Download 112C_syllabus

Math 112C Suggested Syllabus
Text: A First Course in Partial Differential Equations, H.F Weinberger
Plus supplementary notes found at:
http://www.math.uci.edu/sites/math.uci.edu/files/Turing.pdf
http://www.math.uci.edu/sites/math.uci.edu/files/nonlinear.pdf
http://www.math.uci.edu/sites/math.uci.edu/files/firstorder.pdf
Lecture
Section
1
2
3
4
5
6
38
38
39
40
40
41
7
42
8
9
10
11
12
13
14
15 -16 -17 -18 -19 -20 -21 -22 -23 -24
25
26
27
28
29
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42
43
43
44
45
Topic
Some properties of eigenvalues and eigenfunctions
Cont.
Equations with singular endpoints
Some properties of Bessel functions
Cont.
Vibrations of a circular membrane
Forced vibrations of a circular membrane, natural frequencies and
resonance
Cont.
The Legendre polynomials and associated Legendre functions
Cont.
Laplace’s equation in the sphere
Poisson’s equation and Green’s functions for the sphere
Review
Midterm
First order PDEs and the derivation of transport equations
Linear 1st order PDEs of type ut + cux = 0 and the method of
characteristics
Equations of type ut + c(x; t)ux = 0
Equations of type a(x; t)ut + b(x; t)ux + c(x; t)u =F(x; t)
Nonlinear 1st order PDEs: the inviscid Burgers equation. Implicit
solutions
Inviscid Burgers: the method of characteristics
Inviscid Burgers: compression and rarefaction waves
Inviscid Burgers: shock formation
Inviscid Burgers: conservation laws and construction of shock
solutions
Cont.
Viscous Burgers equations
Cont.
Reaction-diffusion equations and Turing instability
Cont.
Review