Math 442 Schedule

Date	Sections	Lecture Notes	Homework	Other readings	Videos/software
1/18(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
1/23(T)	1.2	Lecture 2	Homework 1 (due Jan 26)		Matlab: plotting a solution of 1st PDE Diffusion (intuition) Diffusion
1/25(R)	1.3	Lecture 3		Laplace operator in polar/spherical coordinate spherical coordinates Divergence
1/30(T)	1.3	Lecture 4	Homework 2: (due Feb 2)	Diffusion Molecular diffusion diffusion coefficient Fick's law Fourier's law heat equation Laplace operator	Matlab(transport equation): pulse
2/1(R)	1.4,1.5,1.6	Lecture 5 ODE reference		Wave equation vibrating string vibration of drum Jean le Rond d'Alembert continuity equation	Vibration of strings
2/6(T)	2.1	Lecture 6	Homework 3: (due Feb 9)	1st order linear ODE 2nd order linear ODE	Matlab(wave equation): plucked string hammer
2/8(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
2/13(T)	2.3, 2.4	Lecture 8	Homework 4: (due Feb 16)	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
2/15(R)	2.4, 2.5				gravitational waves: Einstein field equation, linearized equation another one
2/20(T)	4.1	Lecture 9	Homework 5: (due Feb 23)		Matlab: eigenfunction 1, 2, 3, Robin Eigenvalue
2/22(R)	4.2-4.3	Lecture 10		Joseph Fourier pi Leibniz formula for π Euler's formula for pi trig formulas 14 proofs of Euler's formula
2/27(T)	5.1	Lecture 11	reference	Legendre Polynomial wavelet
3/1(R)			Midterm Exam	Turing pattern talk quantum graph talk
3/3-11	Spring Break

Date	Sections	Lecture	Homework	Other readings	Programs
3/12(T)	5.2	Lecture 12	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 26)	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 April 2)
3/28(R)	6.4	Lecture 17		force gravitational force electrostatic force
4/3(T)	8.1, 8.2	Lecture 18	Homework 9: (due April 9)	Green's identities, Green's function, Newton potential	Matlab PDE
4/5(R)	8.2	Lecture 19		Kelvin tranform eigenfunction of disk spherical harmonics Legendre polynomials
4/10(T)	7.1-7.2	Lecture 20	Homework 10: (due April 16)	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
4/12(R)	10.1,10.4	Lecture 21
4/17(T)	12.1-12.2	Lecture 22	Homework 11: (due April 25)	Papers on Morphogen Gradient bacteria growth pattern
4/19(R)	12.3	Lecture 23		NIST Fourier transform
4/24(T)	12.4-12.5			Fisher's equation Schrodinger's equation KdV equation Soliton Peregrine soliton Sine-Gordon equation breather
4/26(R)	research topics	Lecture 24		Quantum graph Turing instability Turing 1952 Kondo-Miura 2010
5/7(M)			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)

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Zhouping Xin's course

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UIUC course