Latest update: January 2, 2007
http://fy.chalmers.se/~kinaret/mathphys.html

Mathematical Physics


Mathematical Physics: 3.0p, lp II
Examinator: Prof. Jari Kinaret Department of Applied Physics

Latest information:

Final exam and all homework sets have been graded. Results posted on the door to my office. Note that the ECTS grades are preliminary and may be adjusted after the projects have been graded.

I will be here until January 5, and then again for one day on January 12, and more continuously from January 17 on.

Deadline for project is January 12. PDF file is OK.

Cremona has sold out the Bender and Orszag book but they have ordered more.

Last lecture (review) is here (PDF).

Examples of old exam problems are here (PDF).

Jari's visiting hours are Thursdays 11-12.

First lecture on Wednesday, November 1, at 1000-1145 in FL71.

Book(s) for the fall 2006 decided: Frederick W. Byron and Robert W. Fuller, Mathematics of Classical And Quantum Physics, ISBN 048667164X, Dover, 1992, and Carl M. Bender and Steven A. Orszag, Advanced Mathematical Methods for Scientists and Engineers, ISBN 0387989315, Springer, 1999. There are equivalent alternatives to the first book (e.g. Arfken, or Matthews and Walker), but the second one is more unique. However, we only cover parts of both books, so you may wish to organize yourselves so that not everybody needs to buy both books.
On August 24, 2006, the cheapest book prices I could find are SEK 176 for the first book (Byron and Fuller) at Amazon.com and SEK 562 for the second book (Bender and Orszag) at Amazon.ca, including postage.



General information regarding the course

In this course you will refresh much of the mathematical knowledge that you have learned in other courses, apply it to various physical systems, and even learn some new mathematical techniques that are a useful part of a physicist's vocabulary. We will focus on analytic methods, and discuss computational approaches only in exceptional cases.

The grade is based on weekly home problems (45%), a final written exam (45%), and a voluntary project (10%). A passing grade requires satisfactory performance in both home problems and the final examination (performance at 30% level minimum in both components).
Limits for the different grades are as usual: for 3/5 a minimum of 40%, for 4/5 a minimum of 60%, and for 5/5 a minimum of 80%.
Since there have been a few questions on grading, here are two examples: Assume that the maximum number of points attainable in home problems is 64, and in the final exam 24. Student A has received 45 points in home problems, and 19 points in the final, and chooses not to write an project. Student B has 19 points from home problems and 15 from the final, no project. Student C has 22 points from home problems, 15 from the final, and 9/10 from the project. The total scores for the three students are A: 0.45x(45/64) + 0.45x(19/25) = 0.658406, B: 0.45x(19/64) + 0.45x(15/25) = 0.403594, C: 0.45x(22/64) + 0.45x(19/25) + 0.1x(9/10) = 0.586688. The grades for the three students are consequently A: 4/5, B: 0/5 (performance on home problems below the 30% limit of 0.3x64 = 19.2), C: 3/5.

Transparencies of first lecture are here.
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Schedule (see also schedule (PS))

Lectures: Recitations:
First lecture: Wednesday, November 1, 1000-1145, FL71

Final exam: Tuesday, December 19, in the morning
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Contact information

Lecturer:

Tutor: Visiting hours:
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Material

We will use two course books:

1. Frederick W. Byron and Robert W. Fuller, Mathematics of Classical And Quantum Physics, ISBN 048667164X, Dover, 1992,
2. Carl M. Bender and Steven A. Orszag, Advanced Mathematical Methods for Scientists and Engineers, ISBN 0387989315, Springer, 1999.

The book by Byron and Fuller replaces the previously used book by Matthews and Walker which is no longer readily available. A list of the chapters covered is given in the PostScript schedule (see above).

There are nearly equivalent alternatives to the first book (e.g. Arfken, or Matthews and Walker, which are actually better but more expensive or unavailable), but the second one is more unique. However, we only cover parts of both books, so you may wish to organize yourselves so that not everybody needs to buy both books.

Other supporting material:
1. G.B. Arfken and H. Weber, Mathematical Methods for Physicists (Academic Press, 2001)
2. R. Courant and D. Hilbert, Methods of Mathematical Physics, vol. 1 (Wiley, New York, 1989)
3. P.M. Morse and H. Feshbach, Methods of Theoretical Physics, vols. 1 and 2 (New York, 1953)
4. J. Mathews and R.L. Walker, Mathematical Methods of Physics (Addison, 1970)

Additional notes are here (pdf).
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Project

You may write a voluntary project.
The project should contain up to two suggestions for new home problems, and up to two suggestions for new exam problems, all with solutions. Each suggested problem must cover a different topic. Each suggested home problem should be of comparable difficulty as those currently in use, provide training in at least one topic covered by the course, and be solvable using the text books used in the course. Solutions should not be readily available either in the course text books, or in other books that are easily accessible at Chalmers. Suggested exam problems may be in the form Describe how you would proceed if you were asked to solve the following problem:, or in a different form that lends itself to being solved without access to text books or notes. The proposed exam problems should not be of the essay type (e.g. Define a retarded Green's function and discuss its uses would not be acceptable}. The exam problems should take at most 20 minutes to answer, and their solution should demonstrate that the student has learned and understood the techniques .

Projects are graded based on the originality of the problems, their relevance to the course, and the extent to which they complement problems in the current list of problems. The quality of problems is more important than the quantity, and a maximum grade for the project does not require that a maximum number (=4) of problems are submitted. Some of the suggested problems may appear as home problems or exam problems in the following years. Note: If you choose to submit a project, be sure to list all references you have used. Copying unreferenced sources constitutes plagiarism, which is a serious offense with disciplinary consequences.
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Home problems.

A collection of home problems is available here (PostScript file).

Issues related to home problems (typos, deadlines, graders etc.) will be published here.