SIO239: Math Methods for Geophysics, 2008

Instructors: Glenn Ierley and Bob Parker

Notice

This is the website for a class taught in the Fall Quarter of 2008, now ended. Links to homework solutions have been removed, but those to the class notes remain in place.

Organization and Syllabus

The class is organized loosely around the text Mathematical Methods for Physics and Engineering by Riley, Hobson and Bence. We will select chapters from the text, or provide additional notes, to cover topics essential to geophysics as we teach it at IGPP. In particular we will certainly cover linear algebra and Fourier analysis. Depending on the students' needs we may treat complex variables, mathematical optimization, or calculus of variations, among other things.

There will be weekly homework and your grade in the class will be determined on your performance in whole or in part, depending on whether we decide to hold a Final Examination, which at this point is an open question. The homework questions will be posted on this website.

Diary

11/27/08: And here is the final homework assignment and its associated data set. Your solution must be handed in on or before 12/11/08.

11/26/08: Prof Ierley has asked me to post the MATLAB script for the solution of the survey problem covered in class yesterday: here it is.

11/06/08: I have posted Prof Ierley's second assignment.

11/03/08: I have graded your last homework, which I will return tomorrow. My solution to set 5 is now available, including a proof that that sech(&pi t) is its own FT.

10/30/08: Here is the first of Prof Ierley's homework.

10/28/08: Here is the official solution to homework set 4 that you have all been waiting for. Stayed tuned for set 5.

10/21/08: The 5th and final homework assignment has been posted. Your answers are due as usual next Tuesday.
There is a typo in equation (5.21) of the Notes, p 20: The first exponential factor has the wrong sign and should be
exp(+2&pi i m M &Delta t &Delta &nu)
This could be important for the 5th homework. You may also wish to read the solution to set 3. Question 2 seems to have mystified most of you, so I hope these pages will give enlightenment.

10/15/08: For next time here is the 2nd batch of Fourier transform notes.

10/14/08: I have uploaded my solutions to the 2nd homework. Many of you did a great deal of algebra for these exercises. If you seem to need massive algebra, you are probably doing something wrong, so think again, and if that fails, come and see me for a hint.
And, speaking of homework, here is the 4th set, due next Tuesday.

10/08/08: First here are some notes on the Fourier transform which we take up tomorrow. Also I have written and uploaded a page on how the SH Addition Theorem is a special case of rotation of coordinates, which may have been a bit confusing in class yesterday.

Finally, here for your amusement is a file of matlab M-files illustrating the shapes of multipole potentials; I will we running through these tomorrow and you may want to experiment with them yourself.

10/07/08: The solution to the first homework has been uploaded. Also here is the third homework set, due next Tuesday. I will post the next set of lecture notes later today or tomorrow.

10/02/08: I have simplified the Section 6 which was a bit messy. Here is the improved version. Also you might like to see the geoid power spectrum which will briefly discuss today.

10/01/08: I decided rather than go onto Fourier transforms, to insert a discussion of spherical harmonics. Here is the notes for tomorrow's class.

9/30/08: I have uploaded the second homework set. It is due next Tuesday. This one requires the use of MATLAB. You should all have computer accounts and access to this program by now.

9/26/08: I would like to revise the new class start time to 2:00 PM. I will be in the Munk Conference Room on Tuesday 9/30/08 at that time.
The outline of Fourier material that appeared earlier on this site has been moved to here.

9/24/08: Here is the first set of notes on Fourier series viewed as orthogonal functions. And getting off to a good start, the first homework set due next Tuesday.