University of Arizona | Department of Mathematics | Ildar Gabitov | MATH 424/524

MATH 424/524
Theory of Complex Variables

Section 001, Spring 2010

Classroom:  MLNG 312, TR, 2:00pm–3:15pm
Instructor:  Ildar Gabitov
office:  MATH East 249C
e-mail:  gabitov@math.arizona.edu
phone:  (520) 626-8853
Office Hours:  Tue 4–5pm, Wed 2–3pm, Thu 9:30–10:30am (subject to change) and by appointment
Text:  linear algebra textbook S. D. Fisher, Complex Variables, 2nd ed. (Dover, 1999)

Course description: Complex numbers, complex-valued functions, analytic functions, elementary functions, series, residues and poles, mapping by elementary functions, conformal mapping, the Schwarz-Christoffel transformation, integral formulas of Poisson type.

MATH 424/524 Calendar / Syllabus

Homework: Homework will be assigned regularly. Selected homework problems will be graded and a final score equivalent to one test, 100 points, will be assigned. Homework is an essential component of the course, whether it is assigned for grading or not. A grade of "00" will be assigned for homework that is not handed in on time. The two lowest homework grades will be dropped.

HW1 Section 1.1, 1.2, 1.3 Exercises Page 9: 4, 8, 15, 19; Page 20: 2, 11, 29; Page 28: 2, 15, 17 due Jan 29, 4:30pm
HW2 Section 1.4, 1.5 Exercises Page 41: 6, 14, 16, 22; 28, 34; Page 53: 4, 6, 19; 23, 29 due Feb 5, 4:30pm
HW3 Section 1.6 Exercises: Prove inequality on the page 61; Page 73: 1, 3, 4, 6, 8, 9 due Feb 12, 4:30pm
HW4 Section 1.6, 2.1 Exercises Page 73: 10, 13, 17, 20; Page 84: 1, 8, 10, 14, 21, 25 due Feb 19, 4:30pm
HW5 Section 2.2, 2.3, Exercises Page 103: 3, 5, 7, 10; Page 116: 1, 7, 9, 18; due Feb 26, 4:30pm
HW6 Section 2.4, 2.5 Exercises Page 133: 1, 6, 10, 20, 23; 24, 25; Page 150: 1, 5; due Mar 5, 4:30pm
HW7 Section 2.5 Exercises Page 150: 7, 9, 13, 15, 19, 22(c), 23(b), 26, 27(e,f); due Mar 12, 4:30pm
Review for Test 2 Examples Cauchy-Reimann Equations, page 79: examples: 10, 11;
Review for Test 2 Examples Cauchy's Theorem and Formula, page 106: examples: 6, 8, 10; page 125: examples: 1, 2;
Review for Test 2 Examples Laurent Series, page 141: examples: 7, 11, 12;
Review for Test 2 Examples The Residue Theorem, page 153: examples: 1, 2;
HW8 Section 2.6 Exercises Page 167: 1, 3, 4, 5, 6, 9, 10; due Apr 2, 4:30pm
HW9 Section 2.6 Exercises Page 167: 13, 15, 16, 17, 18, 21, 22; due Apr 9, 4:30pm
HW10 Section 2.6, 3.1 Exercises Page 167: 26a, 26c 32, 34; Page 179: 2, 6, 12, 18, 20 due Apr 16, 4:30pm
HW11 Section 3.3 Exercises Page 204: 2, 4b, 4c, 7c, 11, 15, 16, 20; due Apr 23, 4:30pm
HW12 Section 3.4 Exercises Page 218: 2, 4, 6, 10, 12, 15; due Apr 30, 4:30pm
Review for Final Test Examples Click here

Tests: The two in-class tests are scheduled for Tue, Feb 2 and Tue, Mar 23. Each test will be worth 100 points. The Final Exam will be worth 200 points. The University's Exam regulations for final exam week will be strictly followed, in particular those regarding students with multiple exams on a single day. The regulations can be found at registrar.arizona.edu/schedule084/exams/examrules.htm.

Grades: The total number of points available on tests and homework is 500. More points — higher grade. Learn more at “how grades work” page about points↔grade correspondence, anout withdrawing from the course, and about incomplete grade.

Students with disabilities: If you anticipate issues related to the format of requirements of this course, please meet with your instructor to discuss ways to ensure your full participation in the course. If you determine that formal, disability-related accommodations are necessary, it is very important that you be registered with Disability Resources (621-3268; drc.arizona.edu). You should notify your instructor of your eligibility for reasonable accommodations by Friday, August 31. You and your instructor can then plan how best to coordinate your accommodations.