Instructor: Ed BuelerOffice: Chapman 301C.Phone: 474-7693eMail: elbueler@alaska.edu |
Class Times & Room: MWF 9:15--10:15 Bunnell 410CRN: 34426Text: Gamelin, Complex Analysis, Corrected ed., Springer 2003 |

In more detail, we will cover these topics:

- complex numbers and their (easy) algebra
- analytic (= complex-differentiable) functions
- Cauchy-Riemann equations and harmonic functions
- mean value property and maximum principle
- conformal mappings
- major theorems: Cauchy's, Liouville's, Goursat's, and Morera's
- Cauchy integral formula
- power series
- residues

- gain a clearer and deeper understanding of algebra (e.g. polynomials) and calculus (e.g. limits and power series), as they might appear in high school and college courses in which you might be the teacher,
- possess a toolbox useful for applications (e.g. power series, residue calculus, conformal maps), including the differential equations of mathematical physics and engineering, and
- begin to understand the topology and geometry of two-dimensional manifolds (e.g. through seeing the Riemann surfaces of multi-valued functions), for learning more advanced mathematics and theoretical physics.

There will be two in-class Midterm Exams and one primarily in-class Final Exam. In fact a small part of the Final Exam will be take-home, but the majority in-class.

In summary:

WorkHomework Midterm Exam I Midterm Exam II Final Exam |
Percent of Grade 45% 15% 15% 25% |
Dates weekly in class, Friday 19 February in class, Friday 1 April in class, Thursday 5 May, 8:00--10:00am |

Based on your raw homework and exam scores, I guarantee grades according to the following schedule:

90 - 100 % =

This schedule is a guarantee. I reserve the right to increase your grade above this schedule based on the actual difficulty of the work and/or upon average class performance.

The catalog also says, accurately, that: May be taken independently of MATH F421.

If you have taken Math 302 or equivalent then this is a good course for you. It is probably true that those students who have taken more 300-level Math courses will have an easier time in this course, on average, than those who have taken fewer. This is what math professors call the effect of having more "mathematical maturity." It is a nebulous thing, really ...