestions, etc.  solutions and notebook 
21Nov2013  #10  Hints, suggestions, etc.  solutions 
03Dec2013  #11  Hints, suggestions, etc.  solutions 
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Date Out  Handout  Comments 

07Aug2013  Excerpts from Wigner article  "The Unreasonable Effectiveness of Mathematics in the Natural Sciences" by Eugene Wigner (1960). 
07Aug2013  Trilogue on # of constants  Three articles by Lev Okun, Gabriele Veneziano, and Michael Duff, who have differing views on the number of fundamental dimensional constants in physics. 
19Aug2013  Jackson covers  The inside covers of J.D. Jackson's "Classical Electrodynamics" text with vector calculus stuff. 
19Aug2013  Using δ's and ε's  Summary and examples of how to use the Kronecker delta function and the LeviCivita (epsilon) symbol. 
02Oct2013  Excerpts from Blatt article  "Practical Points Concerning the Solution of the Schr\"odinger Equation" by John M. Blatt (1967). 
02Nov2013  Excerpt from Hassani text  Defining a delta function at the origin in spherical coordinates (i.e., ignorable coordinates and so on). 
06Oct2013  Excerpt from Jackson 7.10  Causality and KramersKronig dispersion relation. 
20Nov2013  PDE's numerically  Brief notes on solving PDE's by finite difference methods and integral equations with linear algebra and gaussian quadrature. 
20Nov2013  Excerpt from Jackson 2.2  A brief introduction to the finite element menthod 
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The notes are in PDF format only.
Class Date  Notes  Comments 

21Aug2013  lecture 1  Course overview and using δ_{ij}/ε_{ijk} 
23Aug2013  lecture 2  Complex variables and functions 
26Aug2013  lecture 3  More on complex variables/functions and complex integration 
28Aug2013  lecture 4  Continuing with different contour integrals 
30Aug2013  lecture 5  Integrals with poles on the xaxis 
04Sep2013  lecture 6  Loose ends on complex variables plus Start of series solutions for differential equations. 
06Sep2013  lecture 7  Frobenius and asymptotic methods for differential equations. 
09Sep2013  lecture 8  Loose ends on PS#3 problems; gamma function 
11Sep2013  lecture 9  Followups to PS#3, including Mathematica and numerical solutions of differential equations; start of Fourier series 
13Sep2013  lecture 10  Solving differential equations with Fourier series 
16Sep2013  lecture 11  Loose ends on Fourier series. 
18Sep2013  lecture 12  How Mathematica does (some) integrals; Gibbs overshoot (pdf of Mathematica notebook); midterm comments. 
20Sep2013  lecture 13  Followup to Gibbs overshoot, Fourier series convergence question, leadin to generalized functions. 
23Sep2013  lecture 14  Midterm summary and core competencies for generalized functions.. 
27Sep2013  lecture 15  Properties and applications of delta functions. 
02Oct2013  lecture 16  Identifying errors and midterm followups. 
04Oct2013  lecture 17  Introduction to Fourier transforms and applications. Mathematica notebook with an animation of the solution to a diffusion problem. 
07Oct2013  lecture 18  More on Fourier transforms. 
11Oct2013  lecture 19  Loose ends on Fourier transforms. 
16Oct2013  lecture 20  Vector calculus review. 
18Oct2013  lecture 21  Convolution example; electrostatic I (Coulomb's law, Gauss's law, scalar potential) 
21Oct2013  lecture 22  Mathematica items, delta functions in Poisson's equation, electrostatic work, boundary conditions for electric field at a surface. 
23Oct2013  lecture 23  Comments on PS#7 problem 3, electrostatic energy, capacitance, first pass at Green function solution to Poisson's/Laplace's equation 
28Oct2013  lecture 24  Recap and comments on PS#8, Dirichlet Green function 
30Oct2013  lecture 25  Comments on Green functions 
01Nov2013  lecture 26  Application of master formula with BC's, image charge example, conducting sphere in uniform field, preview of transform and expansion methods 
04Nov2013  lecture 27  Emphasis points for midterm, Cartesian separation of variables, orthogonal functions 
08Nov2013  lecture 28  Summary points for image charges, Dirichlet Green function for rectangular box by expansions and division of region methods 
13Nov2013  lecture 29  Comments on midterm, PS#9 comments/recap of Green function ideas, Laplace's equation in cylindrical coordinates (part 1) 
15Nov2013  lecture 30  Comments on PS#9 problem 5c, expansions (see ps9_checks.nb), Laplace's equation in cylindrical coordinates (part 2, with z dependence) 
18Nov2013  lecture 31  Recap of cylinder problems, orthogonality proofs, Green function in cylindrical coordinates, spherical coordinate expansions with azimuthal symmetry (example plus Green function). 
20Nov2013  lecture 32  SturmLiouville theory, spherical harmonics expansions, Gaussian quadrature. 
22Nov2013  lecture 33  Recap and loose ends on PS#10, generating function for Legendre polynomials and recursion relations. 
25Nov2013  lecture 34  Warmup problems on expansions, spherical harmonics expansions of Dirichlet Green function, multipole expansion introduction, numerical solution of Laplace's equations (relation method and finite element method). 
02Dec2013  lecture 35  PS#11 comments; final exam review comments 
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The call number is linked to the OSCAR library entry. In some cases, this entry includes the table of contents of the book. Some of these will be on reserve at the library.
Author(s)  Title  Call no.  Comments 

