MATH 456/556: Partial Differential Equations
SYLLABUS
Course Syllabus (PDF)
NOTES
PDE's as conservation laws (PDF)
d'Alembert's solution to the wave equation (PDF)
Linearity and Linear Operators (PDF)
Greens functions and formulas (PDF)
Method of characteristics (PDF)
Exam 2 review problems (from Haberman's text) (PDF)
HOMEWORK/EXAMS
Homework 1 due Jan 25
Homework 2 due Feb 6
Homework 3 due Feb 13
Homework 4 due Feb 20
Exam 1, Feb 25.
Homework 5 due Feb 29
Homework 6 due Mar 12
Homework 7 due Apr 2
Exam 2, April 9.
Homework 8 due Apr 11
Homework 9 due Apr 21
Homework 10 due Apr 30
Homework 11 due May 7
Exam 3, May 2.
Other web resources
Can you hear the
shape of a drum?
Notes,
examples of 1-D Green's function (courtesy J. Lega)
One of many
Green's function tutorials
Brief table of Fourier transforms
Movies / graphics
Sine series example (movie) of
f(x) = 1 on [L/4,3L/4], 0 otherwise.
Diffusion equation (Dirichlet BC)
Diffusion equation (Neumann)
Vibrations of a rectangular drum head
Bessel functions
Vibrations of a
circular drum head
Historical note on George Green
Seismological Green's functions
Lord Kelvin and the age of the earth
Fundamental solution of the diffusion equation
Fundamental solution of the linearized KdV equation
Diffuse shock movie
Dispersive waves
Instabilities leading to patterns:
Instability of the KS equation: melting snow
Dewetting instability
Turing instabilies
Gray-Scott reaction diffusion model.
Look here for more pictures.