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Department of Physics

Physics 7701: Analytic and Numeric Methods of Physics
Autumn, 2013

Welcome to the Physics 7701 home page!
URL: https://www.asc.ohio-state.edu/physics/ntg/7701/7701.php
The course information is available here plus lots of supplementary info. Please check this page regularly.

Recent changes to this page:



Required Readings (before the due date!)

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 e-book).

Reading DueReadingTopic
21-Aug-2013 Lea, chapter 1 excerpt review of vector calculus and matrices
23-Aug-2013 Lea, chapter 2 excerpt survey of complex analysis
23-Aug-2013 Cahill, sections 5.1, 5.4, 5.6, 5.10 derivatives of complex functions, Cauchy-Riemann, Laurent expansion
23-Aug-2013 Arfken 6th, sections 6.1-6.6 introduction to complex analysis
23-Aug-2013 Arfken 7th, sections 1.8, 11.1-11.2, 11.5 complex numbers and functions, Cauchy-Riemann, Laurent expansion
26-Aug-2013 Cahill, chapter 5 complex-variable theory
26-Aug-2013 Arfken 6th, sections 7.1 and 7.2 evaluating contour integrals; dispersion relations
26-Aug-2013 Arfken 7th, chapter 11 introduction to complex analysis
06-Sep-2013 Cahill, sections 6.1-6.3, 6.19 Differential equations and Frobenius method
06-Sep-2013 Arfken 6th, sections 9.4 and 9.5 Singular points of a differential equation and series solutions (Frobenius' method)
06-Sep-2013 Arfken 7th, chapter 7 (sections 7.4 and 7.5) Singular points of a differential equation and series solutions (Frobenius' method)
06-Sep-2013 Lea, chapter 3 excerpt differential equations (particularly Frobenius method and asymptotic solutions)
11-Sep-2013 Cahill, chapter 2 Fourier series
11-Sep-2013 Lea, chapter 4 excerpt Fourier series
11-Sep-2013 Arfken 6th, chapter 14 Fourier series
11-Sep-2013 Arfken 7th, chapter 19 Fourier series
25-Sep-2013 Lea, chapter 6 excerpt Generalized functions in physics
25-Sep-2013 Cahill, section 2.10 Delta function and Fourier series
25-Sep-2013 Arfken 6th, section 1.15 Delta function
25-Sep-2013 Arfken 7th, section 1.11 Delta function
04-Oct-2013 Lea, chapter 7 excerpt Fourier transforms
04-Oct-2013 Cahill, chapter 3 Fourier transforms
04-Oct-2013 Arfken 6th, sections 15.1-15.7 Fourier transforms
04-Oct-2013 Arfken 7th, sections 20.1-20.6 Fourier transforms
16-Oct-2013 Lea, chapter 1 excerpt review of vector calculus
16-Oct-2013 Arfken 7th, chapter 3 summary of vector calculus
16-Oct-2013 Arfken 6th, chapter 1 plus 2.1-2.5 summary of vector calculus
18-Oct-2013 Jackson 1.1 to 1.4; Zangwill 3.1 to 3.4 Coulomb's law, electric field, scalar potential, Gauss's law
21-Oct-2013 Jackson 1.5 to 1.7; Zangwill 7.1, 8.1 Poisson and Laplace equations, electrostatic work
23-Oct-2013 Jackson 1.11; Zangwill 3.5 to 3.6, 5.4 to 5.6 Electrostatic energy, capacitance
28-Oct-2013 Jackson 1.8 to 1.10; Zangwill 7.2 to 7.3, 8.2 to 8.5 Green's theorem, Green functions
01-Nov-2013 Jackson 2.1 to 2.8; Zangwill 7.4 to 7.8 Method of images, boundary value problems in electrostatics, expansions
08-Nov-2013 Lea, Appendix C excerpt Green's functions
08-Nov-2013 Arfken 6th, Sections 9.7 and 10.5 Green's functions
08-Nov-2013 Arfken 7th, Chapter 10 Green's functions
20-Nov-2013 Lea, chapter 8 excerpt Sturm-Liouville theory
20-Nov-2013 Arfken 6th, chapter 10 Sturm-Liouville theory
20-Nov-2013 Arfken 7th, chapter 8 Sturm-Liouville theory
20-Nov-2013 Jackson chapter 3 (except 3.4,3.13) and 4.1,4.2; Zangwill 4, 7, 8.1-8.5 Boundary value problems in electrostatics (spherical and cylindrical) and basics of multipole expansions

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Problem Sets and Hints

Click on the problem set number to get a pdf copy of the assignment.

Due DateAssignmentCommentsSolutions
27-Aug-2013 #1 Hints, suggestions, etc. solutions and notebook
04-Sep-2013 #2 Hints, suggestions, etc. solutions and notebook
10-Sep-2013 #3 Hints, suggestions, etc. solutions and notebook
18-Sep-2013 #4 Hints, suggestions, etc. solutions and notebook
03-Oct-2013 #5 Hints, suggestions, etc. solutions and notebook
15-Oct-2013 #6 Hints, suggestions, etc. solutions and notebook
23-Oct-2013 #7 Hints, suggestions, etc. solutions and notebook
31-Oct-2013 #8 Hints, suggestions, etc. solutions
14-Nov-2013 #9 Hints, suggestions, etc. solutions and notebook
21-Nov-2013 #10 Hints, suggestions, etc. solutions
03-Dec-2013 #11 Hints, suggestions, etc. solutions

