Complex Analysis, 6 credits

Komplex analys, 6 hp

TATA45

Main field of study

Mathematics Applied Mathematics

Course level

First cycle

Course type

Programme course

Examiner

Lars Alexandersson

Director of studies or equivalent

Mikael Langer

Education components

Preliminary scheduled hours: 60 h
Recommended self-study hours: 100 h
ECV = Elective / Compulsory / Voluntary
Course offered for Semester Period Timetable module Language Campus ECV
6CYYY Applied Physics and Electrical Engineering, Master of Science in Engineering 3 (Autumn 2025) 2 1 Swedish Linköping, Valla C
6CTMA Engineering Mathematics, Master of Science in Engineering 3 (Autumn 2025) 2 1 Swedish Linköping, Valla C
6CIEI Industrial Engineering and Management - International, Master of Science in Engineering, Chinese 7 (Autumn 2025) 2 1 Swedish Linköping, Valla E
6CIEI Industrial Engineering and Management - International, Master of Science in Engineering, French 7 (Autumn 2025) 2 1 Swedish Linköping, Valla E
6CIEI Industrial Engineering and Management - International, Master of Science in Engineering, German 7 (Autumn 2025) 2 1 Swedish Linköping, Valla E
6CIEI Industrial Engineering and Management - International, Master of Science in Engineering, Japanese 7 (Autumn 2025) 2 1 Swedish Linköping, Valla E
6CIEI Industrial Engineering and Management - International, Master of Science in Engineering, Spanish 7 (Autumn 2025) 2 1 Swedish Linköping, Valla E
6CIII Industrial Engineering and Management, Master of Science in Engineering 7 (Autumn 2025) 2 1 Swedish Linköping, Valla E
6KMAT Mathematics, Bachelor's Programme 3 (Autumn 2025) 2 1 Swedish Linköping, Valla C

Main field of study

Mathematics, Applied Mathematics

Course level

First cycle

Advancement level

G2F

Course offered for

  • Master of Science in Industrial Engineering and Management - International
  • Master of Science in Industrial Engineering and Management
  • Bachelor's Programme in Mathematics
  • Master of Science in Applied Physics and Electrical Engineering
  • Master of Science in Engineering Mathematics

Prerequisites

Linear Algebra and Calculus in ona and several variables or equivalent. Vector calculus is recommended but not necessary.

Intended learning outcomes

After completing the course, the student should be able to

  • choose and apply methods to problems in all parts I-III of the course, as they are described in the course content
  • present and justify solutions to tasks within the course content using relevant concepts and clear reasoning

 

Course content

Part I: Numbers, Functions and Images Complex numbers and functions. Limits, continuity and derivatives. Analytical and harmonic functions. Elementary functions. Conformal mapping, especially Möbius mapping.

Part II: Integrals and Series Complex curve integrals. Primitive functions. Cauchy's integral theorem and integral formula. The maximum principle. Numerical series and power series. Taylor and Laurent series. Zero points and singularities.

Part III: Residual calculus and the argument principle Residues and the residue clause. Integrals of trigonometric and rational functions. Fourier-type integrals. Indented contours and keyhole contours. The argument principle and Rouché's theorem.

Teaching and working methods

Lectures and lessons.

Examination

TEN1Written examination6 creditsU, 3, 4, 5
UPG1Optional Assignments0 creditsU, G
UPG2Optional Assignments0 creditsU, G
UPG3Optional Assignments0 creditsU, G

The optional assignments may give bonus points on the written examination.

Grades

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

Other information

Supplementary courses: Fourier analysis, Complex analysis second course 

About teaching and examination language

The teaching language is presented in the Overview tab for each course. The examination language relates to the teaching language as follows: 

  • If teaching language is “Swedish”, the course as a whole could be given in Swedish, or partly in English. Examination language is Swedish, but parts of the examination can be in English.
  • If teaching language is “English”, the course as a whole is taught in English. Examination language is English.
  • If teaching language is “Swedish/English”, the course as a whole will be taught in English if students without prior knowledge of the Swedish language participate. Examination language is Swedish or English depending on teaching language.

Other

The course is conducted in such a way that there are equal opportunities with regard to sex, transgender identity or expression, ethnicity, religion or other belief, disability, sexual orientation and age.

The planning and implementation of a course should correspond to the course syllabus. The course evaluation should therefore be conducted with the course syllabus as a starting point. 

The course is campus-based at the location specified for the course, unless otherwise stated under “Teaching and working methods”. Please note, in a campus-based course occasional remote sessions could be included.  

Department

Matematiska institutionen

Course literature

Books

Compendia

  • Lars Alexandersson, TATA45 Komplex analys (kompendium)
Code Name Scope Grading scale
TEN1 Written examination 6 credits U, 3, 4, 5
UPG1 Optional Assignments 0 credits U, G
UPG2 Optional Assignments 0 credits U, G
UPG3 Optional Assignments 0 credits U, G

The optional assignments may give bonus points on the written examination.

Books

Compendia

Lars Alexandersson, TATA45 Komplex analys (kompendium)

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
TEN1

                            
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
TEN1

                            
2.2 Experimentation, investigation, and knowledge discovery
X

                            
2.3 System thinking

                            
2.4 Attitudes, thought, and learning
X
X
TEN1

                            
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

                            
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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