SIO 215b Math Methods for Oceanographers 2010
M. Hendershott - mhendershott@ucsd.edu
G. Ierley - grierley@ucsd.edu
C. Winant - cwinant@ucsd.edu

Class meets in the Munk conference room (west end of IGPP bldg) on Tu-Th @9:30

This term each instructor will directly mail out in pdf form all class handouts, homeworks and assignments.  As before, all assignments are due back typeset (not handwritten) in pdf documents.

Syllabus

Date
Tentative Topic
Reading
  5 Jan
Wave equation and Helmholtz equation, 1-d initial value problem by characteristics

  7 Jan
Initial value problems in 3-d
12 Jan
Plane waves, waveguide modes, 1-dl forced initial value problem
14 Jan
1-d waveguide forced initial value problem, harmonically  forced 1-d and 2-d solutions
19 Jan
Bessel functions, normal modes circular basin
21 Jan
Plane wave incident on cylinder, waves in gulf
26 Jan
Numerical 1 transition to 2D problems via the advection-diffusion equation;
28 Jan
Numerical 2 advancing in time by means of a propagator (applicable to parabolic or hyperbolic)

 2 Feb
Numerical 3 Gaussian quadrature (to add to the general tool box)
 4 Feb
Mid-term
 9 Feb
Waves in non-homogeneous media:WKB
11 Feb
One-d non-linear: eta_t+c(eta)eta_x=0
Witham
16 Feb
Burger: the Cole-Hopf transformation

18 Feb
Burger: Steepening

23 Feb
KdV

25 Feb
Numerics 2: nonlinear PDEs - the material above will have laid the
groundwork by way of direct motivation & with some sense of how the solutions *ought* to behave.

 2 Mar
Numerics 2: With nonlinearity, the challenges are enough that it will be back to 1D, as with the evolution eqs above.
 4 Mar
Numerics 2 Numerical stability here is a key idea, but now very much more subtle than solving the linear recurrence relations from fall quarter.
 9 Mar
Non-linear: rectification I

11 Mar
Non-linear: rectification II