Date

Tentative
Topic

Reading

5 Jan

Wave equation and Helmholtz equation, 1d
initial value problem by characteristics



7 Jan

Initial value problems in 3d 

12 Jan

Plane waves, waveguide modes,
1dl forced initial value problem 

14 Jan

1d waveguide forced initial
value problem, harmonically forced 1d and 2d 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 advectiondiffusion 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

Midterm 

9 Feb

Waves in nonhomogeneous
media:WKB 

11 Feb

Oned nonlinear:
eta_t+c(eta)eta_x=0

Witham

16 Feb

Burger: the ColeHopf
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

Nonlinear: rectification I


11 Mar

Nonlinear: rectification II

