Math 442 Schedule


Date
Sections
Homework
Other readings
Programs
Homework answer
1/16(R)
1.1, 1.2
Homework 0(optional): Page 5 (5,6,7,8,9)
differential equation  PDE(wiki) PDE(scholarpedia)  millennium problems  Survey article
Applications of PDE: image processing climate Tsunami biology finance
Wolfram Alpha

1/21(T)
1.2
Homework 1 (due Jan 24): Page 5 (2a,2b,2c,2e,3d,3e,3f,11,12) Page 9 (1,3,6,9), Page 19 (6,9)
Chinese New Year Matlab: plotting a solution of 1st PDE
HW1 solution
1/23(R)
1.3

Laplace operator in polar/spherical coordinate
spherical coordinates  Divergence


1/28(T)
1.3
Homework 2: (due Jan 31): pdf file
Diffusion Molecular diffusion  diffusion coefficient
Fick's law Fourier's law heat equation Laplace operator 
Matlab(transport equation):
pulse
HW2 solution
1/30(R)
1.4,1.5,1.6
Wave equation  vibrating string vibration of drum
Jean le Rond d'Alembert  continuity equation


2/4(T)
2.1, 2.2
Homwork 3: (due Feb 7) Page 38 (2,3,8), Page 41 (2,5), Page 45 (1,4)
Joseph Liouville
Matlab(wave equation):
plucked string  hammer
HW3 solution
2/6(R)
2.3, 2.4


Youtube (calculate integral of exp(-x^2)
2/11(T)
2.4, 2.5
Homework 4: (due Feb 14) Page 52 (4,9,15,16)(if you do not know how to solve 6, see Youtube video in "programs"), Page 89(2,3,4)
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
HW4 solution
2/13(R)
4.1
Project



2/18(T)
4.2, 4.3
Homework 5: (due Feb 21) Page 92(2,4), Page100(1,9,11)

Matlab: eigenfunction 1, 2, 3, Robin Eigenvalue
HW5 solution
2/20(R)
5.1
Midterm exam 1 (due Mar 11) Joseph Fourier  pi Leibniz formula for π
Euler's formula for pi trig formulas

Exam 1 solution
2/25(T)
5.2, 5.3

Legendre Polynomial wavelet Matlab: fourier 1, 2, 3, 4 wave with boundary 1, 2

2/27(R)


Turing pattern talk quantum graph talk


3/1-3/9
Spring Break





Date
Sections
Homework
Other readings
Programs
Homework Answers
3/11(T)
5.4,
Homework 6: (due March 14) Page 111(2,4,8), Page 118(11,12), Page 123(8)

HW 6 solution
3/13(R)
5.5, Pi day Project title due (see below for possible topics) trig formula Gibbs Phenomenon
Matlab: Dirichlet, Gibbs

3/18(T)
6.1
Homework 7: (due March 21) Page134(1,7) Page 160(2,4,5,11) Page 164(1,3) Possion's equation Laplace equation
Matlab pdetool
HW7 solution
3/20(R)
6.2

Laplace in 3D
spherical harmonics


3/25(T)
6.3,6.4
Homework 8: (due March 28) Page172(2),Page176(3,6),Page184(2,5)


HW8 solution
3/27(R)
7.1-7.2

force gravitational force electrostatic force

4/1(T)
10.1, 10.4
Homework 9: (due April 4) Page264(4), Page 281(1,2)
Green's identities, Green's function, Newton potential
Matlab PDE
HW9 solution
4/3(R)
Turing patterns
Matlab PDE toolbox
bifurcation talk
Kelvin tranform eigenfunction of disk spherical harmonics
Legendre polynomials


4/8(T)
8.1-8.2
A talk of numerical solutions
Homework 10: (due April 11) Page 209(1,3,5)

Matlab: Forward Neumann
Forward Dirichlet
HW10 solution
4/10(R)
8.1-8.2
notes for numerical scheme



4/15(T)
some applications
Midterm exam 2(first draft for Math 300 paper due 4/21 Monday, email) Papers on Morphogen Gradient bacteria growth pattern

4/17(R)
presentation
Naman, Dan, Jamie, Joseph, Kaitlyn



4/22(T)
presentation
David, Haomiao, Robert, Samantha, Avi, Luke
Fisher's equation  Schrodinger's equation

4/24(R)
presentation
Arya, Sydney, Michael, Leslie, Guangxiong, Jintong,
KdV equation Soliton  Peregrine soliton
Sine-Gordon equation breather


5/4(F)

Exam 2 due 5/2 (Friday) 5pm (Jones 117), 



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