# Course Details for A.Y. 2018/2019

#### Name:

**Complex analysis / Complex analysis**

### Basic information

##### Credits:

*:* Master Degree in Mathematical Engineering 6 CFU (b)

##### Degree(s):

Master Degree in Mathematical Engineering 1^{st} 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.
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- W. Rudin, Real and complex analysis , Mc Graw Hill.
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### 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*