Math 442 Schedule

Date	Sections	Lecture Notes	Homework	Other readings	Programs	Homework answer
1/21(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 biology finance econnomics socio-economic sciences	Wolfram Alpha
1/26(T)	1.2	Lecture 2	Homework 1 (due Jan 29)		Matlab: plotting a solution of 1st PDE	HW1 solution
1/28(R)	1.3	Lecture 3		Laplace operator in polar/spherical coordinate spherical coordinates Divergence
2/2(T)	1.3	Lecture 4	Homework 2: (due Feb 5)	Diffusion Molecular diffusion diffusion coefficient Fick's law Fourier's law heat equation Laplace operator	Matlab(transport equation): pulse	HW2 solution
2/4(R)	1.4,1.5,1.6	Lecture 5		Wave equation vibrating string vibration of drum Jean le Rond d'Alembert continuity equation
2/9(T)	2.1	Lecture 6	Homework 3: (due Feb 12)	Joseph Liouville Chinese New Year	Matlab(wave equation): plucked string hammer	HW3 solution
2/11(R)	2.2	Lecture 7			Youtube (calculate integral of exp(-x^2) solution of diffusion equation and wave equation (Pugh) Silvestre's solver
2/16(T)	2.3, 2.4	Lecture 8	Homework 4: (due Feb 22)	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
2/18(R)	2.4, 2.5	Lecture 9			gravitational waves: Einstein field equation, linearized equation another one
2/23(T)	4.1	Lecture 10	Homework 5: (due March 2)		Matlab: eigenfunction 1, 2, 3, Robin Eigenvalue	HW5 solution
2/25(R)	4.2-4.3			Joseph Fourier pi Leibniz formula for π Euler's formula for pi trig formulas 14 proofs of Euler's formula		Exam 1 solution
3/1(T)	5.1	Lecture 11	Midterm exam 1 (due Mar 15) reference	Legendre Polynomial wavelet
3/3(R)				Turing pattern talk quantum graph talk
3/5-13	Spring Break

Date	Sections	Lecture	Homework	Other readings	Programs	Homework Answers
3/15(T)	5.2	Lecture 12	Homework 6: (due March 18)	Matlab Fourier series fitting	Matlab: fourier 1, 2, 3, 4 wave with boundary 1, 2	HW 6 solution
3/17(R)	5.3-5.4	Lecture 13		trig formula Gibbs Phenomenon	Matlab: Dirichlet, Gibbs
3/22(T)	5.5	Lecture 14	Homework 7: (due March 25)	Possion's equation Laplace equation	Matlab pdetool	HW7 solution
3/24(R)	6.1-6.2	Lecture 15		Laplace in 3D spherical harmonics
3/29(T)	6.3,6.4	Lecture 16				HW8 solution
3/31(R)	7.1-7.2	Lecture 17	Homework 8: (due April 1)	force gravitational force electrostatic force
4/5(T)	7.2-7.3	Lecture 18		Green's identities, Green's function, Newton potential	Matlab PDE	HW9 solution
4/7(R)	7.3-7.4	Lecture 19		Kelvin tranform eigenfunction of disk spherical harmonics Legendre polynomials
4/12(T)	7.4, 10-11	Lecture 20	Homework 9: (due April 13, Wednesday)	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	HW10 solution
4/14(R)	12.1-12.2	Lecture 21
4/19(T)	12.3-12.4	Lecture 22	Homework 10: (due April 27, Wednesday)	Papers on Morphogen Gradient bacteria growth pattern
4/21(R)	12.5	Lecture 23		NIST Fourier transform
4/26(T)	8.1-8.2	Lecture 24	Midterm exam 2	Fisher's equation Schrodinger's equation KdV equation Soliton Peregrine soliton Sine-Gordon equation breather
4/28(R)	research topics	Lecture 25		Quantum graph Turing instability Turing 1952 Kondo-Miura 2010
5/6(F)			Exam 2 due 5/6 (Friday) 12noon (Jones 117),

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