| TATA78 |
Complex analysis, second course, 6 ECTS credits.
/Komplex analys fk/
For:
Mat
MMAT
Y
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OBS! |
The course is only offered every second year. It will be offered during 2017.
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Prel. scheduled
hours: 48
Rec. self-study hours: 112
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Area of Education: Science
Main field of studies: Mathematics, Applied mathematics
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Advancement level
(G1, G2, A): A
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Aim:
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.
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Prerequisites: (valid for students admitted to programmes within which the course is offered)
Complex analysis or equivalent. In addition, Real analysis, honours course, or another more advanced course in mathematics is recommended.
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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Organisation:
Lectures and problem seminars.
The course runs over the entire spring semester.
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Course contents:
More about the argument principle: the criteria of Routh-Hurwitz and Schur-Cohn. More about conformal mappings with applications, in particular Schwarz-Christoffel transformations. More about residue calculus. Complex analysis on the Riemann sphere. Analytic and meromorphic continuation. Explicit Riemann surfaces. Abstract Riemann surfaces.
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Course literature:
Jones-Singerman, Complex functions: An algebraic and geometric viewpoint.
Lars Alexandersson, TATA45 Komplex analys (compendium, 2015 or later)
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Examination: |
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Assignments and oral presentation
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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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