Teaching plan for the course unit

 

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General information

 

Course unit name: Complex Analysis of One or More Variables

Course unit code: 568181

Academic year: 2018-2019

Coordinator: Joaquin Ortega Cerda

Department: Department of Mathematics and Computer Science

Credits: 6

Single program: S

 

 

Estimated learning time

Total number of hours 150

 

Face-to-face learning activities

64

 

-  Lecture

 

32

 

-  Lecture with practical component

 

32

Supervised project

(Final assignment.)

38

Independent learning

(Problem study and resolution.)

48

 

 

Recommendations

 


Students should have completed a subject in complex variables.

 

 

Competences to be gained during study

 


— Capacity for rigorous analysis of theoretical or practical problems under conditions of uncertainty, for the purpose of expanding knowledge and later developing research and working in multidisciplinary contexts. 
 
— Ability to access the bibliographic items available that are required to achieve the above.
 
— Understanding of rigorous mathematical arguments and the capacity for rigorous expression in mathematical language.
 
— Capacity for the exchange of ideas when working on a group project.

 

 

 

 

Learning objectives

 

Referring to knowledge


— To understand elements of potential theory, harmonic and subharmonic functions, and the relationship with holomorphic functions.

 


— To understand the role of the Cauchy-Riemann equation in the study of holomorphic functions.

 


— To identify the basic differences between the theory of functions of a complex variable and that of several variables.

 

Referring to abilities, skills


— To perform introductory mathematical research in this field, starting with the appropriate bibliographical sources.

 

 

Teaching blocks

 

1. The inhomogeneous Cauchy-Riemann equation and applications

2. Harmonic functions and the Dirichlet problem

3. Subharmonic functions and zeros of holomorphic functions

4. Functions of several variables; Local theory

 

 

Teaching methods and general organization

 


The different subject areas are introduced in lecture classes. A collection of problems relating to each teaching block is handed out, and the procedures for solving them are explained and discussed in class; Students are required to submit completed answers to some or all of the problems on the list; Once the answers have been marked, they are discussed in class

 

 

Official assessment of learning outcomes

 

Assessment is based on the submitted answers to problems. There is also a final project that has

to presented.

 

 

Reading and study resources

Consulteu la disponibilitat a CERCABIB

Book

M. Andersson: Topics in Complex Analysis, Universitext: Tracts in Mathematics, Springer 1997

J. Bruna, J. Cufí: Complex Analysis, EMS Textbooks in Mathematics 2013

S. Krantz: Function theory of several complex variables , AMS-chelsea 1992

L. Hörmander: Complex analysis in several variables, North Holland 1973

T. Ransford: Potential Theory in the Complex Plane, London Math Society.

W. Rudin: Real and Complex Analysis McGraw-Hill, New. York, 1966

Web page

J. Korevaar-J. Wiegerinck: Lecture notes several complex variables