Jean-Luc Thiffeault's Homepage

Math 322 Applied Mathematical Analysis II: Spring 2017


Lecture Room: B139 Van Vleck
Lecture Time: 11:00–11:50 MWF
Lecturer: Jean-Luc Thiffeault
Office: 503 Van Vleck
Email: jeanluc@[domainname],
where [domainname] is math point wisc point edu
Office Hours: Wed 13:00–14:00, Thu 13:15–14:15

Final exam

The final is this Saturday May 6, 2017 at 10:05–12:05, room Van Vleck B239.

Syllabus

See the official syllabus.

Textbook

The textbook for the class is Partial Differential Equations and Boundary Value Problems With Applications by Mark A. Pinsky (Third Edition).

I will also give a few lectures from D. J. Acheson's Elementary Fluid Dynamics (Oxford University Press). ISBN: 0198596790. This is not a required book.

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 02/03 02/06 0.1.1: 2,4,7; 0.1.2: 1–4, 0.1.4: 1–3; 0.1.5: 1–4; 0.2.2: 1–3; 0.2.3: 1–8; 0.2.4: 1–4
2 02/20 0.3: 1,2,3,6,10,15; 1.1: 2,3,4,9,10,18,26,27,29,33,34; 1.2: 1,5,6,7,13,16; 1.3: 1,4,10–13; 1.4: 2,3; 1.5: 1,3
[Correction: in 0.3.3 for some printings f-bar should be f-hat.]
3 03/06 03/10 1.6: 1,6,8,10; 2.1: 1,2,4,5,10,11,12,13,14,21; 2.2: 1,3,7,8,12,14,18,21
4 03/27 2.3: 1,3,8,11; 2.4: 1,4,5,7,17,18
5 04/05 2.5: 1,6,14,15; 3.1: 4,5,8,9,10,18,26
6 04/19 3.3: 1,8,9; 5.1: 2,3,4,5,7,15,16; 5.2.6: 1,2,6,7,8

Course Policy and Grading

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

Homework40%
Midterm exam30%
Final exam30%

Exam Dates

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

Midterm exam Monday March 6, 2017 at 17:30–19:00, room Van Hise 114 [solutions] (average 82%, standard dev 12%)
Final exam Saturday May 6, 2017 at 10:05–12:05, 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 01/18 0.1.1–3 Introduction: What is a PDE?
2 01/20 0.1.4 Heat equation
3 01/23, 01/25 0.1.5; 0.2 Classification; Separation of variables
4 01/25, 01/27 0.2 Separation of variables with BC
5 01/27 0.3 Orthogonal functions
6 01/30 0.3 Orthogonal functions (cont'd)
7 02/01, 02/06 1.1 Orthogonal functions (end); Fourier series
02/03 Homework discussion
8 02/06, 02/08 1.2 Convergence of Fourier series
9 02/10 1.3 The Gibb's phenomenon
10 02/13 1.4–1.5 Parseval's theorem; Complex form of Fourier series
11 02/15, 02/17 1.6 Sturm-Liouville eigenvalue problems
12 02/20, 02/24 1.6.4–1.6.5 General Sturm-Liouville problems [Matlab code for fig 1.6.2]
13 02/22, 02/24 4.2.2 Legendre's equation
14 02/27, 03/01 2.1.2–2.1.5 The heat equation in three dimensions [extra notes for general boundary condition]
15 03/03, 03/08 2.2.1–2.2.3 Initial Value Problem in a slab
03/06 Discussion of homework
17,18 03/10 2.3 Nonhomogeneous boundary conditions [example]
19 03/13 2.4.1–2.4.5 The vibrating string
20 03/15 2.4 The vibrating string (cont'd)
20 03/17 2.4 Resonant behavior
21 03/27 2.5 Multidimensional problems
22 03/29 2.5 Nodal lines
23 03/28 3.1.1–3.1.3 BVPs in cylindrical coordinates
24 04/03 3.1.6,3.1.7 BVPs in cylindrical coordinates (cont'd)
25 04/05 3.2,3.3.1 Wave equation and Bessel functions
26 04/08 5.1 Fourier transforms
27 04/10 5.1,5.2 Fourier transforms (cont'd)
28 04/12 5.2.4–5.2.6 Method of images
30 04/14–20 Acheson 229–232 Viscous flow and corner eddies (Start at bottom of page, at "Example".)
33 04/24 7.2 Numerical solution
34 04/26 7.2 Numerical solution examples (Matlab programs)
04/28, 05/01 Discussion of homework
04/28–05/03 Discussion of homework