 |
 |
 |
|
||||
|
|
 |
|
|
 |
||
 |
||||||
|
|
|
|
|
||||
|
|
|
|
|
|
||
|
|
||||||
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.
Recent changes to this page:
| Reading Due | Reading | Topic |
|---|---|---|
| 22-Aug-2012 | Lea, chapter 1 excerpt | review of vector calculus (and matrices) |
| 22-Aug-2012 | Arfken 7th, chapter 3 | summary of vector calculus |
| 22-Aug-2012 | Arfken 6th, chapter 1 plus 2.1-2.5 | summary of vector calculus |
| 29-Aug-2012 | Lea, chapter 2 excerpt | survey of complex analysis |
| 29-Aug-2012 | Arfken 6th, sections 6.1-6.6 | introduction to complex analysis |
| 29-Aug-2012 | Arfken 6th, sections 7.1 and 7.2 | evaluating contour integrals; dispersion relations |
| 29-Aug-2012 | Arfken 7th, section 1.8 | complex numbers and functions |
| 29-Aug-2012 | Arfken 7th, chapter 11 | introduction to complex analysis |
| 12-Sep-2012 | Arfken 6th, sections 9.4 and 9.5 | Singular points of a differential equation and series solutions (Frobenius' method) |
| 12-Sep-2012 | Arfken 7th, chapter 7 (sections 7.4 and 7.5) | Singular points of a differential equation and series solutions (Frobenius' method) |
| 12-Sep-2012 | Lea, chapter 3 excerpt | differential equations (particularly Frobenius method and asymptotic solutions) |
| 17-Sep-2012 | Lea, chapter 4 excerpt | Fourier series |
| 17-Sep-2012 | Arfken 6th, chapter 14 | Fourier series |
| 17-Sep-2012 | Arfken 7th, chapter 19 | Fourier series |
| 27-Sep-2012 | Lea, chapter 6 excerpt | Generalized functions in physics |
| 27-Sep-2012 | Arfken 6th, section 1.15 | Delta function |
| 27-Sep-2012 | Arfken 7th, section 1.11 | Delta function |
| 03-Oct-2012 | Lea, chapter 7 excerpt | Fourier transforms |
| 03-Oct-2012 | Arfken 6th, sections 15.1-15.7 | Fourier transforms |
| 03-Oct-2012 | Arfken 7th, sections 20.1-20.6 | Fourier transforms |
| 15-Oct-2012 | Lea, chapter 8 excerpt | Sturm-Liouville theory |
| 15-Oct-2012 | Arfken 6th, chapter 10 | Sturm-Liouville theory |
| 15-Oct-2012 | Arfken 7th, chapter 8 | Sturm-Liouville theory |
| 31-Oct-2012 | Lea, Appendix C excerpt | Green's functions |
| 31-Oct-2012 | Arfken 6th, Sections 9.7 and 10.5 | Green's functions |
| 31-Oct-2012 | Arfken 7th, Chapter 10 | Green's functions |
| TBA | Lea, chapter 5 excerpt | Laplace transforms |
Return to Contents
Click on the problem set number to get a pdf copy of the assignment.
| Due Date | Assignment | Comments | Solutions |
|---|---|---|---|
| 30-Aug-2012 | #1 | Hints, suggestions, etc. | solutions and notebook |
| 06-Sep-2012 | #2 | Hints, suggestions, etc. | solutions and notebook |
| 13-Sep-2012 | #3 | Hints, suggestions, etc. | solutions and notebook |
| 20-Sep-2012 | #4 | Hints, suggestions, etc. | solutions and notebook |
| 01-Oct-2012 | #5 | Hints, suggestions, etc. | solutions and notebook |
| 09-Oct-2012 | #6 | Hints, suggestions, etc. | solutions and notebook |
| 18-Oct-2012 | #7 | Hints, suggestions, etc. | solutions and notebook |
| 29-Oct-2012 | #8 | Hints, suggestions, etc. | solutions and notebook |
| 05-Nov-2012 | #9 | Hints, suggestions, etc. | solutions and notebook |
| 15-Nov-2012 | #10 | Hints, suggestions, etc. | solutions and notebook |
| 30-Nov-2012 | #11 | Hints, suggestions, etc. | solutions |
Return to Contents
Handouts with dates from 2011 are from the 834 Mathematical Methods course that was the predecessor to Physics 7701.
| 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. |
| 03-Dec-2012 | Excerpt from Jackson 2.2 | A brief introduction to the finite element menthod | .
