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| MATH0220-2 | Functions of complex variables
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| Duration : | 30h Th, 10h Pr, 20h Mon. WS |
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| Number of credits : |
| Master in Mathematical Sciences, in-depth approach, 1st year | | 8 |
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| Master in Mathematical Sciences, didactic approach, 1st year | | 8 |
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| Master in Mathematical Sciences, professional focus in management, 1st year | | 8 |
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| Master in Mathematical Sciences, professional focus in computer science, 1st year | | 8 |
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| Master en sciences mathématiques, à finalité spécialisée en statistique, 1st year | | 8 |
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| Master in Mathematical Sciences, specialized approach, 1st year | | 8 |
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| Master in Mathematical Sciences | | 8 |
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| Lecturer : | Jean-Pierre Schneiders |
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Language(s) of instruction :
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| French language |
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Organisation and examination :
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| Teaching in the second semester |
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Course contents :
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| This course is a sequel to the course on functions of one complex variable for second year students. This year, it will deal with the following subjects:
- Local structure and prolongation of holomorphic functions
- Biholomorphic functions and conformal representation
- Runge, Mittag-Leffler and Weierstrass theorems
- Elliptic integrals and elliptic functions
- Riemann surfaces
- Holomorphic linear differential equations
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Learning outcomes of the course :
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| After this course, the students should have understood how to solve a few classical global problems of the theory of holomorphic functions and gathered important tools for a more advanced study of complex analysis. |
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Prerequisites and co-requisites/ Recommended optional programme components :
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| A good knowledge of the results of the theory of holomorphic functions studied during the second year course is essential. |
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Planned learning activities and teaching methods :
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| The course consists of blackboard lessons, exercises sessions and a personal work.
During the lessons, the main theoretical results are introduced, established and illustrated with examples.
During the exercises sessions, the students are trained to solve by themselves various problems using the results considered in the lessons
The personal work consists of the preparation of a short paper presenting and establishing a result related to the course but not considered during the lessons. |
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Mode of delivery (face-to-face ; distance-learning) :
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| Face-to-face course. |
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Recommended or required readings :
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| Lecture notes are handed out to the students at the beginning of the course. |
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Assessment methods and criteria :
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| An examination comprising an oral part on the theory and a presentation of the personal work is organized during the first session. A similar examination is organized during the second session. |
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Work placement(s) :
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Organizational remarks :
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| The course follows the official schedule handed out to the students at the beginning of the academic year. |
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Contacts :
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| Jean-Pierre Schneiders
Département de Mathématique (Bât. B37, Bureau 1/60)
Grande Traverse 12 - 4000 Liège (Sart-Tilman)
Phone: (04) 366.94.01 - E-Mail: jpschneiders@ulg.ac.be
Web page: http://www.analg.ulg.ac.be/jps/ |
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| Items online : |
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| Web page of the course |
| Web page giving access to various informations on the course and to the electronic version of the notes. |
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