| TATA45 |
Complex Analysis, 6 ECTS credits.
/Komplex analys/
For:
FyN
I
Ii
Mat
Y
Yi
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Prel. scheduled
hours: 60
Rec. self-study hours: 100
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Area of Education: Science
Main field of studies: Mathematics, Applied Mathematics
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Advancement level
(G1, G2, A): G2
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Aim:
The course will give basic proficiency in one-variable complex analysis required for subsequent studies. After completing this course, students should
- be able to define and explain basic concepts such as analytic function och harmonic function, and discuss connections between these function classes
- be familiar with the elementary functions and their properties
- be able to classify different types of singular points and discuss their characteristic properties
- be able to formulate and use central results in complex analysis such as the Cauchy-Riemann equations, the Cauchy integral theorem and formula and their applications, the maximum principle, Taylor and Laurent expansions of analytic functions, the residue theorem and its applications, the argument principle and how to use it
- know the fundamental properties of linear fractional transformations and how to use them in conformal mapping.
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Prerequisites: (valid for students admitted to programmes within which the course is offered)
Linear Algebra and Calculus in ona and several variables or equivalent. Vector calculus is recommended but not necessary.
Note: Admission requirements for non-programme students usually also include admission requirements for the programme and threshhold requirements for progression within the programme, or corresponding.
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Supplementary courses:
Fourier analysis
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Organisation:
Lectures and lessons.
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Course contents:
Complex numbers. The notion of analytic function. Elementary functions. Complex line integrals. Cauchy's integral theorem and formula. Taylor and Laurent series. Residue calculus. The argument principle. Linear fractional transformations.
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Course literature:
Lars Alexandersson, TATA45 Komplex analys (kompendium)
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Examination: |
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Written examination
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6 ECTS
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Course language is Swedish.
Department offering the course: MAI.
Director of Studies: Jesper Thorén
Examiner: Lars Alexandersson
Link to the course homepage at the department
Course Syllabus in Swedish
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