First cycle
degree courses
Second cycle
degree courses
Single cycle
degree courses
School of Science
MATHEMATICS
Course unit
COMPLEX ANALYSIS
SCN1037789, A.A. 2015/16

Information concerning the students who enrolled in A.Y. 2015/16

Information on the course unit
Degree course Second cycle degree in
MATHEMATICS
SC1172, Degree course structure A.Y. 2011/12, A.Y. 2015/16
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Degree course track ALGANT [001PD]
Number of ECTS credits allocated 6.0
Type of assessment Mark
Course unit English denomination COMPLEX ANALYSIS
Website of the academic structure http://matematica.scienze.unipd.it/2015/laurea_magistrale
Department of reference Department of Mathematics
Mandatory attendance No
Language of instruction English
Branch PADOVA
Single Course unit The Course unit can be attended under the option Single Course unit attendance
Optional Course unit The Course unit can be chosen as Optional Course unit

Lecturers
Teacher in charge PIETRO POLESELLO MAT/05

Mutuating
Course unit code Course unit name Teacher in charge Degree course code
SCN1037789 COMPLEX ANALYSIS PIETRO POLESELLO SC1172

ECTS: details
Type Scientific-Disciplinary Sector Credits allocated
Core courses MAT/05 Mathematical Analysis 6.0

Course unit organization
Period Second semester
Year 1st Year
Teaching method frontal

Type of hours Credits Teaching
hours
Hours of
Individual study
Shifts
Practice 3.0 24 51.0 No turn
Lecture 3.0 24 51.0 No turn

Calendar
Start of activities 01/03/2016
End of activities 15/06/2016
Show course schedule 2019/20 Reg.2011 course timetable

Examination board
Board From To Members of the board
6 Analisi Complessa - a.a. 2018/2019 01/10/2018 30/09/2019 POLESELLO PIETRO (Presidente)
D'AGNOLO ANDREA (Membro Effettivo)
BARACCO LUCA (Supplente)
MARASTONI CORRADO (Supplente)
ROSSI FRANCESCO (Supplente)
5 Analisi Complessa - 2016/2017 01/10/2016 30/11/2017 POLESELLO PIETRO (Presidente)
D'AGNOLO ANDREA (Membro Effettivo)
BARACCO LUCA (Supplente)
CARAVENNA LAURA (Supplente)
MARASTONI CORRADO (Supplente)
4 Analisi Complessa - a.a. 2015/2016 01/10/2015 30/11/2016 POLESELLO PIETRO (Presidente)
D'AGNOLO ANDREA (Membro Effettivo)
BARACCO LUCA (Supplente)
CARAVENNA LAURA (Supplente)
MARASTONI CORRADO (Supplente)

Syllabus
Prerequisites: - undergraduate courses in Calculus and Geometry

- elementary notions on complex functions of one complex variable. In particular:
Cauchy-Riemann identities and complex differentiation; holomorphic functions. Line integrals of complex functions and their homotopy invariance.
Logarithm of a path and winding number. Cauchy formula for a circle. Analiticity of holomorphic functions.
Zero-set of a holomorphic function; the identity theorem. Open mapping theorem.
Laurent series and isolated singularities. Residue theorem, and its use for the computation of integrals.
Target skills and knowledge: Advanced notions on complex functions of one complex variable, with applications
Examination methods: Written exam with possible additional oral exam
Assessment criteria: standard
Course unit contents: The argument principle and applications
The Schwarz reflection principle
Conformal maps and the Riemann Mapping theorem
Runge's theory and applications
Mittag-Leffler's theorem
The Weierstrass factorization theorem
Principal ideals of holomorphic functions
Some special functions (Gamma, Zeta)
The Prime Number theorem
Planned learning activities and teaching methods: Lectures and exercises
Additional notes about suggested reading: Additional references:

Giuseppe De Marco - Basic Complex Analysis (2011)

Giuseppe De Marco, Selected Topics of Complex Analysis (2012).

Reinhold Remmert - Theory of Complex Functions, Graduate Texts in Mathematics, Springer-Verlag (1991)

Robert B. Ash, W. P. Novinger - Complex Variables: Second Edition, Dover Books on Mathematics (2007)
Textbooks (and optional supplementary readings)
  • Jean-Pierre Schneiders, Fonctions de Variables Complexes. Université de Liège: self published, 2010. the pdf will be available from the course's home page
  • Rudin, Walter, Real and complex analysisWalter Rudin. New York [etc.]: McGraw-Hill, --. Cerca nel catalogo
  • Gamelin, Theodore W., Complex analysisTheodore W. Gamelin. New York [etc.]: Springer, --. Cerca nel catalogo
  • Remmert, Reinhold, Classical topics in complex function theoryReinhold Remmerttraslated by Leslie Kay. New York [etc.]: Springer, --. Cerca nel catalogo