Complex Analysis Field of study: Mathematics
Programme code: W4-N2MT19.2023

Module name: Complex Analysis
Module code: W4-MT-N2-23-AZes
Programme code: W4-N2MT19.2023
Semester: winter semester 2023/2024
Language of instruction: Polish
Form of verification: exam
ECTS credits: 6
Purpose and description of the content of education:
Moduł obejmuje wykłady i ćwiczenia konwersatoryjne w zakresie zagadnień analizy zespolonej, leżącej u podstaw klasycznego wykształcenia matematycznego. Ramowy zakres modułu obejmuje następujące tematy: 1. Liczby zespolone. Płaszczyzna domknięta. Granica, ciągłość, pochodna funkcji zespolonej; równania Cauchy’ego-Riemanna. Elementarne funkcje zespolone. 2. Całka funkcji zespolonej; całka krzywoliniowa. Funkcja pierwotna. Indeks. 3. Funkcje holomorficzne. Wzór całkowy Cauchy’ego; twierdzenie Cauchy’ego. 4. Niemal jednostajna granica funkcji holomorficznych; twierdzenie Weierstrassa. Szeregi potęgowe. Szeregi Laurenta. 5. Punkty osobliwe odosobnione. 6. Twierdzenie o residuach.
List of modules that must be completed before starting this module (if necessary): not applicable
Learning outcome of the module Codes of the learning outcomes of the programme to which the learning outcome of the module is related [level of competence: scale 1-5]
prezentuje gotowość do studiowania zagadnień i rozwiązywania zadań w ramach realizowanego modułu [AZes_1]
 K_K01 [5/5]
prezentuje aktywność w dyskusji pojęć i faktów analizy zespolonej oraz w dążeniu do ich precyzyjnego formułowania i uzasadniania [AZes_2]
 K_K02 [4/5] K_K05 [4/5]
potrafi efektywnie wyrażać studiowane treści analizy zespolonej [AZes_3]
 K_U02 [3/5]
zna podstawowe pojęcia i narzędzia analizy zespolonej [AZes_4]
 K_W01 [3/5]
zna podstawowe twierdzenia obejmowane modułem [AZes_5]
 K_W03 [3/5]
potrafi konstruować rozumowania by przeprowadzać dowody wybranych twierdzeń analizy zespolonej [AZes_6]
 K_W02 [3/5] K_U01 [3/5]
Form of teaching Number of hours Methods of conducting classes Assessment of the learning outcomes Learning outcomes
lecture [AZes_fns_1] 15 Formal lecture/ course-related lecture [a01]  exam AZes_3 AZes_4 AZes_5 AZes_6
discussion classes [AZes_fns_2] 30 Activating method – peer learning [b08] 
Laboratory exercise / experiment [e01]  		course work AZes_1 AZes_2 AZes_3 AZes_4 AZes_5
The student's work, apart from participation in classes, includes in particular:
Name Category Description
Literature reading / analysis of source materials [a02] Preparation for classes
reading the literature indicated in the syllabus; reviewing, organizing, analyzing and selecting source materials to be used in class
Developing practical skills [a03] Preparation for classes
activities involving the repetition, refinement and consolidation of practical skills, including those developed during previous classes or new skills necessary for the implementation of subsequent elements of the curriculum (as preparation for class participation)
Getting acquainted with the syllabus content [b01] Consulting the curriculum and the organization of classes
reading through the syllabus and getting acquainted with its content
Verification / adjustment / discussion of syllabus provisions [b02] Consulting the curriculum and the organization of classes
consulting the content of the syllabus, possibly in the presence of the year tutor or members of the class group, and, if necessary, reassessing the provisions concerning special conditions for class participation, e.g., space and time requirements, technical and other requirements, including conditions for participation in classes outside the walls of the university, classes organized in blocks, organized online, etc.
Consulting the schedule [b03] Consulting the curriculum and the organization of classes
getting acquainted with the class schedule, possibly in the presence of the year tutor, in order to optimize participation in classes, including those supplementary to the core subjects listed in the pursued study programme
Determining the stages of task implementation contributing to the verification of learning outcomes [c01] Preparation for verification of learning outcomes
devising a task implementation strategy embracing the division of content, the range of activities, implementation time and/or the method(s) of obtaining the necessary materials and tools, etc.
Attachments
Module description (PDF)
Information concerning module syllabuses might be changed during studies.
Syllabuses (USOSweb)
Semester Module Language of instruction
(no information given)