Physics 834: Mathematical Methods
Autumn, 2011

Welcome to the Physics 834 Mathematical Methods home page!
URL: http://www.physics.ohio-state.edu/~ntg/834/834.php
The course information is available here plus lots of supplementary info. Please check this page regularly.

Recent changes to this page:

04-Dec-2011 --- Here is the formula sheet for the final exam (which will be given to you).
03-Dec-2011 --- *** For the final exam, you will be given formulas such as those from the Jackson covers, for Fourier coefficients, the Sturm-Liouville form, and any integrals you need (except for our favorite contour integrals). ***
02-Dec-2011 --- Solutions for PS#10 are available below.
30-Nov-2011 --- Lecture notes for today are available below under Class notes. The MATLAB codes used today are laplace_relax_random.m, laplace_relax.m, laplace_relax_pbc.m, and eqheat.m.
26-Nov-2011 --- A handout with brief notes on solving PDE's by finite difference methods and integral equations with linear algebra and gaussian quadrature, which we'll touch on in the final two lectures, is linked below under Handouts.
23-Nov-2011 --- Added spherical harmonics, gaussian quadrature, and Green's function (under differential equations) example notebooks to the Mathematica examples page.
22-Nov-2011 --- An interesting paper with three views on the number of fundamental constants is linked below under Handouts.

Course description and info
Assignments
- Reading due dates
- Assigned problems, hints, and solutions
General handouts
- PDF copies of handouts
- Class notes
Resources
- Mathematical Methods References --- recommended supplementary books available at the Science and Engineering Library (reserved in many cases)
- Other supplementary texts --- additional references that may be useful
- Mathematica examples

Assignments

Required Readings (before the due date!)

Reading Due	Reading	Topic
21-Sep-2011	Lea, chapter 1 excerpt	review of vector calculus (and matrices)
21-Sep-2011	Arfken, chapter 1 plus 2.1-2.5	summary of vector calculus
26-Sep-2011	Lea, chapter 2 excerpt	survey of complex analysis
26-Sep-2011	Arfken, sections 6.1-6.6	introduction to complex analysis
28-Sep-2011	Arfken, sections 7.1 and 7.2	evaluating contour integrals; dispersion relations
05-Oct-2011	Arfken, sections 9.4 and 9.5	Singular points of a differential equation and series solutions (Frobenius' method)
05-Oct-2011	Lea, chapter 3 excerpt	differential equations (particularly Frobenius method and asymptotic solutions)
12-Oct-2011	Lea, chapter 4 excerpt	Fourier series
12-Oct-2011	Arfken, chapter 14	Fourier series
24-Oct-2011	Lea, chapter 6 excerpt	Generalized functions in physics
24-Oct-2011	Arfken, section 1.15	Fourier series
02-Nov-2011	Lea, chapter 7 excerpt	Fourier transforms
02-Nov-2011	Arfken, sections 15.1-15.7	Fourier transforms
09-Nov-2011	Lea, chapter 8 excerpt	Sturm-Liouville theory
09-Nov-2011	Arfken, chapter 10	Sturm-Liouville theory
23-Nov-2011	Lea, Appendix C excerpt	Green's functions
23-Nov-2011	Arfken, Sections 9.7 and 10.5	Green's functions
TBA	Lea, chapter 5 excerpt	Laplace transforms

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Problem Sets and Hints

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

Due Date	Assignment	Comments	Solutions
28-Sep-2011	#1	Hints, suggestions, etc.	solutions
05-Oct-2011	#2	Hints, suggestions, etc.	solutions
12-Oct-2011	#3	Hints, suggestions, etc.	solutions
17-Oct-2011	#4	Hints, suggestions, etc.	solutions
26-Oct-2011	#5	Hints, suggestions, etc.	solutions and notebook
03-Nov-2011	#6	Hints, suggestions, etc.	solutions and notebook
09-Nov-2011	#7	Hints, suggestions, etc.	solutions and notebook
17-Nov-2011	#8	Hints, suggestions, etc.	solutions and notebook
23-Nov-2011	#9	Hints, suggestions, etc.	solutions and notebook
01-Dec-2011	#10	Hints, suggestions, etc.	solutions and notebook

