Ed Bueler: ffelb@uaf.edu,
x7693
MWF 9:15--10:15 Duckering 354
Text:
Link to Syllabus Here
image of Newton's method convergence for p(z) = 3z5 + z3 + 13z + 4, produced by polyfractal.m; click for image itself:
LINKS:
MWF 9:15--10:15 Duckering 354
Text:
- Churchill and Brown, Complex Variables and
Applications,
7th edition, 2004
Link to Syllabus Here
image of Newton's method convergence for p(z) = 3z5 + z3 + 13z + 4, produced by polyfractal.m; click for image itself:
LINKS:
- Möbius tranformations revealed, a youtube.com video; by D. Arnold
- wikipedia
page
on Möbius transformations
- D. Arnold's very cool Graphics for Complex Analysis page; definitely do click on the "animation" links!
- H. Lundmark's cool complex
analysis page
and maximally cool domain
coloring
page
- alternate free textbook: G. Cain, Complex Analysis
- the
Wikipedia
page "complex analysis"; not great in Jan 2008
Schedule: (version 5/7/08 FINAL)
| Day | Chapter |
Topic |
Assigned
or
Due |
| F 1/25 |
1 |
complex
numbers |
Assignment #1 (PDF) |
| M 1/28 |
1 |
multiplication,
conjugates,
proofs by induction |
|
| W 1/30 |
1 |
exponential
(polar)
form |
A
#1 Due Grading scheme (PDF) |
| F 2/1 |
1 |
multiplication,
division,
and roots, by polar form |
Assignment #2 (PDF) |
| M 2/4 |
1 |
open
sets, closed sets, regions |
|
| W 2/6 |
1 |
cont |
A
#2 Due Assignment #3 (PDF) |
| F 2/8 |
2 |
functions |
|
| M 2/11 |
2 |
visualizing
functions |
|
| W 2/13 |
2 |
limits |
A
#3 Due Assignment #4 (PDF) |
| F 2/15 |
2 |
limits and the complex
derivative |
|
| M 2/18 |
2 |
continuity |
|
| W 2/20 |
2 |
complex derivative | A #4 Due |
| F 2/22 |
class cancelled |
||
| M 2/25 |
2 |
Cauchy-Riemann equations |
|
| W 2/27 |
2 |
C-R eqns cont. |
A
#4 Due Assignment #5 (PDF) |
| F 2/29 | 2 |
C-R
eqns, consequences, polar coordinates Midterm I: IN CLASS |
|
| M 3/3 |
2 |
analytic functions,
harmonic functions |
A
#5 Due
at 5pm sharp;
solutions posted at 5pm |
| W 3/5 |
Midterm I IN CLASS: covers through page 69 of text. | Midterm
#1 (PDF) |
|
| F 3/7 |
3 |
harmonic
functions, exponential function |
|
| 3/10--14 |
SPRING BREAK (no
classes) |
||
| M 3/17 |
3 |
logarithms,
branch
cuts |
Assignment #6 (PDF) |
| W 3/19 |
4 |
parameterized
curves,
integrals along curves |
|
| F 3/21 |
4 |
contour
integrals |
|
| M 3/24 |
4 |
cont. |
A
#6 Due Assignment #7 (PDF) |
| W 3/26 |
4 |
antiderivs |
on an integral I did poorly
in class (PDF) Matlab/octave code to approxmate that integral: complexint.m |
| F 3/28 |
4 |
cont. |
|
| M 3/31 |
4 |
Cauchy-Goursat theorem w two proofs | A
#7 Due Assignment #8 (PDF) |
| W 4/2 |
4 |
extensions of
Cauchy-Goursat |
|
| F 4/4 | Midterm II IN CLASS: covers through page 142 of text. | Midterm
#2 (PDF) |
|
| M 4/7 |
4 |
Cauchy integral formula |
|
| W 4/9 |
4 |
cont.; derivatives by
integration |
A
#8 Due Matlab/octave code to compute integral done in class: intfourth.m |
| F 4/11 |
4 |
Liouville and FT of Algebra |
|
| M 4/14 |
4 |
cont |
Assignment
#9: pp 162--163: # 1abcd,3,4,5,7,8 pp 171--173: # 1,2,6,7,10 |
| W 4/16 |
5 |
cont.; sequences and series | polyfractal.m: Matlab code which produced fractal above left |
| F 4/18 |
UAF SpringFest (no classes) | ||
| M 4/21 |
5 |
Taylor series: theory |
A
#9 Due Assignment #10: pp 181--182: # 3, 4, 9 pp 188--190: # 2, 5, 7, 8, 10 |
| W 4/23 |
5 |
Taylor series: examples |
|
| F 4/25 |
5 |
cont |
|
| M 4/28 |
5 |
cont |
A
#10 Due See me for graded A#10. |
| W 4/30 |
5 |
Laurent series | Take-home Final Exam (PDF) |
| F 5/2 |
5 |
examples; Dirichlet
problem on a disc |
|
| M 5/5 |
5 |
Dirichlet problem and
Poisson kernel |
|
| F 5/9 |
FINAL Due |
TAKE-HOME
FINAL
Due 5pm in my box or at my office |
TAKE-HOME FINAL Due 5pm in my box or at my office |