Charchil Building The Graduate School
  Sylabus

complex functions and integral transform - 104221
  Lecture Tutorial Project/
Seminar 		Laboratory
Weekly
Hours 		3 2    
Credit
Points
4.0
 

Prerequisites: differential and integral calculus 2t 104013
or differential and integral calculus 2t 104014
or differential and integral calculus 2m/1 104020
or differential and integral calculus 2m/2 104022
or infinitesimal calculus 2 104281
or differential and integral calculus 2t 104013
Overlapping Courses: complex function theory 1 104122
fourier series and integral transforms 104214
math. methods for computer applications 234299
Incorporated Courses: complex functions a 104215


Complex numbers, complex functions. Derivatives, analyticity and the
cauchy-riemann equations. Harmonic functions, the extended complex plane,
conformal mappings. Line integrals, the cauchy and liouville theorems.
The cauchy formula for a function and its derivatives. Power series, radius of
convergence, laurent series. Zeroes, singular points and their classification.
The residuum theorem and calculation of residua. Application to real integrals.
The argument theorem and rouche's theorem. The fourier transform and its properties.
the inverse transform, the plancharel equality, convolutions and the delta function.
applications to pdes. The laplace transform, its properties and inversion.
applications to signal analysis. the z-transform.

 
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Created in 21/05/2013 Time 22:22:32