Math 442 Schedule


Date
Sections
Lecture Notes
Homework
Other readings
Videos/software
1/17(R)
1.1, 1.2
Lecture 1
Homework 0 (do not turn in)
differential equation  PDE(wiki) PDE(scholarpedia) 
millennium problems  Survey article
Applications of PDE: image processing
climate Tsunami developmental biology
finance econnomics socio-economic sciences
Wolfram Alpha
1/22(T)
1.2
Lecture 2
Homework 1 (due Jan 25)

Matlab: plotting a solution of 1st order PDE
Diffusion (intuition)
Diffusion
1/24(R)
1.3
Lecture 3

Laplace operator in polar/spherical coordinate
spherical coordinates  Divergence

1/29(T)
1.3
Lecture 4
Homework 2: (due Feb 1)
Diffusion Molecular diffusion  diffusion coefficient
Fick's law Fourier's law heat equation Laplace operator 
Matlab(transport equation):
pulse
1/31(R)
1.4,1.5,1.6 Lecture 5


Wave equation  vibrating string vibration of drum
Jean le Rond d'Alembert  continuity equation
Vibration of strings
2/5(T)
2.1
Lecture 6
Homework 3: (due Feb 11)
1st order linear ODE
2nd order linear ODE

Matlab(wave equation):
plucked string  hammer
2/7(R)
2.2
Lecture 7
Joseph Liouville Youtube (calculate integral of exp(-x^2)
solution of diffusion equation and wave equation (Pugh)
Silvestre's solver
2/12(T)
2.3, 2.4 Lecture 8 Homework 4: (due Feb 15)
random walk  Brownian motion binomial distribution   
Normal Distribution error function
random walk  random walk 2d random walk 3d Brownian motion Binomial dis Normal dis
heat eq 1 heat eq 2
2/14(R)
2.4, 2.5
Lecture 9

gravitational waves: Einstein field equation, linearized equation
another one
2/19(T)
4.1-4.3
Lecture 10 Homework 5: (due Feb 22)

Matlab: eigenfunction 1, 2, 3, Robin Eigenvalue
2/21(R)
5.3
Lecture 11
Joseph Fourier pi Leibniz formula for π 
Euler's formula for pi trig formulas
14 proofs of Euler's formula

2/26(T)
5.1-5.2 Lecture 12 reference
Legendre Polynomial wavelet
2/28(R)


Midterm Exam
Turing pattern talk quantum graph talk

3/2-10
Spring Break





Date
Sections
Lecture
Homework
Other readings
Programs
3/12(T)
5.2

Homework 6: (due March 15)
Matlab Fourier series fitting
Matlab: fourier 1, 2, 3, 4
wave with boundary 1, 2
3/14(R)
5.3-5.4 Lecture 13

trig formula Gibbs Phenomenon
Matlab: Dirichlet, Gibbs
3/19(T)
5.5
Lecture 14
Homework 7: (due March 22) Possion's equation Laplace equation
Matlab pdetool
3/21(R)
6.1-6.2
Lecture 15

Laplace in 3D   spherical harmonics
3/26(T)
6.3
Lecture 16
Homework 8: (due March 29)

3/28(R)
6.4
Lecture 17

force gravitational force electrostatic force
4/2(T)
8.1, 8.2
Lecture 18
Homework 9: (due April 5) Green's identities, Green's function, Newton potential
Matlab PDE
4/4(R)
8.2
Lecture 19

Kelvin tranform eigenfunction of disk spherical harmonics
Legendre polynomials

4/9(T)
7.1-7.2
Lecture 20
Homework 10: (due April 12)

Can One Hear the Shape of a Drum? (Amer. Math. Monthly, 1966)  (Wiki: Hearing the shape of a drum)Drums That Sound the Same (Amer. Math Monthly, 1995)
Rayleigh–Faber–Krahn inequality isoperimetric inequality
Matlab: Forward Neumann
Forward Dirichlet
4/11(R)
10.1,10.4
Lecture 21



4/16(T)
12.1-12.2
Lecture 22
Homework 11: (due April 19)
Papers on Morphogen Gradient bacteria growth pattern
4/18(R)
12.3
Lecture 23

NIST Fourier transform

4/23(T)
12.4-12.5


Fisher's equation  Schrodinger's equation KdV equation Soliton  Peregrine soliton
Sine-Gordon equation breather

4/25(R)
research topics
Lecture 24

Quantum graph  Turing instability Turing 1952 Kondo-Miura 2010

4/30(T)


Final Exam


Possible Math 300 topics
  1. Derive wave equation: Strings, Chains, and Ropes (SIAM Review 2006) (The Equations for Large Vibrations of Strings, Antman, 1980)
  2. How realistic is the D’Alembert plucked string (Euro. J. Phys, 1999)
  3. Can One Hear the Shape of a Drum? (Amer. Math. Monthly, 1966)  (Wiki: Hearing the shape of a drum)
  4. Drums That Sound the Same (Amer. Math Monthly, 1995)
  5. Eigenvalues of Laplace on a L-shaped domain
    a link    Review paper (SIAM 1984)  For equilateral triangle (SIAM 1980)  a REU work   From Cleve Moler (creater of Matlab) Matlab logo
  6. Music and wave equation (a course in Columbia) (The Mathematics of Musical Instruments, Amer. Math. Monthly, 2001)
  7. Transport process in environmental studies (a course in MIT)
  8. Modeling mixing problem for multiple tanks with PDE (ODE setting, two tank problem)
Other courses using the same textbook

Peter Olver's course
   

Staffilani's course

Bei Hu's course

Zhouping Xin's course

UCSD course

U Penn course

UIUC course