Lecturer		Teaching assistants
Ph236c  Lee Lindblom    extension: 4911  email: lindblom {at} tapir.caltech.edu Lectures: 9:00 - 10:30 AM Monday, Wednesday 107 Downs		Hua Fang  165B West Bridge email: hua {at} caltech.edu   Geoffrey Lovelace 127 Bridge Annex extension: 4221 email: geoffrey {at} caltech.edu

Information relevant to Ph236:

Readings for the class are available here. This area of the website is available only to the class because of copyright issues. When you link to the readings page, you will be prompted for a name and password. The name is Ph236. The password was given out in lecture. If you have problems accessing this page, email Geoffrey.

Assignments, solutions, and other handouts for both terms are available:

• Ph 236a
• Ph 236b
• Ph 236c

• Procedures and outlines
Course outline (updated March 27, 2006)
• Week 21
• Assignment 21 (due Monday, April 3)
• Solution set 21
• Week 22
• Assignment 22 (due Wednesday, April 12)
• Solution set 22
• Week 23
• Assignment 23 (due Wednesday, April 19)
• Solution set 23 - for the analytic problems.
• Solution set 23 - finite difference advection equation. I wrote this code to be easy to understand rather than to worry about efficiency. Also, there may be some bugs that I haven't caught yet, so take this "solution" with a grain of salt. However, it does appear to be working more or less correctly; I include a convergence plot and a plot of the solution at several times that demonstrate this. I didn't include the plots of how things go bad when you use the wrong boundary condition or a step size bigger than the Courant limit. If you are actually using this solution, it will be more useful for you to get the code and play with it than to glance through it and say "That's what I would have done!" So I left these graphs out, so you can tinker with the code to see how breaking it affects the results. The solution is in C++ (the language we use in the numerical relativity group here at Caltech). For Mac OS X users, I include an xcode project. Email me (Geoffrey) if you are having trouble getting this code to work.
• Week 24
• Lecture Notes
• Assignment 24 (due Friday, April 28)
• Solution set 24
• Week 25
• Assignment 25 (due Monday, May 8)
• Week 27
• Assignment 27 (due Monday, May 15)
• Solution Set 27
• Week 28
• Assignment 28 (due Friday, May 26)
• Notes on Spectral Differentiation These notes from Lee tell you how to use Gauss-Lobatto colocation points, which are at the extrema of the Chebyshev polynomial of order 2N (the points suggested on set 23 were at the zeroes of the Chebyshev polynomials of order 2N). The advantage of Gauss-Lobatto points is that they include a point at x=-1 and x=+1, which means you can apply boundary conditions there. I never got my spectral code to work until I switched to Gauss-Lobatto points, but after switching, everything worked fine. --Geoffrey

• Procedures and outlines
Course outline (updated January 4, 2006)
• Week 11
• Assignment 11 (due Wednesday, January 11)
• Solution set 11
• Week 12
• Assignment 12 (due Wednesday, January 18 at the beginning of class)
• Solution Set 12
• Week 13
• Assignment 13 (due Wednesday, January 25 at the beginning of class)
• Solution Set 13
• Week 14
• Assignment 14 (due Wednesday, February 1, at the beginning of class)
• Solution Set 14
• Week 15
• Assignment 15 (due Wednesday, February 8, at the beginning of class)
• Solution Set 15
• Week 16
• Assignment 16 (due Wednesday, February 15 at the beginning of class)
• Solution set 16
• Week 17
• Assignment 17 (due Wednesday, February 22 at the beginning of class)
• Solution Set 17
• Week 18
• Assignment 18 (due Wednesday, March 1 at the beginning of class)
• Solution Set 18
• Week 19
• Assignment 19 (due Wednesday, March 8 at the beginning of class)
• Solution 19: Part 2 (problem 2-5)

• Assignment 20 (no due date; will not be graded)
• Solution Set 20
• Ph136 Assignment 27 (no due date; will not be graded)

