Autumn, 2013

Welcome to the
Physics 7701 home page!

URL: http://www.physics.ohio-state.edu/~ntg/7701/7701.php

The course information is available here plus lots of supplementary
info. Please check this page regularly.

- 10-Dec-2013 --- Final exam scores are posted on Carmen. The class average was 61/75 or about 81/100. A solution key for the final exam with grading guidance is available. Course grades will be posted later this week, once the PS#11 grading is completed. [Note: You can stop by M2048 to look at your exam, but you can't have it back until grades are finalized.]
- 23-Nov-2013 --- Note: There are spherical harmonics, gaussian quadrature, and Green's function (under differential equations) example notebooks on the Mathematica examples page.
- 20-Nov-2012 --- A short excerpt from Jackson on the finite element method is linked below under Handouts.
- 07-Aug-2013 --- While you are impatiently awaiting the start of 7701 classes, you might enjoy a classic (and appropriate) essay by Eugene Wigner entitled "The Unreasonable Effectiveness of Mathematics in the Natural Sciences". (A username and password are needed, which will be revealed in an email you should receive soon.) Another interesting paper with three views on the number of fundamental constants ("Trilogue 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 example notebooks

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 Due | Reading | Topic |
---|---|---|

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

Due Date | Assignment | Comments | Solutions |
---|---|---|---|

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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.

Date Out | Handout | Comments |
---|---|---|

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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The notes are in PDF format only.

Class Date | Notes | Comments |
---|---|---|

21-Aug-2013 | lecture 1 | Course overview and using δ_{ij}/ε_{ijk} |

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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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 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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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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furnstahl.1@osu.edu