4320-Complex Analysis (Spring 2016)

MATH 4320
Instructor: Jean Bellissard
Professor of Mathematics and Physics
School of Math, Skiles 132,
Phone: (404) 385-2179 (Math),
Fax: (404) 894-4409
e-mail: jeanbel@math.gatech.edu
 Lecture Skiles 271 Monday-Wednesday-Friday 12:05-12:55pm
Office Hours
Monday-Wednesday 2-3pm or by appointemnt
Skiles 132

Calendar of the Month
Final Exam:
Friday April 29th,
8:00-10:50am Skiles 271

(to full Fall calendar )

April 25, 2016
Last day of class

Lecture: Review and Questions

Course Outline

Topics
Complex numbers: algebra and geometry, square roots, polar coordinate, n-th roots
Analytic functions: Cauchy-Riemann equations, harmonic functions, reflection principle
Elementary functions: exponential, logarithm, branches, trigonometric & hyperbolic functions
Integral: definitions, contour integrals, Cauchy formula, Liouville Theorem, roots of polynomials
Bounded linear functions, Riesz representation theorem, and the Lax-Milgram theorem
Series: Taylor's and Laurent's series expansions, convergence, algebra for power series.
Residues and Poles: Cauchy's residue Theorem, zeros of analytic functions
Application of Residues: computation of integrals, branch cuts, Laplace transform
Mappings: examples provided by elementary functions
Conformal Mapping and applicationss

Textbook

Official textbook
James Ward Brown, Ruel V. Churchill,
"Complex Variables and Applications", Ninth edition,
McGraw-Hill Education, New York, 2014

Homework

One compulsory homework will be offered once every 2 weeks

Final Exam

Friday April 29th,   8:00-10:50am    Skiles 271    ( to calendar)
An absence to the final exam will be graded 0 (zero). However if the absence is justified (disease, injury, ...), the student must (i) warn the instructor as soon as possible, in any case before the end of the exam week, (ii) bring the documents justifying the absence to the Instructor.
Then the student will receive an I (incomplete) and will be responsible to take action during the following semester to complete his/her curriculum.