• Procedures and outlines
Course procedures (updated Oct. 1, 2005)
Questionaire
Course Outline

• Week 1 (office hour: Geoffrey Lovelace)
• Assignment 1 (due October 5,2005 at the beginning of class)
• Solutions set 1
• Rob Owen's solutions for set 1 (problems 1-7 only).
• A note on trigonometry and problem 1.4
• Week 2 (office hour: Hua Fang)
• Assignment 2 (due October 12, 2005)
• Solution set 2: part 1 (for problem 1-3), part 2 (problem 4-13) and part 3 (problem 14)
• Week 3 (office hour: Yi Pan)
• Assignment 3 (due October 19, 2005 at the beginning of class)
• Solution set 3
  
• Week 4 (office hour: Geoffrey Lovelace)
  • Assignment 4 (due Thursday, October 27 at 5PM in the tray in 124 Bridge Annex)
  • Solutions to set 4 (except for problem 8...Geoffrey will post problem 8's solution as soon as possible)
  • Geoffrey's notebook for coordinate basis calculations and set 4 solutions Right click and choose "Save as..." to download. If you just click the link, your browser will load the entire notebook as plain text, which may take a good approximation of forever to finish. Warning! This is provided for you to learn from. Feel free to employ any code you see here in your future problem sets, but I make no warranty about its accuracy [ I always wanted to write an EULA :-) ], and I will have no sympathy on wrong answers on problem sets due to not understanding the code you are using! Make sure you give me credit if you copy this code for some project of your own (beyond the problem sets).
• Week 5 (office hour: Hua Fang)
  • Assignment 5 (due Thursday, November 3 at 5PM in the tray in 124 Bridge annex)
  • Solution set 5
    
• Week 6 (office hour: Yi Pan)
  • Assignment 6 (due Thursday, November 10 at 5PM in the tray in 124 Bridge annex)
  • Solution set 6
    
• Week 7 (office hour: Geoffrey Lovelace)
  • Assignment 7
  • Solutions to set 7 (except 7.3b,7.7, and 7.8)
  • Solutions to 7.3b, 7.7, and 7.8
• Week 8 (office hour: Hua Fang)
  • Assignment 8 (due Wednesday, November 23 at 5PM due to the Thanksgiving Holiday)
  • Solution set 8
• Week 9 (office hour: Yi Pan)
  • Assignment 9 (due Thursday, December 1 at 5PM in the tray in 124 Bridge annex)
    
  • Solution set 9
    
• Week 10 (office hour: Geoffrey Lovelace, Tuesday, from 4-6PM, in Geoffrey's office)
• Assignment 10 (due Thursday, December 8 at 5PM in the tray in 124 Bridge annex)
  
• Solution set 10

• A short sample Maple calculation in the de Sitter spacetime has been written by Rob Owen. If you're not familiar with Maple or Mathematica yet, this can be sort of a nitty-gritty introduction.
PDF, Maple Source
• If you're interested in doing calculations in Mathematica, a very good resource is Jim Hartle's new book Gravity: an Introduction to Einstein's General Relativity . The book was written in the post-mathematica age, and notebook files are included to produce such things as Christoffel symbols, curvature tensor components and such. Some are even included in the companion website.
• A list of software packages for symbolic differential geometry and tensor algebra calculations can be found by clicking on the links button here.
• A link to the Ph236 homepage for 1995-1996 (includes some possibly useful information about setting up and using various tensor manipulation software packages at ITS and in Wonderland. WARNING: some of this may be severely out of date.)
• Current information about using GRTensorII in Wonderland.
• Instructions on installing and using GRTensorII on your ITS account.

Other links

• TAPIR, the Caltech Theoretical Astrophysics and Relativity Group.
• No self-respecting web page for a course on general relativity at Caltech would be complete without the obligatory link to LIGO.
• The gr-qc eprint archive at Los Alamos contains recent papers on general relativity and cosmology.
• If you're in the mood to kill some time, but want something more interesting than computer solitaire, you might dig the Purdue University Math Problem of the Week.