Jean-Luc Thiffeault's Homepage

Math 321: Applied Mathematical Analysis I (Spring 2016)
(Vector and Complex Calculus for the Physical Sciences)


Lecture Room: 104 Van Hise
Lecture Time: 13:20–14:10 MWF
Lecturer: Jean-Luc Thiffeault
Office: 503 Van Vleck
Email: jeanluc@[domainname],
where [domainname] is math point wisc point edu
Office Hours: Mon 2:10–3:00, Wed 11:50–12:30

Final Exam

Don't forget that the final is on Wednesday May 11, 2016 at 17:05–19:05 in Ingraham 19.

The final exam covers the material of Chapters 2 and 3. There will be a definite emphasis on complex variables and complex integration. Update: The exam will consist of 5 questions, 3 of which deal with complex variables (60% of marks).

Here are some things that you should definitely know how to do for the final:

Office hours on exam week:

Ivan's review sessions on exam week:

Syllabus

See the official syllabus.

Textbook

There is no official textbook for the class. We will follow Prof. Waleffe's lecture notes fairly closely.

Here are some textbooks you might consult for some extra exercises and background. Be warned that they may use different notation and present the material in a different order from the class.

Prerequisites

Math 222 and 234.

Homework

Every week a few questions will be assigned, mostly from the course notes. The homework will be due on Friday in class. One or two random questions will be explictly graded, and the rest graded for completion.

The homework is posted on the webpage of Ivan Ongay Valverde, the TA for the class.

Course Policy and Grading

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

Homework20%
Midterm exam 120%
Midterm exam 220%
Final exam40%

Exam Dates

The midterm exams will be given in the evening on the dates below. No notes, calculators, or anything else other than basic writing implements is allowed.

Midterm exam 1 Monday February 22, 2016 at 17:30–19:00, room B130 [solutions]
Midterm exam 2 Monday April 4, 2016 at 17:30–19:00, room B130
Final exam Wednesday May 11, 2016 at 17:05–19:05, Ingraham 19


Schedule of Topics

lecture date pages topic
1 01/20 Introduction; Autonomous flight (TED talk)
2 01/22 1–5 Review of vectors in 2D and 3D
3 01/25 6–10 Addition and scaling of vectors; General vector spaces
4 01/27 11–13 Points and coordinates
5 01/29 12–19 Dot product; Orthonormal bases
6 02/01 20–24 Dot product and norm in Rn; Cross product; Double cross product
7 02/03 24–30 Orientation of bases; Levi–Civita symbol
8 02/05 30–34 Einstein sum convention
9 02/08 34–37 Mixed product and determinant
10 02/10 39–45 Lines and planes; Change of Cartesian basis
11 02/12 Discussion of exercises
12 02/15 46–48 Matrices
13 02/17 48–52 Euler angles; Gram–Schmidt procedure
14 02/19 57–59 Vector calculus; Motion of a particle
15 02/22 Discussion of exercises
16 02/24 59–62 Central force motion
17 02/26 66–69 Curves
18 02/29 66–70 Frenet–Serret formulas
19 03/02 70–73 Integrals along curves
20 03/04 73–79 Surfaces
21 03/07 80–81 Surface integrals
22 03/09 80–81 Examples of surface integrals
23 03/11 82–84 Volume integrals
24 03/14 85–87 Mappings and curvilinear coordinates
25 03/16 88,92 Change of variables
26 03/18 93–97 Gradient
27 03/28 97–99 Div and curl; vector identities
28 03/30 99–102 Div, grad, curl in polar coordinates
29 04/01 104–110 Fundamental theorems of vector calculus
30 04/04 Discussion of exercises
31 04/06 110–116 Gauss' theorem
32 04/08 110–116 Gauss' theorem with singularities
33 04/11 117–122 Review of complex numbers
34 04/13 122–136 Review of complex numbers (cont'd)
35 04/15 137–141 The Cauchy–Riemann equations
36 04/18 151–152 Complex integration
37 04/20 152–154 Cauchy's theorem
38 04/22 154–157 Laurent series and residues
39 04/25 157–161 Cauchy's formula
40 04/27 161–163 Complex methods for real integrals
41 04/29 163–166 Complex methods for real integrals (cont'd)
42 05/02 168–169 Branch cuts
43 05/04 Discussion of exercises
44 05/06 Discussion of exercises