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

4/25(T)

11.1-11.2
Lecture 25 Midterm 2: (due 5/5)
Papers on Morphogen Gradient bacteria growth pattern

4/27(R)

applications


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
  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)