Politecnico di Torino
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Politecnico di Torino
Academic Year 2009/10
01IMDFD, 01IMDFN, 01IMDGA
Complex Analysis
1st degree and Bachelor-level of the Bologna process in Electrical Engineering - Torino
1st degree and Bachelor-level of the Bologna process in Mathematics In Engineering - Torino
Master of science-level of the Bologna process in Electrical Engineering - Torino
Teacher Status SSD Les Ex Lab Tut Years teaching
Codegone Marco ORARIO RICEVIMENTO     36 20 0 0 6
SSD CFU Activities Area context
MAT/05 5 C - Affini o integrative Cultura scientifica, umanistica, giuridica, economica, socio-politica
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 I-II 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", McGraw-Hill Book Company, (London 1962)
R.Murray - Spiegel, "Complex Variables", Schaum's Outline Series, McGraw-Hill 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 multiple-choice test items concerning all the topics of the program of the course.

Programma definitivo per l'A.A.2008/09
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