


Politecnico di Torino  
Academic Year 2009/10  
01IMDFD, 01IMDFN, 01IMDGA Complex Analysis 

1st degree and Bachelorlevel of the Bologna process in Electrical Engineering  Torino 1st degree and Bachelorlevel of the Bologna process in Mathematics In Engineering  Torino Master of sciencelevel of the Bologna process in Electrical Engineering  Torino 





Objectives of the course
Skills in understanding basic ideas and ability to deal with complex variable functions, distributions and Fourier end Laplace transforms.

Expected skills
The aim is training the student to calculate the modulus and the argument of a function of one complex variable, line integrals in the complex field using residue theorem, Jordan Lemma to compute improper integrals. Training to classify singularities, to decompose a rational function in partial fraction by residue method. To evaluate the Fourier and Laplace Transform of functions and distributions by means of transform properties. Develop ability in computing Zeta transform for recursive equations.

Prerequisites
Calculus of function of one or many variables, elements of plane geometry and space geometry. Contents of the Mathematical Analysis III and Geometry courses.

Syllabus
Complex exponential
Analytic functions Cauchy theorems and Laurent Series Residues and partial fraction decomposition using residues Distributions, differentiation and limits in the sense of distributions Fourier transform of functions and distributions Transform properties and main transform evaluation Fourier transform of periodic distributions Laplace Transform and the inversion formula Zeta transform 
Laboratories and/or exercises
The tutorial lectures will concern the ability to deal with analytical functions, distributions and Fourier and Laplace transform.

Bibliography
A.Papoulis. "The Fourier Integral and its Applications", McGrawHill Book Company, (London 1962)
R.Murray  Spiegel, "Complex Variables", Schaum's Outline Series, McGrawHill Companies (London 1968) 
Check availability at the library 
Revisions / Exam
Written exam, 1h 45m, no book, but formulary is allowed; short oral examination will follow.
Written examination will consist in three open exercises (the student have to develop all calculation) and seven multiplechoice test items concerning all the topics of the program of the course. 
