Math 442 Schedule

Date	Sections	Lecture Notes	Homework	Other readings	Videos/software
1/23(R)	Chapter 1	Lecture 1		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
1/28(T)	2.1, 2.2	Lecture 2	HW1 (due 1/31): 1.1(bce), 1.4(bce), 1.5(bf), 1.10(b), 1.17(bce), 1.25, 2.1.1, 2.1.3(cd), 2.1.6, 2.2.2(ad), 2.2.3(ad), 2.2.4	1st order linear ODE 2nd order linear ODE Calculus, ODE formula sheet	Matlab: plotting a solution of 1st order PDE
1/30(R)	2.2, 2.3	Lecture 3			Matlab: plotting waves at several times Matlab: plotting level curves of f(t,x)
2/4(T)	2.4	Lecture 4	HW2 (due 2/7): 2.2.17, 2.2.20(ab), 2.2.27, 2.2.29, 2.4.1, 2.4.2, 2.4.4(ad), 2.4.8, 2.4.11	Wave equation vibrating string vibration of drum Jean le Rond d'Alembert deriving wave equation	Vibration of strings deriving wave equation
2/6(R)	3.1	Lecture 5		Trig formula sheet
2/11(T)	3.1	Lecture 6	HW3 (due 2/14): 3.1.2(b), 3.1.4(b), 3.2.1(ad), 3.2.2(a), 3.2.6(ad),
2/13(R)	3.2	Lecture 7		Diffusion Molecular diffusion diffusion coefficient Fick's law Fourier's law heat equation random walk Brownian motion binomial distribution	Matlab: random walk random walk 2d random walk 3d Brownian motion Binomial dis Normal dis
2/18(T)	3.3, 3.4	Lecture 8	HW4 (due 2/21): 3.2.14(adg), 3.2.15(d), 3.2.16(3.2.14(adg), 3.2.15(d)), 3.2.19(f), 3.2.40(a), 3.2.42(cosh(mx) only), 3.2.43, 3.2.51(ce), 3.2.53	Joseph Fourier 14 proofs of Euler's formula Legendre Polynomial wavelet B-spline	Matlab: Fourier 1, 2, 3, 4 Diffusion (intuition) Diffusion
2/20(R)	4.1	Lecture 9		Matlab Fourier series fitting	Matlab: eigenfunction 1, 2, 3, Robin Eigenvalue
2/25(T)	4.1,4.2	Lecture 10	HW5 (due 2/28): 4.1.6(abcd), 4.1.10(b), 4.1.16(ab), 4.2.3(cf), 4.2.6(abc)	pi Leibniz formula for π Euler's formula for pi	Matlab: wave diffusion
2/27(R)	4.2
3/3(T)	4.3	Lecture 11
3/5(R)	Midterm exam
3/7-15	Spring Break

Date	Sections	Lecture	Homework	Other readings	Programs
3/17(T)	COVID-19
3/19(R)	COVID-19
3/24(T)	4.3	Lecture 12	HW6 (due 3/30):4.3.10(a), 4.3.14, 4.3.25(ad), 4.3.27(a), 4.3.31	Possion's equation Laplace equation
3/26(R)	4.3	Lecture 13
3/31(T)	5.1	Lecture 14	HW7 (due 4/6): 4.3.34(e), 5.1.1(c), 5.1.2(c), 5.1.3(c), pdf
4/2(R)	5.2	Lecture 15
4/7(T)	6.1, 6.2	Lecture 16	HW8 (due 4/13) 6.1.1(ce), 6.1.4(a), 6.1.6(a), 6.2.6(a), 7.1.1(bg)
4/9(R)	7.1,7.2	Lecture 17		Fourier transform
4/14(T)	7.3,8.1	Lecture 18	HW9 (due 4/20) pdf	NIST Fourier transform FFT convolution Convolution and machine learning kernel
4/16(R)	8.1	Lecture 19 Black-Scholes notes		Normal Distribution error function
4/21(T)	11.1, 11.2	Lecture 20	HW10 (due 4/27) pdf	Fermat two-square Legendre three-square Lagrange four-square sum of three cubes 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
4/23(R)	11.2, 11.3	Lecture 21		eigenfunctions on disk
4/28(T)	11.4, 11.5	Lecture 22
4/30(R)	topic	Lecture 23
5/8(F)			Final Exam (2-5pm)

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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