MATH 435, SPRING 2015-COURSE LOG

Problems in boldface: HW (turn in written solutions)

Chapter 1: read, identify interesting problems (for Tuesday)

1/8 Introduction, course policies/ uniform transport equation (2.2)

suggested:

2.2: 2, 3d, 5, 8, 9, 10 (HW1=3d,5)

1/13 Nonuniform transport (2.2)

2.2: HW1=17, 20, 22 (due 1/15)

other: 18, 19, 21

1/15 Examples (problems from text)-uniform and non-uniform transport

1/20 Non-uniform transport: examples/1D Wave equation (d'Alembert's solution) (2.4)

HW2 (due 1/27): (2.2.19) (Use a symmetric "bump function" with support in [-1,1] as initial condition.)

1/22 Non-hom 1DWE (2.2): resonance, almost-periodicity

Problems from (2.4): 1,2, 4(d)(e), 7,8,10,11,12,13,15,18,19

HW2: problems in boldface above.

(Some will be discussed in class, others included in HW2)

1/27: 1DWE: discussion of problems

1/29 1DWE: discussion of problems

HW3: (due Thursday, 2/6): 2.4:15,18,19/ 3.1: 4, 5

2/3: 3.1 Linear differential operators and separated solutions/ 3.2 Fourier series (start)

2/5: 3.2: Fourier series

HW4 (due 2/12): 3.2: 3, 6abd, 19ade, 27, 3.3: 1, 2

HW4 solutions

2/10 Solution of HW3/ integration and differentiation of Fourier series (3.3)

Remark: complex Fourier series (p.89) and change of scale (sect. 3.4) are independent reading assignments.

2/12: uniform convergence, decay of coefficients, functions defined by Fourier series (3.5)

2/17: university closed due to inclement weather

2/19: problems from Chapter 3

HW5 (now due 3/3): 3.4.2 (b), (d)/3.5.5 c,d,e,i (graph the functions f_n)/3.5.11 a,d,g/ 3.5.20/ 3.5.22 a,b,c

2/24: university closed due to inclement weather

2/26: L2 convergence (3.5): best approximation in L2 norm, Bessel's inequality, Plancherel's equality.

HW 6 (due 3/3): 3.5.27 abcd (discuss also uniform convergence); 3.5.29

3/3: Discussion of HW problems/ (4.1) heat equation on the circle or interval

HW 6 due

HW5&6-solutions

3/5:(4.1), (4.2): heat and wave equation in bounded intervals/circle (not included in Exam 1)

3/10: Exam 1 (open book, closed notes)

Exam 1 (with solutions)

3/12: problems from sect. 4.1 [10b, 13, 15], 4.2 [3b, 34a, 35]

HW7 (due 3/26): (4.1) 8, 17 (4.2) 3f, 25, 29

3/17, 3/19: Spring Break

3/24 Tu: (4.3) Planar Laplace and Poisson equations

HW8: 4.3.10 (a). 4.3.14, 4.3.18, 4.3.25(a), 4.3.34 (c),(d)

3/26 Th: (6.1) Generalized functions

HW7&8-solutions

3/31 Tu (6.2) Green's functions in one dimension

HW 8 due

Practice problems:

6.1: 2,7,9/ 6.2: 1,8,9,11,12

Practice problems-solutions

4/2 Th Review, problems

4/7 Tu Exam 2: Sections 4.1, 4.2, 4.3, 6.1, 6.2

Exam2 (with solutions)

exam2, page 3

4/9 Th (6.3, 12.3) Uniqueness theorems via vector calculus/ Green's functions for the Poisson equation in R2 and R3

HW9 (due 4/16)- 6.3.4, 6.3.9, 6.3.14(a), 12.3.1, 12.3.3

HW9 solutions

4/14 Tu (6.3, 12.3) Green's functions for bounded regions-method of image charges.

4/16 Th (8.1) From Green's function to the Poisson kernel/ Exam 3 given (take-home)- sections 4.3, 6.2, 6.3, 12.3

HW9 due

Exam 3 (with solutions)

4/21 Tu (12.2) heat kernel, Cauchy problem for heat equation/ exam 3 collected

Problems on the heat kernel

4/23 Th (last day) Problems on the heat kernel, discussion of exam 3

FINAL EXAM: Thursday, April 30, 12:30 PM (comprehensive)

Final Exam