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 trig formulas 14 proofs of Euler's formula
2/26(T)	5.1	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	Lecture 13	Homework 6: (due March 15)	Matlab Fourier series fitting	Matlab: fourier 1, 2, 3, 4 wave with boundary 1, 2
3/14(R)	5.4	Lecture 14		pi Leibniz formula for π Euler's formula for pi	Matlab: Dirichlet, Gibbs
3/19(T)	5.5	Lecture 15	Homework 7: (due March 22)	trig formula Gibbs Phenomenon	Matlab pdetool
3/21(R)	6.1	Lecture 16		Possion's equation Laplace equation Laplace in 3D spherical harmonics
3/26(T)	6.2-6.3	Lecture 17	Homework 8: (due March 29)
3/28(R)	6.3-6.4, 7.1	Lecture 18		force gravitational force electrostatic force
4/2(T)	8.1, 8.2	Lecture 19	Homework 9: (due April 8)	Green's identities, Green's function, Newton potential	Matlab PDE
4/4(R)	8.2			Kelvin tranform eigenfunction of disk spherical harmonics Legendre polynomials	Matlab: Forward Neumann Forward Dirichlet
4/9(T)	12.1-12.3	Lecture 20	Homework 10: (due April 15)
4/11(R)	12.3-12.4			NIST Fourier transform FFT convolution Convolution and machine learning kernel
4/16(T)	10.1, 10.4	Lecture 21		Fermat two-square Legendre three-square Lagrange four-square
4/18(R)	research topics	Lecture 22		Quantum graph Turing instability Turing 1952 Kondo-Miura 2010 Papers on Morphogen Gradient bacteria growth pattern	Turing system Turing patterns
4/23(T)				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
4/25(R)				Fisher's equation Schrodinger's equation KdV equation Soliton Peregrine soliton Sine-Gordon equation breather
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