Return to Contents
The notes are in PDF format only.
| Class Date | Notes | Comments |
|---|---|---|
| 22-Aug-2012 | lecture 1 | Course overview and using δij/εijk |
| 24-Aug-2012 | lecture 2 | Review of vector calculus basics |
| 27-Aug-2012 | lecture 3 | Continued review of vector calculus basics |
| 29-Aug-2012 | lecture 4 | Complex variables and functions |
| 31-Aug-2012 | lecture 5 | More on complex variables/functions and complex integration |
| 05-Sep-2012 | lecture 6 | More on complex integration |
| 07-Sep-2012 | lecture 7 | Continuing with different contour integrals |
| 10-Sep-2012 | lecture 8 | Integrals with poles on the x-axis |
| 12-Sep-2012 | lecture 9 | Start of series solutions for differential equations. |
| 14-Sep-2012 | lecture 10 | Frobenius and asymptotic methods for differential equations. |
| 17-Sep-2012 | lecture 11 | Midterm notes, differential equations in Mathematica, numerical solutions of diff eqs., gamma function, Fourier series (pass 1) |
| 19-Sep-2012 | lecture 12 | Loose ends on numerical solutions and Frobenius, plus Fourier series (passes 0 and 2) |
| 21-Sep-2012 | lecture 13 | Midterm examples, plus solving differential equations with Fourier series and fourier_series.nb Mathematica notebook |
| 24-Sep-2012 | lecture 14 | Follow-ups on Fourier series with (yet another) Mathematica notebook on Fourier series. |
| 26-Sep-2012 | lecture 15 | Loose ends on Fourier series. |
| 28-Sep-2012 | lecture 16 | Midterm comments and overview of generalized functions.. |
| 01-Oct-2012 | lecture 17 | Properties and applications of delta functions. |
| 05-Oct-2012 | lecture 18 | Wrap-up on delta functions. Mathematica notebook on defining simplication rules. |
| 08-Oct-2012 | lecture 19 | Introduction to Fourier transforms and applications. Mathematica notebook with an animation of the solution to a diffusion problem. |
| 10-Oct-2012 | lecture 20 | More on Fourier transforms. |
| 12-Oct-2012 | lecture 21 | Loose ends on Fourier transforms. |
| 15-Oct-2012 | lecture 22 | Introduction to Sturm-Liouville theory. |
| 17-Oct-2012 | lecture 23 | More on Sturm-Liouville theory. |
| 22-Oct-2012 | lecture 24 | Mostly comments on PS#8 plus spherical harmonics expansion. |
| 24-Oct-2012 | lecture 25 | Sphere expansion example revisited without azimuthal symmetry. |
| 29-Oct-2012 | lecture 26 | Gaussian quadrature and intro to Green's functions. |
| 02-Nov-2012 | lecture 27 | Emphasis points for 2nd midterm. |
| 05-Nov-2012 | lecture 28 | Recap of Green's functions and PS#9 problems 2 and 5. |
| 09-Nov-2012 | lecture 29 | Follow-ups to PS#9 problem 2 and spherical Bessel functions plus comments/background on PS#10. |
| 14-Nov-2012 | lecture 30 | Comments on midterm 2 and PS#10; Green's functions in more than one dimension. |
| 16-Nov-2012 | lecture 31 | Inhomogeneous boundary conditions, part I. |
| 19-Nov-2012 | lecture 32 | Inhomogeneous boundary conditions, part II (Green's Theorem); spherical and cylindrical applications. |
| 26-Nov-2012 | lecture 33 | Guide to PS#11 problems 1 through 4. |
| 28-Nov-2012 | lecture 34 | Loose ends on PS#11 topics and brief introduction to numerical methods for PDE's and integral equations. |
| 03-Dec-2012 | lecture 35 | Stability of finite difference diffusion equation plus introduction to finite element method. |
Return to Contents
Mathematical Methods
ReferencesThe 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 text, said to be undergraduate level but suitable for a graduate course. This is probably 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. |
Return to Contents
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. |
Return to Contents