Math 442 Schedule


Date
Sections
Homework
Other readings
Programs
Homework answer
1/19(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

1/24(T)
1.2
Homework 1 (due Jan 27): 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
1/26(R)
1.3

Laplace operator in polar/spherical coordinate
spherical coordinates  Divergence


1/31(T)
1.3
Homework 2: (due Feb 3): pdf file
Diffusion Molecular diffusion  diffusion coefficient
Fick's law Fourier's law heat equation Laplace operator 
Matlab(transport equation):
pulse
HW2 solution
2/2(R)
1.4,1.5,1.6
Wave equation  vibrating string vibration of drum
Jean le Rond d'Alembert  continuity equation


2/7(T)
2.1, 2.2
Homwork 3: (due Feb 10) Page 38 (2,3,8), Page 41 (2,5), Page 45 (1,4)
Joseph Liouville
Matlab(wave equation):
plucked string  hammer
HW3 solution
2/9(R)
2.3, 2.4


Youtube (calculate integral of exp(-x^2)
2/14(T)
2.4, 2.5
Homework 4: (due Feb 17) 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
2/16(R)
4.1




2/21(T)
4.2, 4.3
Homework 5: (due Feb 27) Page 92(2,4), Page100(1,9,11)

Matlab: eigenfunction 1, 2, 3, Robin Eigenvalue
HW5 solution
2/23(R)
5.1
Midterm exam 1 (due Mar 13) Joseph Fourier  pi Leibniz formula for π
Euler's formula for pi trig formulas

Exam 1 solution
2/28(T)
5.2, 5.3

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

3/1(R)

Project title/abstract due (see below for posisble topics)
Turing pattern talk quantum graph talk


3/3-3/11
Spring Break





Date
Sections
Homework
Other readings
Programs
Homework Answers
3/13(T)
5.4, Pi day
Homework 6: (due March 19) Page 111(2,4,8), Page 118(11,12), Page 123(8)

HW 6 solution
3/15(R)
5.5

trig formula Gibbs Phenomenon
Matlab: Dirichlet, Gibbs

3/20(T)
6.1
Homework 7: (due March 23) Page134(1,7) Page 160(2,4,5,11) Page 164(1,3) Possion's equation Laplace equation
Matlab pdetool
HW7 solution
3/22(R)
6.2

Laplace in 3D
spherical harmonics


3/27(T)
6.3,6.4
Homework 8: (due March 30) Page172(2),Page176(3,6),Page184(2,5)


HW8 solution
3/29(R)
7.1

force gravitational force electrostatic force

4/3(T)
7.2-7.4
Homework 9: (due April 9) Page187(1), Page196(1,3,5,6,7)
Green's identities, Green's function, Newton potential

HW9 solution
4/5(R)
10.1,10.2,10.3,11.6

Kelvin tranform eigenfunction of disk spherical harmonics
Legendre polynomials


4/10(T)
12.1
Homework 10: (due April 20) Page337(4,12),Page342(2),Page349(9),Page352(1,2)
prove Page345 (7) and Page346 (iii)
distribution Dirac delta function Dirac Laurent Schwarz
fundamnetal solution

HW10 solution
4/12(R)
12.2

Fourier Transform
Laplace transform
convolution

4/17(T)
12.3

Airy function  Laplace transform


4/19(R)
12.4,12.5
Midterm exam 2(first draft for Math 300 paper due 4/23 Monday)
Papers on Morphogen Gradient bacteria growth pattern


4/24(T)
Presentation
Heidi, Nicholas, Matt L, Jonathan,
Fisher's equation  Schrodinger's equation

4/26(R)
Presentation
Gunhee, Kiah, Matt D KdV equation Soliton  Peregrine soliton
Sine-Gordon equation breather


5/1(T)
Presentation (9am)
Matt B, Albert, Tim, Amy, Julie, Christy


5/4(F)

Exam 2 due 5/4 (Friday) 5pm (Jones 122), project paper due 5/7 (Monday) 5pm (by email)


Posisble project ideas: (group projects: 1-2, 5-6, 13-14)

sample paper 1 2 3

  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. (Julie) Large-Amplitude Periodic Oscillations in Suspension Bridges (SIAM Review 1990)
  4. (Gunhee) Diffusion equation from Brownian motion (original paper by Robert Brown in 1827, paper (and English translation)
  5. (Christy) Can One Hear the Shape of a Drum? (Amer. Math. Monthly, 1966)  (Wiki: Hearing the shape of a drum)
  6. Drums That Sound the Same (Amer. Math Monthly, 1995)
  7. (Matt B) Two-lane traffic-flow model paper (PRE 2010)
  8. (Albert) Red blood cell model paper (Chaos 2009)
  9. Cellular Automata approach of biological models (JMB 1993)
  10. 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
  11. Tsunami and wave equation:  Tsunami and water wave equations (JDDE 2006)
        A talk by Walter Craig
        Another paper
  12. (Tim) Alan Turing's work of diffusion-induced instability: Turing100 conf1 conf2, Alan Turing year 1952 paper on biological pattern formation
  13. (Matt D) Cancer modeling (Roose, Chapman, Maini, SIAM Review 2007)
  14. (Heidi) Tumor modeling (Friedman 2010 AMS Notices; 2006 book chapter)
  15. Music and wave equation (a course in Duke; a course in UIUC; a course in Columbia) (The Mathematics of Musical Instruments, Amer. Math. Monthly, 2001)
  16. Transport process in enviromrntal studies (a course in MIT; a course in Duke)
  17. (Nicholas) Black-Scholes equation
  18. (Kiah) PDE models in neural studies
  19. (Amy) Evolutionary Game Theory in Economics
  20. Wave and Diffusion in quantum graph (possible CSUMS research)
  21. Reflection of waves and diffusion equations (Section 3.1-3.2) (use Matlab to simulate related solutions)
  22. Waves in 2D and 3D (Section 9.1-9.2) (use Matlab to simulate related solutions)
  23. (Jonathan, Matt L)Diffusion, Schrodinger and hytrogen atom equations (Section 9.4-9.5) (use Matlab to simulate related solutions)
  24. Bessell's equation, functions (Section 10.2, 10.5) (use Matlab to simulate related solutions)
  25. Spherical harmonics (Section 10.3, 10.6) (use Matlab to simulate related solutions)
  26. Shock waves, traffic flow model (Section 14.1)
  27. Solitons (Section 14.2)
  28. Water wave equation (Section 14.5)

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