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Complex Analysis, 6 credits
Komplex analys, 6 hp
TATA45
Main field of study
Mathematics Applied MathematicsCourse level
First cycleCourse type
Programme courseExaminer
Lars AlexanderssonDirector of studies or equivalent
Mikael LangerEducation components
Preliminary scheduled hours: 60 hRecommended self-study hours: 100 h
ECV = Elective / Compulsory / Voluntary
Main field of study
Mathematics, Applied MathematicsCourse level
First cycleAdvancement level
G2FCourse 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
| 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.
Grades for examination modules are decided in accordance with the assessment criteria presented at the start of the course.
Grades
Four-grade scale, LiU, U, 3, 4, 5Other 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 institutionenCourse 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.
Grades for examination modules are decided in accordance with the assessment criteria presented at the start of the course.
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
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X
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X
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TEN1
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| 1.2 Fundamental engineering knowledge (G1X level) |
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| 1.3 Further knowledge, methods, and tools in one or several subjects in engineering or natural science (G2X level) |
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| 1.4 Advanced knowledge, methods, and tools in one or several subjects in engineering or natural sciences (A1X level) |
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| 1.5 Insight into current research and development work |
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| 2. PERSONAL AND PROFESSIONAL SKILLS AND ATTRIBUTES | ||||||
| 2.1 Analytical reasoning and problem solving |
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X
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X
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TEN1
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| 2.2 Experimentation, investigation, and knowledge discovery |
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X
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| 2.3 System thinking |
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| 2.4 Attitudes, thought, and learning |
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X
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X
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TEN1
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| 2.5 Ethics, equity, and other responsibilities |
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| 3. INTERPERSONAL SKILLS: TEAMWORK AND COMMUNICATION | ||||||
| 3.1 Teamwork |
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| 3.2 Communications |
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X
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| 3.3 Communication in foreign languages |
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| 4. CONCEIVING, DESIGNING, IMPLEMENTING AND OPERATING SYSTEMS IN THE ENTERPRISE, SOCIETAL AND ENVIRONMENTAL CONTEXT | ||||||
| 4.1 External, societal, and environmental context |
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| 4.2 Enterprise and business context |
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| 4.3 Conceiving, system engineering and management |
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| 4.4 Designing |
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| 4.5 Implementing |
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| 4.6 Operating |
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| 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 |
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| 5.2 Economic conditions for knowledge development |
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| 5.3 Identification of needs, structuring and planning of research or development projects |
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| 5.4 Execution of research or development projects |
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| 5.5 Presentation and evaluation of research or development projects |
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