Introduction to the Theory of Complex Functions
Some basic information about the module
The aim of studying and bibliography
The main aim of study:
Extending the concept of real numbers - the concept of complex numbers and algebraic operations on complex numbers, analogies and differences in terms of operations on real numbers. Extending the concept of complex functions of a complex variable functions. The ability to calculate derivatives oran borders. Interpretations of these concepts.
The general information about the module:
The module consists of 30 hours of lectures and 15 hours of exercises. It ends with an exam
Bibliography required to complete the module
| 1 | Franciszek Leja | Funkcje zespolone | PWN Warszawa. | 2008 |
| 2 | J. Chądzyński | Wstęp do analizy zespolonej | Wydawnictwo Naukowe PWN. | 2000 |
| 1 | Bolesław Szafnicki | Zadania z funkcji zespolonych | PWN Warszawa, Kraków. | 1971 |
| 2 | J. Krzyż | Zbiór zadań z funkcji analitycznych | Wydawnictwo Naukowe PWN,. | 2005 |
| 1 | A. Ganczar | Analiza Matematyczna w zadaniach | Wydawnictwo Naukowe PWN. | 2010 |
Basic requirements in category knowledge/skills/social competences
Formal requirements:
The student satisfies the formal requirements set out in the study regulations
Basic requirements in category knowledge:
Basic knowledge of the concepts of limit, continuity and differentiation for real functions of one and two real variables. Basic information of analytic geometry in the plane,
Basic requirements in category skills:
It can set the boundaries of sequences and functions. It can calculate the derivatives and partial derivatives of elementary functions.
Basic requirements in category social competences:
Is aware of the level of their knowledge and skills in mathematics, particularly in complex analysis and the need to raise.
Module outcomes
| MEK | The student who completed the module | Types of classes / teaching methods leading to achieving a given outcome of teaching | Methods of verifying every mentioned outcome of teaching | Relationships with KEK | Relationships with PRK |
|---|---|---|---|---|---|
| MEK01 | Familiar with the concept of a complex number and its relationship to real numbers. It can perform actions in the set of complex numbers, describe and represent collections on the complex plane. Familiar with the concept of numerical sequences and series (in the set of complex numbers) | lectures, tutorials | colloquium or exam |
K-W01+ K-U01+ K-K01+ |
P6S-KK P6S-UK P6S-WK |
| MEK02 | Familiar with the basic functions of complex, in the fields of real and complex, familiar with the term limit and continuity of complex functions. | lectures, tutorials | colloquium or exam |
K-W02+ K-W03+ K-U01+ K-K01+ |
P6S-KK P6S-UK P6S-WG P6S-WK |
| MEK03 | Familiar with the concept of a complex derivative and formal derivative of complex functions. It can set the derivatives of .basic complex functions. | lectures, toutorial | colloquium or exam |
K-W04++ K-W05+ K-K01+ |
P6S-KK P6S-WG P6S-WK |
The syllabus of the module
| Sem. | TK | The content | realized in | MEK |
|---|---|---|---|---|
| 4 | TK01 | W01-W15, C01-C15 | MEK01 | |
| 4 | TK02 | W01-W15, C01-C15 | MEK02 | |
| 4 | TK03 | W01-W15, C01-C15 | MEK03 |
The student's effort
| The type of classes | The work before classes | The participation in classes | The work after classes |
|---|---|---|---|
| Lecture (sem. 4) | contact hours:
30.00 hours/sem. |
complementing/reading through notes:
5.00 hours/sem. Studying the recommended bibliography: 10.00 hours/sem. |
|
| Class (sem. 4) | The preparation for a Class:
5.00 hours/sem. The preparation for a test: 5.00 hours/sem. |
contact hours:
15.00 hours/sem. |
Finishing/Studying tasks:
4.00 hours/sem. |
| Advice (sem. 4) | The preparation for Advice:
1.00 hours/sem. |
The participation in Advice:
1.00 hours/sem. |
|
| Exam (sem. 4) | The preparation for an Exam:
7.00 hours/sem. |
The written exam:
2.00 hours/sem. |
The way of giving the component module grades and the final grade
| The type of classes | The way of giving the final grade |
|---|---|
| Lecture | written exam |
| Class | test, activity |
| The final grade |
Sample problems
Required during the exam/when receiving the credit
(-)
Realized during classes/laboratories/projects
(-)
Others
(-)
Can a student use any teaching aids during the exam/when receiving the credit : no
The contents of the module are associated with the research profile yes
| 1 | M. Nunokawa; K. Piejko; J. Sokół | Applications of Jack’s lemma | 2024 |
| 2 | K. Piejko; J. Sokół; K. Trąbka-Więcław | Coefficient bounds in the class of functions associated with Sakaguchi\'s functions | 2023 |
| 3 | K. Piejko; J. Sokół; K. Trąbka-Więcław | On q-starlike functions | 2023 |
| 4 | K. Piejko; J. Sokół | On convolution and q-calculus | 2020 |