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:
(1) a traditional waves course taken by most physics undergraduates,
(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.
Problem Sets and Solutions
Lamont Doherty Earth Observatory
Palisades, NY 10964