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Complex variables


Denominazione del corso: Complex variables
Corso di studi: I4W - Laurea magistrale in Ingegneria Matematica
Quadrimestre/Semestre:
Anno:
Numero di moduli: 1
Crediti: 3
Ore: 30
Tipologia: B - Attivitą caratterizzanti
Struttura: monodisciplinare
Settore Scientifico Disciplinare: MAT/05 (Analisi Matematica)

Docente: Rosella Colomba Sampalmieri (30 ore). Titolo copertura: retribuita/gratuita
Orario di ricevimento: Please contact the Teacher by e-mail: rosella.sampalmieri@univaq.it


Programma sintetico del corso:

Complex variable, complex integration, Laplace and Fourier Transform and applications

Programma esteso del corso:

Link Programma completo (PDF)    (Aggiornato il 10-10-2018)

Complex plane, main complex functions and their characteristics, holomorphic functions, properties of holomophic functions, Cauchy - Riemann equations, zeros of holomorphic functions, power series, analyticity of holomorphic functions,complex path integrals, Cauchy Theorem, Cauchy Formulas, isolated singularities , Laurent series, residues, Residue theorem, Jordan Lemma (both versions), applications to the calculus of real and complex integrals, Fourier transform, Riemann-Lebesgue Theorem, properties, Fourier anti-transform, Fourier transform and convolution, Parseval Identity, applications, Laplace transform, the set of Laplace transformable functions, holomorphicity of of the transformed function, properties, Laplace transform and convolution, Laplace anti-trasform, applications.


Testi consigliati:

Complex Analysis M.W.Wong World Scientific Ed.

Mathematical Analysis for Engineers Dacorogna-Tanteri

Schaum's Outlines Complex Variables, McGraw Hill Ed.

Schaum's Outlines Laplace Transform, McGraw Hill Ed.

            
            
                         


Modalità d'esame:

written test


Risultati di apprendimento previsti:

Knowing the basic concepts and techniques of complex analysis and its applications


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