George Arfken and Hans Weber  Mathematical Methods for Physicists  QA37.2 .A74 2005  This book is commonly used in graduate math methods courses but the organization of topics is better for a reference than a textbook. The link is to an ebook for the 6th edition (there is a 7th edition now). 
Susan Lea  Mathematics for Physicists  QC20 .L43 2004  A good pedagogical text that we have used the last two years as a guide to many of the topics and the order in which we cover them (also many problems). 
M. L. Boas  Mathematical methods in the physical sciences  QA37.2 .B59 2006  Excellent text, said to be undergraduate level but suitable for a graduate course. This may be your best choice for more basic (or at least alternative) introductions to the topics we will study in 7701. Good problems as well. 
M. R. Spiegel  Schaum's Outline of Advanced Mathematics for Engineers and Scientists  TA333 .S6 1971eb  The link is to an Ebook version. This is a reasonable source of concise summaries of formulas but even better as a source of mostly worked out problems and extra problems with answers (but not solutions). The table of contents matches the 7701 syllabus rather well. Costs less than $15 on Amazon.com. 
J. J. Kelly  Graduate mathematical physics: with MATHEMATICA supplements  QC20.K42 2006  Text for a onesemester course similar to 7701, with integrated examples for using Mathematica. Comes with a Mathematica CDROM. 
M. Stone and P. Goldbart  Mathematics for physics: a guided tour for graduate students  QC20.S76 2009  The link is to the Ebook. 
R. Courant and D.Hilbert  Methods of Mathematical Physics (2 volumes)  QC20 .C851 1953  Classic reference that has everything you need, but not so easy. Available in a new printing (but it is not cheap!). The library has the second volume on differential equations as an ebook. 
P. M. Morse and H. Feshbach  Methods of Theoretical Physics (2 volumes)  QC20.M67 1953  Another classic with some things you won't find elsewhere. From the 1950's but now back in print at Feshbach Publishing. 
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The call number is linked to the OSCAR entry. In some cases, this entry includes the table of contents of the book.
Author(s)  Title  Call no.  Comments 

M. Abramowitz and I. A. Stegun  Handbook of mathematical functions  online version  Great source of formulas for special functions and other useful things. You can download a pdf version here (but the quality is not so good). 
R. V. Churchill and J. W. Brown  Complex Variables and Applications  QA331.7 .C524 2009  Recommended reference for the theory of analytic functions. 
A. L. Fetter and J. D. Walecka  Theoretical Mechanics of Particles and Continua  QA808.2 .F47  Has good treatments of the general string equation, SturmLiouville problems, Green's functions, and more. 
I. S. Gradshteyn and I. M. Ryzkhik  Table of Integrals, Series, and Products  QA55.G6613 2007eb  Still indispensible, although Mathematica can replace a lot of it. The link is to an ebook. 
S. Hassani  Mathematical methods for students of physics and related fields  QC20.H394 2009eb  Advanced undergraduate level. The link is to the Ebook. 
J. D. Jackson  Classical Electrodynamics  QC631.J3 1999  Treats boundaryvalue problems of electromagnetism and other topics such as dispersion theory. 
M. J. Lighthill  Introduction to Fourier Analysis and Generalised Functions  QA404.L73  A great little book on Fourier transforms. 
J. Mathews and R. L. Walker  Mathematical Methods of Physics  QA401.M29 1970  Another classic text, full of useful "tricks". 
H. M. Schey  Div, Grad, Curl, and all that  QA433.S28 2005  Very accessible ("informal") text on vector calculus. 
Sal Mangano  Mathematica Cookbook  Safari  Ebook with many Mathematica examples. 
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