Course Details for A.Y. 2019/2020
Name:
Complex analysis / Complex analysis
Basic information
Credits:
: Master Degree in Mathematical Engineering 6 CFU (b)
Degree(s):
Master Degree in Mathematical Engineering 1st anno curriculum Comune Elective
Language:
English
Course Objectives
Knowledge of basic topics of complex analysis: elementary functions of complex variable, differentiation, integration and main theorems on analytic functions . Ability to use such knowledge in solving problems and exercises
Course Content
- Complex numbers. Sequences. Elementary functions of complex numbers. Limits, continuity. Differentiation. Analytic functions. Armonic functions
- Contour integrals. Cauchy's Theorem. Cauchy's integral formula. Maximum modulus theorem. Liouville's theorem. Morera theorem.
- Series representation of analytic functions. Taylor's theorem. Laurent's series and classification of singularities
- Calculus of residues. The residue theorem. Application in evaluation of integrals on the real line and Principal Value. The logarithmic residue, Rouche's theorem.
- Fourier transform for L^1 functions. Applications. Fourier transform for L^2 functions. Plancherel theorem.
- Laplace transform and applications.
Prerequisites and Learning Activities
Knowledge of all topics treated the Mathematical Analysis courses in the first and second year : real function of real variables, limits, differentiation, integration; sequences and series of funcions; ordinary differential equations
Assessment Methods and Criteria
Written exam and oral exam
Textbooks
- J.E. Marsden, M.J. Hoffman, Basic complex analysis , Freeman New York.
- W. Rudin, Real and complex analysis , Mc Graw Hill.
Course page updates
This course page is available (with possible updates) also for the following academic years:
To read the current information on this course, if it is still available, go to the university course catalogue .
Course information last updated on: 14 settembre 2017, 18:18