# Math 53000

## Spring 2011

Time: Tuesday and Thursday, 3:00 - 4:15 pm
Place: LD 229
Textbook: Complex Analysis, Third Edition, by Lars Ahlfors
Instructor: Michal Misiurewicz
Office: LD 224F
Phone: 274-8101
E-mail: mmisiure@math.iupui.edu
Office Hours: Tuesday and Thursday, 4:30 - 6:30 pm
Course description: This is the course that should teach students thoroughly Complex Analysis. They should know not only theorems, but also their proofs. Moreover, the students should be able to solve appropriate problems that start with "Prove that ...". In particular, after this course the students should be able to pass the Math 53000 Qualifying Exam (if necessary).

Sections covered:
• 1.1: The algebra of complex numbers;
• 1.2: The geometric representation of complex numbers;
• 2.1: Introduction to the concept of analytic function;
• 2.2: Elementary theory of power series;
• 2.3: The exponential and trigonometric functions;
• 3.2: Conformality;
• 3.3: Linear transformations;
• 4.1: Fundamental theorems;
• 4.2: Cauchy's integral formula;
• 4.3: Local properties of analytical functions;
• 4.4: The general form of Cauchy's theorem;
• 4.5: The calculus of residues;
• 4.6: Harmonic functions;
• 5.1: Power series expansions.

Grading policy: Each week there will be homework assigned, to be submitted for grading. The homework scores will constitute 30% of the total score. There will be two tests (after Chapters 3 and 4). The test scores will constitute 40% of the total score. There will be also a comprehensive final examination. The final exam score will constitute 30% of the total score.
You need approximately 80% of the maximum possible score for A-, 66.7% for B-, 53.3% for C-, and 40% for D-.
Final Examination: Thursday, May 5, 3:30 - 5:30 pm.
Withdrawal deadline: Friday, April 1. Details can be found here.

Academic Integrity: The IUPUI Department of Mathematical Sciences expects all students to adhere to the regulations put forth in the "IUPUI Code of Student Rights, Responsibilities, and Conduct" concerning academic or personal misconduct. The Code of Conduct can be found here.
Cheating on assignments and tests or other academic works is a violation of university policy. Any behavior that is construed as cheating or academic dishonesty will not be tolerated in this course. This includes, but it is not limited to, plagiarism, cheating during exams, acquisition of tests or other academic materials, as well as aiding and abetting others in committing the violation. The classroom protocol will be guided by the Student Code of Conduct which, among other things, asserts IUPUI's commitment "to maintain[ing] a spirit of civility in a community in which diversity is welcomed. Every student, staff, and faculty member plays a significant role in promoting an environment that is conducive to academic excellence by fostering a climate of civility and mutual respect."

### Homework assignments:

• Exercise 2, page 37 -- for January 25
• Exercises 1 and 3, page 44 -- for February 1
• Exercises 5 and 6, page 108 -- for February 17
• Exercise 3, page 118 -- for February 24
• August 1998, Problem 1, and January 2001, Problem 4 -- for March 3
• August 2000, Problem 1, and August 2005, Problem 3 -- for March 10
• January 1997, Problem 3, and January 2006, Problem 4 -- for April 7
• August 2005, Problem 2, and January 2007, Problem 3 -- for April 14
• August 2000, Problem 6, and January 2010, Problem 1 -- for April 21

Last updated: April 14, 2011
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