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PDF Copies of Handouts

Date OutHandoutComments
07-Aug-2013 Excerpts from Wigner article "The Unreasonable Effectiveness of Mathematics in the Natural Sciences" by Eugene Wigner (1960).
07-Aug-2013 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.
19-Aug-2013 Jackson covers The inside covers of J.D. Jackson's "Classical Electrodynamics" text with vector calculus stuff.
19-Aug-2013 Using δ's and ε's Summary and examples of how to use the Kronecker delta function and the Levi-Civita (epsilon) symbol.
02-Oct-2013 Excerpts from Blatt article "Practical Points Concerning the Solution of the Schr\"odinger Equation" by John M. Blatt (1967).
02-Nov-2013 Excerpt from Hassani text Defining a delta function at the origin in spherical coordinates (i.e., ignorable coordinates and so on).
06-Oct-2013 Excerpt from Jackson 7.10 Causality and Kramers-Kronig dispersion relation.
20-Nov-2013 PDE's numerically Brief notes on solving PDE's by finite difference methods and integral equations with linear algebra and gaussian quadrature.
20-Nov-2013 Excerpt from Jackson 2.2 A brief introduction to the finite element menthod

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Class Notes

The notes are in PDF format only.

Class DateNotesComments
21-Aug-2013 lecture 1 Course overview and using δijijk
23-Aug-2013 lecture 2 Complex variables and functions
26-Aug-2013 lecture 3 More on complex variables/functions and complex integration
28-Aug-2013 lecture 4 Continuing with different contour integrals
30-Aug-2013 lecture 5 Integrals with poles on the x-axis
04-Sep-2013 lecture 6 Loose ends on complex variables plus Start of series solutions for differential equations.
06-Sep-2013 lecture 7 Frobenius and asymptotic methods for differential equations.
09-Sep-2013 lecture 8 Loose ends on PS#3 problems; gamma function
11-Sep-2013 lecture 9 Follow-ups to PS#3, including Mathematica and numerical solutions of differential equations; start of Fourier series
13-Sep-2013 lecture 10 Solving differential equations with Fourier series
16-Sep-2013 lecture 11 Loose ends on Fourier series.
18-Sep-2013 lecture 12 How Mathematica does (some) integrals; Gibbs overshoot (pdf of Mathematica notebook); midterm comments.
20-Sep-2013 lecture 13 Follow-up to Gibbs overshoot, Fourier series convergence question, lead-in to generalized functions.
23-Sep-2013 lecture 14 Midterm summary and core competencies for generalized functions..
27-Sep-2013 lecture 15 Properties and applications of delta functions.
02-Oct-2013 lecture 16 Identifying errors and midterm follow-ups.
04-Oct-2013 lecture 17 Introduction to Fourier transforms and applications. Mathematica notebook with an animation of the solution to a diffusion problem.
07-Oct-2013 lecture 18 More on Fourier transforms.
11-Oct-2013 lecture 19 Loose ends on Fourier transforms.
16-Oct-2013 lecture 20 Vector calculus review.
18-Oct-2013 lecture 21 Convolution example; electrostatic I (Coulomb's law, Gauss's law, scalar potential)
21-Oct-2013 lecture 22 Mathematica items, delta functions in Poisson's equation, electrostatic work, boundary conditions for electric field at a surface.
23-Oct-2013 lecture 23 Comments on PS#7 problem 3, electrostatic energy, capacitance, first pass at Green function solution to Poisson's/Laplace's equation
28-Oct-2013 lecture 24 Recap and comments on PS#8, Dirichlet Green function
30-Oct-2013 lecture 25 Comments on Green functions
01-Nov-2013 lecture 26 Application of master formula with BC's, image charge example, conducting sphere in uniform field, preview of transform and expansion methods
04-Nov-2013 lecture 27 Emphasis points for midterm, Cartesian separation of variables, orthogonal functions
08-Nov-2013 lecture 28 Summary points for image charges, Dirichlet Green function for rectangular box by expansions and division of region methods
13-Nov-2013 lecture 29 Comments on midterm, PS#9 comments/recap of Green function ideas, Laplace's equation in cylindrical coordinates (part 1)
15-Nov-2013 lecture 30 Comments on PS#9 problem 5c, expansions (see ps9_checks.nb), Laplace's equation in cylindrical coordinates (part 2, with z dependence)
18-Nov-2013 lecture 31 Recap of cylinder problems, orthogonality proofs, Green function in cylindrical coordinates, spherical coordinate expansions with azimuthal symmetry (example plus Green function).
20-Nov-2013 lecture 32 Sturm-Liouville theory, spherical harmonics expansions, Gaussian quadrature.
22-Nov-2013 lecture 33 Recap and loose ends on PS#10, generating function for Legendre polynomials and recursion relations.
25-Nov-2013 lecture 34 Warm-up 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).
02-Dec-2013 lecture 35 PS#11 comments; final exam review comments

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*Mathematical Methods References

Especially Recommended

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)TitleCall 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 e-book 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 E-book 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 one-semester course similar to 7701, with integrated examples for using Mathematica. Comes with a Mathematica CD-ROM.
M. Stone and P. Goldbart Mathematics for physics: a guided tour for graduate students QC20.S76 2009 The link is to the E-book.
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 e-book.
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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Other Useful References

The call number is linked to the OSCAR entry. In some cases, this entry includes the table of contents of the book.

Author(s)TitleCall 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, Sturm-Liouville 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 e-book.
S. Hassani Mathematical methods for students of physics and related fields QC20.H394 2009eb Advanced undergraduate level. The link is to the E-book.
J. D. Jackson Classical Electrodynamics QC631.J3 1999 Treats boundary-value 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 E-book with many Mathematica examples.

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Your comments and suggestions are appreciated.
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Last modified: 01:34 pm, October 16, 2021.