Jean-Luc Thiffeault's Homepage

Math 322 Applied Mathematical Analysis II: Spring 2018


Lecture Room: B123 Van Vleck
Lecture Time: 11:00–12:15 TuTh
Lecturer: Jean-Luc Thiffeault
Office: 503 Van Vleck
Email: jeanluc@[domainname],
where [domainname] is math point wisc point edu
Office Hours: Tue 10:00–11:00, Thu 12:30–13:15

Final exam

The final is Monday May 7, 2018 at 14:45–16:45, room Van Vleck B239.

Syllabus

See the official syllabus.

Textbook

The textbook for the class is Applied Partial Differential Equations by Richard Haberman.

The current edition is the Fifth, but you can use earlier editions if you find them for cheaper. (Earlier edition might be missing a bit of material, so you can use the copy on reserve in the library for reference in those cases.)

Prerequisites

Math 319 and 321.

Homework

Every two weeks or so I will assign homework from the textbook (or other sources) and post it here. The homework will be due in class about two weeks later.

homework due date problems
1 02/08 1.2: 3,5; 1.3: 1,2; 1.4: 1(bceg),2,5,10; 1.5: 1,3,5,12,18,19,22,23.
2 02/22 2.2: 2,3,4; 2.3: 1(bd),2(aceg),3(ab),4,5,7,11; 2.4: 1,2,3,4.
3 03/08 2.4: 7(b); 2.5: 1(bg),2,3(a),5(b),8(b),12; 3.3: 2(c),4,5(a),7,15.
4 03/22 3.4: 9,11; 3.5: 1; 3.6: 2; 4.2: 1; 4.4: 3,7,9,10.
5 04/05 5.3: 2,3,8,9; 5.4: 1; 5.5: 1(de),8; 5.8: 1,6,9,11.
6 04/19 7.2: 2; 7.3: 1(e),4(a),7(b); 7.7: 2(a),3,7.
7 05/03 7.8: 2; 7.9: 1(d),3(a),4(b); 7.10: 2(bd),9(d); 8.2: 1(bf),2(d),3,5,6(b).

Course Policy and Grading

There will be a midterm exam and a cumulative final exam. The final grade will be computed according to:

Homework35%
Midterm exam30%
Final exam35%

Exam Dates

The midterm exam will be given in class on the date below.

Midterm exam Tuesday March 13, 2018 at 11:00–12:15, room Van Vleck B123 (in class) [solutions]
Final exam Monday May 7, 2018 at 14:45–16:45, room Van Vleck B239


Piazza

We'll use Piazza Q&A for discussions about the class and related topics. Feel free to post questions and answers there about homeworks and exams, logistics, or relevant interesting things you found on the web. Note that we will only use Piazza for the Q&A feature, not for posting the actual homeworks.

Schedule of Topics

Note: there is not necessarily a one-to-one correspondence between lectures numbers and dates.

lecture date(s) sections topic
1 01/23 1.1–1.2 Heat equation
2 01/25 1.2–1.3 Heat equation (cont'd); Boundary conditions
3 01/30 1.4–1.5 Equilibrium distribution; Higher dimensions
4 02/01 1.5; 2.1–2.2 Higher dimensions (cont'd); Linearity
5 02/06 2.3 Separation of variables
6 02/08 2.3 Separation of variables (cont'd)
7 02/13 2.4 Separation of variables (cont'd)
8 02/15 2.5 Laplace's equation
9 02/20 2.5.2 Laplace's equation in a disk
10 02/22 2.5.4 Mean value theorem; Maximum principle; Uniqueness
11 02/27 3.1–3.3 Fourier series; Sine and cosine series
12 03/01 3.4–3.6 Differentiation and integration of Fourier series; Complex form
13 03/06 4.1–4.4 Wave equation
14 03/08 4.5; 5.1–5.4 Vibrating membrane; Sturm–Liouville eigenvalue problems
15 03/13 Midterm
16 03/15 5.5 Sturm–Liouville eigenvalue problems
17 03/20 5.8 Sturm–Liouville example
18 03/22 7.1–7.3 Higher-dimensional PDEs
03/27,29 Spring Break
19 04/03 7.7 Vibrating circular membrane; Bessel functions
20 04/05 7.7–7.8 More on Bessel functions
21 04/10 7.9 Laplace in a Cylinder; Modified Bessel functions
22 04/12 7.10 Spherical coordinates; Legendre polynomials
23 04/17 7.10.3–5 Legendre functions; Reactive particle
24 04/19 Reactive particle (cont'd)
25 04/24 8.1–8.3 Nonhomogeneous problems
26 04/26 8.5 Resonance
27 05/01 Discussion of final; Review