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.

- 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
- General handouts
- 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

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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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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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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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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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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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.

[OSU Physics] [Math and Physical Sciences] [Ohio State University]

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