# Physics 466 Mathematical Methods of Theoretical Physics

Mathematical Methods for Theoretical Physics (466-001)

Fall 2004 Mondays and Wednesdays from 15:30 to 16:45 in room 184. My e-mail address is cahill@unm.edu. My office is room 176, and my phone number is 277-5318. My office hours are by appointment. But in fact whenever you see me, I am available for questions about this course.

The grader is Mr. Zahyun Ku. His phone number is 254-2780. His e-mail address is Zahyun@unm.edu.

My handwritten notes are available as the pdf file(s): lectures1-2 and lectures3-4 (On page 29 of lecture 4, (Psi_j)_l should be V*_{jl} not V*_{lj}.).

A pdf file on Fourier series, Fourier transforms, complex-variable theory, and tensors is available as the file nascent book.

Other notes of mine are available as the pdf files pages 1-35, pages 36-70, pages 71-105, pages 106-139, pages 140-184, pages 185-215 (on Lie algebras), pages 216-230, pages 231-239, and examples of contour integration pages 228-252, pages 253-266, 266-282, 283-303, 304-329, 330-336, 337-352, 353-363, 364-382, 383-397, 398-406, 407-419, 420-442, 443-457, and 458-463.

Students should read through chapters 1 - 4 at a sensible pace.

First homework assignment: Do the two problems assigned in class as well as these from Arfken & Weber: 1.1.11, 1.3.4, 1.4.1, 1.4.16, 1.5.5, 1.5.6, 1.5.18. This first homework assignment is due in class on Monday 9/13/4.

Solutions.

Second homework assignment: Do problems 3.1.2, 3.2.(2,7,9,13,14,15,16), 3.3.12, 3.4.(7,9), 3.6.20, and also these special problems:

1. Consider the 2 x 3 matrix A with elements ( 1 2 3) (-3 0 1). (A(1,1) = A(2,3) = 1, etc.) Perform the singular value decomposition A = U S V' where V' is the transpose of V. Find the singular values and the real matrices U and V.

2. Consider the 6 x 9 matrix A with elements A(j,k) = x + x**j + i*(y - y**k) where x = 1.1 and y = 1.02 and * means multiplication while ** means exponentiation. Find the singular values, and the first left and right singular vectors. Lapack is one way to do this problem.

Those who want Lapack on their PCs can get it here, where they will find ways to download linux rpms.

This assignment is due on 10/4.

Solutions.

Third homework assignment: Do problems 14.1.(1,3,8); 14.3.5; & 14.4.(2,9,10,11) by 10/20/4.

Solutions.

Fourth homework assignment: Do problems 15.3.(6, 10, 16); 15.4.(1, 3, 4); 6.1.1; and 6.2.1 by 11/1/4.

Solutions.

Fifth homework assignment: Do problems 6.2.4; 6.4.4; 6.5.8; 6.7.1; 7.1.4; 7.2.(5, 7, 14, 16) by 11/17/4.

Solutions.

Sixth homework assignment: Do problems 8.2.14, 8.3.5, 8.5.5, 8.6.9, 8.6.15, 9.1.4, 9.2.5, 12.3.15, 12.5.15 by 12/1/4.

Solutions.

Take-home-exam problems: 14.3.6, 14.3.7, and 11.7.27. Final problem: Imagine a huge sphere of ice in space that initially is at rest under no pressure (of course, its own gravity will cause increasing pressure as time goes by). How big (in km) must the radius of the sphere be for the ice to be a black hole? Neglect evaporation and use the nominal density of water as the density of ice. Hint: use the relevant equation of the section on black holes near the end of chapter 5 of the notes -- the file "nascent book." You may turn this answer in on the day after the final but no later.

The final examination is from 5:30 to 7:30 pm on Wednesday, 15 December, in room 184. Please turn in your take-home final-exam solutions by that day and the last question by the next day.

Solutions to the problems of the take-home exam.