Math 132, Spring 2000 (Section 1)
Complex Analysis for Applications
What's new:
- Some basic info about the final. (Mar 15)
- Regarding the question of notes etc. for the midterms: no notes, books or calculators are allowed for the mid-terms. A 5x7 index card will be allowed for the final. (Feb 4)
Course
Information:
|
Official stuff |
Stuff specific to 132/1 Winter 2000 |
Lecture notes:
- Week 1: Complex arithmetic, complex sets, limits, differentiation, Cauchy-Riemann equations. [pdf]
- Week 2: Complex analytic functions, harmonic functions, Möbius transforms. [pdf]
- Week 3: Möbius transforms, complex exponential, trig, hyperbolic, and log functions. [pdf]
- Week 4: Complex powers, inverse trig functions, review for first midterm. [pdf]
- Week 5: Contour integration, Fundamental theorem of calculus, Cauchy theorems and applications. [pdf]
- Week 6: Power series,
- Week 7: No lecture notes this week.
- Week 8: Zeroes, singularities, the point at infinity. [pdf]
- Week 9: The residue theorem; trig integrals, rational integrals; trig-rational integrals. [pdf]
- Week 10: Principal value integrals; integrals with branch cuts; argument principle; Rouche's theorem [pdf]
Errata in Week 6 (thanks to Nick Chan):
· p.6, 2nd line, the 2nd term in the right hand side, w_n is placed wrongly
· p.7, 3rd line, z_1 is missing in the series expression
· p.10, in the comparison test, z_n is missing in the second summation
· p.26, -3rd line, a_n * ( z - z_0 )^n is missing in the summation
Erratum in Week 10 (thanks to Chan-Ho Suh): z^5+z+1 should be z^5-z-1 throughout.
Sample Exams:
|
Sample quiz:
|
Sample first midterm:
|
Sample second midterm:
|
Sample final:
|
- Solutions to this quarter's quiz
- Solutions to HW1
- Solutions to HW2
- Solutions to HW3
- Solutions to HW4
- Solutions to HW5
- Solutions to HW6
- Solutions to HW7
- Solutions to HW8
- Solutions to HW9
- Solutions to the first midterm
- Solutions to the second midterm
Java applications
|
|
These applets are not officially part of the course, but are meant to illustrate some geometric aspects of complex arithmetic and analysis. Of course, your browser has to be Java-enabled to view these applets properly (for Netscape, this means checking the Enable Java box in "Edit/Preferences/Advanced"; for IE, check the Java JIT compiler enabled box in "View/Internet Options/Advanced").
Miscellaneous links:
- Do imaginary numbers actually exist?
- The sci.math FAQ on why e^{\pi i} = -1.
- An M.C. Escher print depicting reflection by a sphere (kind of a 3D analogue of the inversion map).
Back to my home page.