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Handouts

PDF Copies of Handouts

Date Out	Handout	Comments
13-Sep-2011	Jackson covers	The inside covers of J.D. Jackson's "Classical Electrodynamics" text with vector calculus stuff.
18-Sep-2011	Using δ's and ε's	Summary and examples of how to use the Kronecker delta function and the Levi-Civita (epsilon) symbol.
18-Sep-2011	Excerpts from Wigner article	"The Unreasonable Effectiveness of Mathematics in the Natural Sciences" by Eugene Wigner (1960).
12-Oct-2011	Excerpts from Blatt article	"Practical Points Concerning the Solution of the Schr\"odinger Equation" by John M. Blatt (1967).
04-Nov-2011	Excerpt from Hassani text	Defining a delta function at the origin in spherical coordinates (i.e., ignorable coordinates and so on).
14-Nov-2011	Excerpt from Landau QM-II text	Conventions for three-dimensional quantum mechanics.
16-Nov-2011	Excerpt from Jackson 7.10	Causality and Kramers-Kronig dispersion relation.
21-Nov-2011	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.
26-Nov-2011	PDE's numerically	Brief notes on solving PDE's by finite difference methods and integral equations with linear algebra and gaussian quadrature.

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Class Notes

The notes are in PDF format only.

Class Date	Notes	Comments
21-Sep-2011	lecture 1	Vector calculus review
26-Sep-2011	lecture 2	Vector calculus follow-ups plus first part of complex variables/functions
28-Sep-2011	lecture 3	More on complex variables/functions and complex integration
03-Oct-2011	lecture 4	Contour integrals
05-Oct-2011	lecture 5	More contour integrals and start of series solutions for differential equations.
10-Oct-2011	lecture 6	Loose ends on complex analysis and Frobenius method and asymptotic solutions for differential equations.
14-Oct-2011	lecture 7	Midterm notes, differential equations in Mathematica, gamma function, numerical solutions of diff eqs., Fourier series (pass 1)
17-Oct-2011	lecture 8	Midterm basic examples, gamma function follow-ups, Fourier series (pass 2) with Mathematica notebook on Fourier series (the original notebook is on the Mathematica examples page)
24-Oct-2011	lecture 9	Midterm comments, continuation of Fourier series with new Mathematica notebook on Fourier series
26-Oct-2011	lecture 10	Follow-ups on Fourier series with (yet another) new Mathematica notebook on Fourier series; overview of generalized functions.
31-Oct-2011	lecture 11	More on delta functions including a Mathematica notebook on delta functions.
02-Nov-2011	lecture 12	Wrap-up on delta functions plus first look at Fourier transforms..
07-Nov-2011	lecture 13	More on Fourier transforms and applications. Two Mathematica notebooks: one on defining simplication rules and another with an animation of the solution to a diffusion problem.
09-Nov-2011	lecture 14	Loose ends on Fourier transforms and introduction to Sturm-Liouville theory.
14-Nov-2011	lecture 15	More on Sturm-Liouville theory.
16-Nov-2011	lecture 16	Still more on Sturm-Liouville theory.
21-Nov-2011	lecture 17	Tail end of Sturm-Liouville theory plus Gaussian quadrature.
23-Nov-2011	lecture 18	Comments on PS#8 and PS#9, introduction to Green's functions.
28-Nov-2011	lecture 19	Continuation of Green's functions. Numerical solutions to PDE's and integral equations.
30-Nov-2011	lecture 20	Loose ends, comments on PS#9 and PS#10, emphasis points for final exam.

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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)	Title	Call no.	Comments
M. L. Boas	Mathematical methods in the physical sciences	QA37.2 .B59 2006	Excellent undergraduate text. This is probably your best choice for more basic (or at least alternative) introductions to the topics we will study in 834. 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 834 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 834, 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)	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, 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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OSU Physics: Physics 845.
Last modified: 08:55 am, December 04, 2011.

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