Math 442

Math 442 Schedule (subject to change)

Date	Sections	Lecture Notes	Homework	Other readings	Videos/software
1/19(R)	1.1-1.5	Lecture 1	Homework 1: (due Jan 27) 1.1(1cd, 2e), 1.2(5,13,19a), 1.3(6), 1.4(1,5), 1.5(13) 1.6(3,5,11,24,26) optional 1.6(29)	differential equation PDE(wiki) PDE(scholarpedia) millennium problems Survey article Applications of PDE: image processing climate Climate change model biology finance economics socio-economic sciences	Wolfram Alpha
1/24(T)	1.6-1.7	Lecture 2
1/26(R)	2.1-2.3	Lecture 3	Homework 2: (due Feb 3) 1.7 (3,11,19c), 2.2(10,11), 2.4(3ac,4a,7), 2.5(2,6),	Laplace operator in polar/spherical coordinate spherical coordinates Divergence Diffusion Molecular diffusion diffusion coefficient Fick's law Fourier's law heat equation Laplace operator	Diffusion (intuition) Diffusion
1/31(T)	2.3-2.4	Lecture 4		Wave equation vibrating string vibration of drum Jean le Rond d'Alembert continuity equation Dimension analysis SI unit Roots of unity Euler equation	Vibration of strings
2/2(R)	2.5-2.6	Lecture 5	Homework 3: (due 2/10) 2.6(4,5), 3.2(4,6bc,14(prove (3.10e))), 3.3(5,9) 3.4(3,4,9,19c,20)		solution of diffusion equation and wave equation (Pugh) Silvestre's solver
2/7(T)	3.1-3.2	Lecture 6		Joseph Liouville trig formula Matlab Fourier series fitting
2/9(R)	3.3-3.4	Lecture 7	Homework 4: (due 2/20) 3.4(21c), 3.5(4,7c),3.6(2,3,6) 4.1(1b,2a,5c,8)	Joseph Fourier pi Leibniz formula for π Euler's formula for pi trig formulas 14 proofs of Euler's formula
2/14(T)	3.5-3.6, 4.1	Lecture 8		Gibbs phenomenon Gibbs phenomenon	Matlab: Fourier 1, 2, 3, 4 Dirichlet, Gibbs, Gibbs2
2/16(R)	4.2-4.3	Lecture 9	Homework 5: (due 2/27 17pm) 4.2(1b,2b,4d,5bc), 4.3(3,9), 4.4(1c,4,9,11) optional (4.3(14ab),4.4(15))	Music course in Columbia The Mathematics of Musical Instruments, Amer. Math. Monthly, 2001
2/21(T)	4.4	Lecture 10 Lecture 10a		MIT course in transport process in the environment
2/23(R)	application	Lecture 11	Midterm 1 (due 3/14 15pm)	2nd order linear ODE reference Turing pattern talk quantum graph talk Alan Turing Turing instability 1952 Turing paper on biological pattern formation	Matlab: Fourier 5 (homework 4)
2/28(T)	5.1	Lecture12
3/2(R)	5.2	Lecture13		traffic flow model
3/7(T) 3/9(R)		Spring break no class

Date	Sections	Lecture Notes	Homework	Other readings	Software
3/14(T)	5.3	Lecture14	Homework 6: (due 3/17) 5.1(3,5,7,20a) 5.2(4,5,6) 5.3(3,4,6)	Pi day	Matlab pulse plucked string hammer wave with boundary 1, 2
3/16(R)	5.4	Lecture 15
3/21(T)	5.5	Lecture 16	Homework 7: (due 3/24) 5.4(2,3,11) 5.5(1,3,5) HW7
3/23(R)	6.1	Lecture 17		Laplace transform table Laplace transform table 1 2 properties
3/28(T)	6.1, 6.3	Lecture 18	Homework 8: (due 3/31) 6.1(2a,3a,5,9a) 6.3(1a,1b) HW8	Fourier transform table 1 2 properties NIST Integral transform Application of Fourier transform	Wolfram Integral Transform
3/30(R)	6.3, 6.4	Lecture 19		2D Fourier transform (image analysis) Fast Fourier Transform
4/4(T)	6.5	Lecture 20	Homework 9: (due 4/10) 6.3(9b,11a),4(1a,6a),6.5(10b) HW9
4/6(R)	9.1-9.2			Wave equation in a rectangle
4/11(T)	9.3	Lecture 21	Homework 10: (due 4/17) HW10 9.2(3c,5a), 9.3(2bc,3a,5), 7.4(2ab),	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)
4/13(R)	9.4	Lecture 22		wave in a disk eigenfunction of Laplacian in a disk Eigenfunction vibration in a disk
4/18(T)	7.4,7.5,9.4	Lecture 23	Homework 11: (due 4/24) HW11 7.5(1b, 4cd), 9.4(1a,1c)
4/20(R)	9.5	Lecture 24		spherical harmonics	Matlab PDE Matlab pdetool
4/25(T)	11.1-11.2	Lecture 25	Midterm 2: (due 5/5)	Papers on Morphogen Gradient bacteria growth pattern	Matlab: Forward Neumann Forward Dirichlet
4/27(R)	applications	Lecture on biological invasion Lecture on Turing instability		Fisher's equation Schrodinger's equation KdV equation Soliton Peregrine soliton Sine-Gordon equation breather Quantum graph Turing instability Turing 1952 Kondo-Miura 2010

Possible Math 300 topics

Derive wave equation: Strings, Chains, and Ropes (SIAM Review 2006) (The Equations for Large Vibrations of Strings, Antman, 1980)
How realistic is the D’Alembert plucked string (Euro. J. Phys, 1999)
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)
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
Music and wave equation (a course in Columbia) (The Mathematics of Musical Instruments, Amer. Math. Monthly, 2001)
Transport process in environmental studies (a course in MIT)
Modeling mixing problem for multiple tanks with PDE (ODE setting, two tank problem)