Complex Analysis, second course, 6 credits

Komplex analys fk, 6 hp

TATA78

Main field of study

Mathematics Applied Mathematics

Course level

Second cycle

Course type

Programme course

Examiner

Lars Alexandersson

Director of studies or equivalent

Jesper Thorén

Education components

Preliminary scheduled hours: 48 h
Recommended self-study hours: 112 h

Available for exchange students

Yes
ECV = Elective / Compulsory / Voluntary
Course offered for Semester Period Timetable module Language Campus ECV
6CYYI Applied Physics and Electrical Engineering - International, M Sc in Engineering 8 (Spring 2017) 1, 2 2, 3 Swedish Linköping E
6CYYI Applied Physics and Electrical Engineering - International, M Sc in Engineering 8 (Spring 2017) 1, 2 2, 4 Swedish/English Linköping E
6CYYI Applied Physics and Electrical Engineering - International, M Sc in Engineering 8 (Spring 2017) 1, 2 2, 4 Swedish/English Linköping E
6CYYI Applied Physics and Electrical Engineering - International, M Sc in Engineering 8 (Spring 2017) 1, 2 2, 4 Swedish/English Linköping E
6CYYY Applied Physics and Electrical Engineering, M Sc in Engineering 8 (Spring 2017) 1, 2 2, 3 Swedish Linköping E
6KMAT Mathematics 6 (Spring 2017) 1, 2 2, 3 Swedish Linköping E
6MMAT Mathematics, Master's programme 2 (Spring 2017) 1, 2 2, 3 Swedish Linköping E
6MMAT Mathematics, Master's programme (Mathematics) 2 (Spring 2017) 1, 2 2, 3 Swedish Linköping E

Main field of study

Mathematics, Applied Mathematics

Course level

Second cycle

Advancement level

A1X

Course offered for

  • Applied Physics and Electrical Engineering, M Sc in Engineering
  • Mathematics, Master's programme
  • Mathematics
  • Applied Physics and Electrical Engineering - International, M Sc in Engineering

Specific information

The course is only offered every second year. It will be offered during 2015.

Entry requirements

Note: Admission requirements for non-programme students usually also include admission requirements for the programme and threshold requirements for progression within the programme, or corresponding.

Prerequisites

Complex analysis or equivalent. In addition, Real analysis, honours course, or another more advanced course in mathematics is recommended.

Intended learning outcomes

To extend and enhance the complex analysis taught in the basic complex analysis course. In the course, the student also practices his/her ability to read and write mathematical text and mathematical proofs. After completing the course, the student should

  • be able to determine when a polynomial has all its zeros in the left half plane and outside the unit disk, and understand the theory behind the corresponding results,
  • have a good understanding of conformal mappings, complex analysis on the Riemann sphere, analytic continuation and branches of analytic functions,
  • be able to cite and explain some essential definitions and theorems about analytic continuation and Riemann surfaces,
  • know the explicit Riemann surfaces for some simple multi-valued functions.

 

Course content

More about the argument principle: the criteria of Routh-Hurwitz and Schur-Cohn. More about conformal mappings with applications. More about
residue calculus. Complex analysis on the Riemann sphere. Analytic and
meromorphic continuation. Explicit Riemann surfaces. Abstract Riemann surfaces.

Teaching and working methods

Lectures

Examination

UPG1Assignments and oral presentation6 creditsU, 3, 4, 5

Grades

Four-grade scale, LiU, U, 3, 4, 5

Department

Matematiska institutionen

Director of Studies or equivalent

Jesper Thorén

Examiner

Lars Alexandersson

Course website and other links

http://www.mai.liu.se/und/kurser/index-amne-tm.html

Education components

Preliminary scheduled hours: 48 h
Recommended self-study hours: 112 h

Course literature

Jones-Singerman, Complex functions: An algebraic and geometric viewpoint. Lars Alexandersson, TATA45 Komplex analys (kompendium) eller Saff-Snider, Fundamentals of complex analysis with applications to engineering and science. Kompletterande material utgivet av institutionen.
Code Name Scope Grading scale
UPG1 Assignments and oral presentation 6 credits U, 3, 4, 5

Regulations (apply to LiU in its entirety)

The university is a government agency whose operations are regulated by legislation and ordinances, which include the Higher Education Act and the Higher Education Ordinance. In addition to legislation and ordinances, operations are subject to several policy documents. The Linköping University rule book collects currently valid decisions of a regulatory nature taken by the university board, the vice-chancellor and faculty/department boards.

LiU’s rule book for education at first-cycle and second-cycle levels is available at http://styrdokument.liu.se/Regelsamling/Innehall/Utbildning_pa_grund-_och_avancerad_niva. 

Jones-Singerman, Complex functions: An algebraic and geometric viewpoint. Lars Alexandersson, TATA45 Komplex analys (kompendium) eller Saff-Snider, Fundamentals of complex analysis with applications to engineering and science. Kompletterande material utgivet av institutionen.

Note: The course matrix might contain more information in Swedish.

I = Introduce, U = Teach, A = Utilize
I U A Modules Comment
1. DISCIPLINARY KNOWLEDGE AND REASONING
1.1 Knowledge of underlying mathematics and science (G1X level)
X
X
X

                            
1.2 Fundamental engineering knowledge (G1X level)

                            
1.3 Further knowledge, methods, and tools in one or several subjects in engineering or natural science (G2X level)

                            
1.4 Advanced knowledge, methods, and tools in one or several subjects in engineering or natural sciences (A1X level)

                            
1.5 Insight into current research and development work

                            
2. PERSONAL AND PROFESSIONAL SKILLS AND ATTRIBUTES
2.1 Analytical reasoning and problem solving
X
X

                            
2.2 Experimentation, investigation, and knowledge discovery
X

                            
2.3 System thinking

                            
2.4 Attitudes, thought, and learning
X
X

                            
2.5 Ethics, equity, and other responsibilities

                            
3. INTERPERSONAL SKILLS: TEAMWORK AND COMMUNICATION
3.1 Teamwork

                            
3.2 Communications
X

                            
3.3 Communication in foreign languages
X

                            
4. CONCEIVING, DESIGNING, IMPLEMENTING AND OPERATING SYSTEMS IN THE ENTERPRISE, SOCIETAL AND ENVIRONMENTAL CONTEXT
4.1 External, societal, and environmental context

                            
4.2 Enterprise and business context

                            
4.3 Conceiving, system engineering and management

                            
4.4 Designing

                            
4.5 Implementing

                            
4.6 Operating

                            
5. PLANNING, EXECUTION AND PRESENTATION OF RESEARCH DEVELOPMENT PROJECTS WITH RESPECT TO SCIENTIFIC AND SOCIETAL NEEDS AND REQUIREMENTS
5.1 Societal conditions, including economic, social, and ecological aspects of sustainable development for knowledge development

                            
5.2 Economic conditions for knowledge development

                            
5.3 Identification of needs, structuring and planning of research or development projects

                            
5.4 Execution of research or development projects

                            
5.5 Presentation and evaluation of research or development projects

                            

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