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 2/17)
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 2/24)
4.2(1b,2b,4d,5bc,6b), 4.3(3,9,14ab)
4.4(


2/21(T)

4.4,
Lecture 10


2/23(R)

5.1-5.2
Lecture 11 Midterm 1


2/28(T)

5.3-5.4
Lecture


3/2(R)


Lecture


3/7(T)







Date
Sections
Lecture Slides
Notes
Homework
Other readings

3/14(T)






3/16(R)






3/21(T)






3/23(R)






3/28(T)






3/30(R)






4/4(T)






4/6(R)






4/11(T)






4/13(R)






4/18(T)






4/20(R)






4/25(T)






4/27(R)






5/4(R)




Final Exam 9am-12pm