Instructor: Olena Ostapyuk
e-mail: ostapyuk@math.uni.edu
Office: WRT 305
Office phone: 319-273-2432
Office hours:  M W F 1:00-1:50 pm, or by appointment

Class schedule: M W F 11:00-11:50 pm, room: Wright 105.
All changes in schedule, if any, will be posted on this page. 

Textbook: Complex Analysis, by Theodore W. Gamelin

Class Syllabus

Homework

Link to Complex Grapher

Lab #0, Introduction to Complex Graphing: Wednesday, Sept. 13th,  11:00-11:50 am (regular class time), WRT 110. This lab is not for credit. You don't have to prepare, just show up!
 Important: make sure your login and password work for machines in WRT 110. (Lab assignment, .pdf)

Lab #1, Exponential, hyperbolic and trigonometric functions: Wednesday, Sept. 20th,  11:00-11:50 am (regular class time), WRT 110. (Lab assignment, .pdf) - due Friday, Sept. 29th.

Attention: I will be out of town starting from Wednesday, Oct. 18th, 3 pm until Sunday. We won't have a class and any meetings/office hours on Friday, Oct. 20th. I plan to reschedule the missed class. The homework assignment #3 will be due Wednesday, Oct. 25th.

The class is rescheduled for Monday, Oct. 30th, 3:00-3:50 pm in WRT 07.


Midterm Exam will be on Wednesday, November 8th, from 11:00 to 11:50 am (regular class time).
The exam will cover Chapters I and II. You may use any books, notes or any other sources of information you'd like to bring with you. Things to review before exam:

• Basic complex functions and their properties, compute the values of given functions (single- and multi-valued), find the image of the region under given function;
  
• Definition of complex derivative and analyticity, check differentiability both by definition and by Cauchy-Riemann equations;
• Geometric properties of the basic functions, conformality, how to find a map from a given region to a given region using basic functions;
• Harmonic functions and harmonic conjugates.

Final Exam (comprehensive) will consist of two parts:

Computational part: Tuesday, Dec. 12^th, 10 am - 11:50 am in WRT 105. You can use any materials you want.
Topics/methods to be covered:

• Basic complex functions and their properties: compute the values of given functions (single- and multi-valued), find the image of the region under given function;
  
• Definition of complex derivative and analyticity: check differentiability both by definition and by Cauchy-Riemann equations, find the points where function is differentiable and/or analytic;
  
• Geometric properties of the basic functions, conformality: check that function is conformal, find a conformal map from a given region to a given region using basic functions;
• Harmonic functions and harmonic conjugates: check that function is/is not harmonic, find harmonic conjugate;
• Line integrals: compute various line integrals by definition, using Green's Theorem, Fundamental Theorem of Calculus; check whether vector field or differential is closed, exact, independent of path; check whether the Mean Value Property holds for the specific function; compute various integrals using Cauchy Theorem and Cauchy Integral Formula.
  

Theoretical home-take part is due Monday, Dec. 11^th, 12:50 pm. Bring hard copy to my office by this time, or, if I am not in, put it into my mailbox or pin it to the board near my door. Alternatively, you can e-mail  typed or legibly handwritten and scanned copy to me at ostapyuk@math.uni.edu by due time. You can use any sources of information you want, but are not allowed to discuss it with each other or anyone else, except myself. Also, in your proofs you can only use theorems and properties we have proved in class, ether during the lectures or in your homework. Clearly cite such theorems and properties.