EESC G9810 - Mathematical Earth Science Seminar: Vibration and Waves
Spring 2003

Welcome to the home page for G9810 - Vibration and Waves. I will try to keep this page updated. The course syllabus, schedule for the lectures, homework problems and solutions will be posted on this page.

The subject (such as it is) of "waves" is enormous. Practically, all the physical and engineering sciences use concepts such as eigenmodes, resonance, and dispersion which fall under this general area. Such is the breadth and applicability of this subject that it is often said (only half jokingly) that as a scientist your goal should be to reduce every phenomenon to the simple harmonic oscillator. Beyond being just tremendously useful, this subject is also mathematically beautiful. Most of the fundamental areas of applied mathematics (functional analysis, integral transforms, asympotics, etc.) arise quite naturally when we try to solve "wave" problems.

This course is really an attempt to combine three courses into one:
(2) an applied mathematics course in linear algebra and PDEs, and
(3) a course on waves in geophysical fluids.
(1) and (2) are rarely seen together, and (3) assumes you already know everything taught in (1) and (2)! Most of you are eager to get to the applications (to ocean-atmosphere waves, etc.), and we will. Unfortunately (or fortunately, depending on your point of view) a lot of conceptual and mathematical ground has to be covered before we can quantitatively treat a problem as complicated as, say, Rossby adjustment. This does not mean, however, that the course will be "too "abstract and mathematical". In fact, we will encounter and solve plenty of "practical" problems (such as computing eigenmodes and phase speeds in the WKBJ limit). Whether this experiment to teach such vast subjects in a unified way will succeed remains to be seen, but to get the most out of this course I highly recommend you do the homework and attend the occasional recitation.

Schedule Class meets Mondays, 10:30 AM - 1:00 pm, at Lamont (Geochemistry Seminar Room).

Required Textbook: Vibrations and Waves, A. P. French (Norton).

Other Recommended Textbooks for Reference:
Vibration and Waves in Physics, I. Main (Cambridge).
Atmosphere-Ocean Dynamics. A. E. Gill (Academic Press).
Elementary Applied Partial Differential Equations, R. Haberman (Prentice Hall).
Geophysical Fluid Dynamics, J. Pedlosky (Springer).
Mathematical Methods in the Physical Sciences, M. Boas (Wiley).
Physics of Waves, W. C. Elmore and M. A. Heald (Dover).
Vibration and Sound, P. M. Morse (Acoustical Society of America).
Waves in the Ocean, P. LeBlond and L. Mysak (Elsevier).

Books on Reserve:
French, Main, Gill, and Haberman will be on reserve in the Geoscience library.

Contact Information:

Samar Khatiwala
Oceanography 201
Lamont Doherty Earth Observatory
Columbia University

Email: spk@ldeo.columbia.edu
Phone: 845-365-8454
Fax: 845-365-8736

1. Acoustic and Vibration Animations
2. Coupled Oscillator MATLAB files:  m-files
3. Gravity Waves in a Layered Fluid:  (Mathematica notebook)
4. Table of Basic Integrals:  http://www.math.unb.ca/sections/integrals/
5. "The Integrator" web page from Mathematica:  http://integrals.wolfram.com/
6. Look-up Table of Integrals:  http://torte.cs.berkeley.edu:8010/tilu
7. Helmholtz Resonance:
http://www.phys.unsw.edu.au/~jw/Helmholtz.html
http://scienceworld.wolfram.com/physics/HelmholtzResonator.html
http://www.physics.brown.edu/Studies/Demo/waves/demo/3d3040.htm
8. Time-reversed Mirrors:
http://www.aip.org/mgr/png/2002/160.htm
9. Photonic Band-Gap Crystals:
http://www.aip.org/mgr/png/2003/178.htm
10. A useful note on uniform convergence of Fourier series and Gibb's phenomenon: http://amath.colorado.edu/courses/4350/2002fall/uniform.html
11. Sounding the ionosphere via dispersion of radar pulses: http://www.ngdc.noaa.gov/stp/IONO/Dynasonde

samar khatiwala