MAT342

MAT 342
Applied Complex Analysis

Summer Session II 2012

If you have any questions about the course, you can contact me at claudio@math.sunysb.edu. You are also encouraged to come to my office hours, which will be held as follows:

Mondays: 11:00-12:00 pm and 1:00-3:00 pm at the MLC.

We will be using the texbook by James W. Brown and Ruel V. Churchill, Complex Variables and Applications, 8th Ed., McGraw-Hill. (ISBN 978-0-07-305194-9).

The final grade will be the weighted average according to the following: homework 30%, Midterm 30%, Final 40%.

This is the schedule/syllabus for the course:

Day	Contents	Sections
07/10	Arithmetic properties of complex numbers, the exponential form and its geometric interpretation.	1-9
07/12	Mappings, limits in the complex plane.	10-16
07/17	Continuity, derivatives, Cauchy-Riemann equations.	17-22
07/19	Analytic and harmonic functions, the exponential and logarithmic functions.	23-30
07/24	Complex exponents, trigonometric functions, derivaties and integrals of curves in the plane.	31-34, 37-38
07/26	Midterm I
07/31	Contour integrals, antiderivatives, the Cauchy-Goursat theorem, simply and multiply connected domains.	39-42, 44, 46, 48,49
08/02	Cauchy's integral formula and its implications, Liouville's theorem, the fundamental theorem of Algebra, maximum modulus principle, sequences and series, Taylor series.	50-57
08/07	Laurent series, absolute and uniform convergence, differentiation and integration of series.	59,60,62,63-66
08/09	Singular points, residues, residue theorem.	68-74
08/14	Application of residues.	75-79, review.
08/16	Final

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