|
Week_Day |
Topic
|
Application |
Text
Reference |
|
|
1_1 |
Complex Numbers |
Oscillation Modes |
1.1-1.5 |
|
|
1_2 |
Functions and Mappings |
|
1.6,2.1,2,2, 2.3 |
|
|
2_1 |
Limits, Branches |
Rotating frames Geostrophic motion |
2.4-2.6 |
|
|
2_2 |
Derivative, Cauchy-Riemann Equations |
|
3.1-3.2 |
|
|
3_1, 3_2 |
Harmonic Functions |
Fluids, Electrostatics |
3.3 |
|
|
4_1 |
Riemann Surfaces, Logarithm, Trig functions |
|
5.1,5.2 |
|
|
5_1 |
Exam |
|
|
|
|
5_2 |
Differential Operators |
|
|
|
|
6_1 |
Sequences, Geometric Series |
Fractals |
4.1,4.2,4.3 |
|
|
6_2 |
Power Series, Inverse Trig functions |
|
4.4, 5.5 |
|
|
7_1 |
Integration, Cauchy Thm |
|
6.1,6.2,6.3 |
|
|
7_2 |
Cauchy Integral Formula |
|
6.4,6.5,6.6 |
|
|
8_1 |
Taylor Series, Laurent Series, Xeros and Poles |
|
7.1,7.2,7.3,7.4 |
|
|
8_2 |
Residue Theorem |
|
8.1,8.2 |
|
|
9_1 |
Integrals |
|
8.3—8,7 |
|
|
9_2 |
Conformal Mapping |
|
9.1—9.4 |
|
|
10_1 |
Harmonic Functions |
|
10.1—10.3 |
|
|
10_2 |
Applications |
Airfoils |
10.4,10.6,10.7 |
|
MTH 332/532 Syllabus
We will cover essentially a chapter a week, but will give little emphasis to chapters 7 and 8.
The more detailed syllabus below is subject to change, and should not be printed out.
I had intended to include many hyperlinks here, but I notice that they, and many others, are on the CD that comes with the book. (Check the folder Internet Resources). Some of the references in book are hyperlinked. It can be difficult to find them. On the CD, use the mathematicaBIG; in appropriate subsections entitled Library research experience for undergraduates, there will be highlighted hyperlinks to online versions of many of the references. However, you will still have to search. The best is to go to the web-book link above where, in the appropriate sections , you will find direct links to articles.
Joukowski airfoils at a (supposedly) elementary school level are demonstrated here:
http://jwilson.coe.uga.edu/olive/Joukowski.Web/Joukowski.Paper.html
The paper uses Geometer’s SketchPad. A demo copy can be downloaded here:
http://www.keypress.com/sketchpad/demo/gsp306dm.hqx
The original NACA reports on the Joukowski airfoil theory:
http://naca.larc.nasa.gov/reports/1922/naca-tm-79/
http://naca.larc.nasa.gov/reports/1922/naca-tm-78/
The Cornu spiral (arises along with Fresnel integrals in diffraction (optics).
Dynamic picture of a Mobius Transformation
