Cycle of education: 2018/2019
The name of the faculty organization unit: The faculty Mathematics and Applied Physics
The name of the field of study: Mathematics
The area of study: sciences
The profile of studing:
The level of study: second degree study
Type of study: full time
discipline specialities : Applications of Mathematics in Computer Science, Applications of Mathematics in Economics
The degree after graduating from university:
The name of the module department : Departament of Discrete Mathematics
The code of the module: 1486
The module status: mandatory for teaching programme Applications of Mathematics in Computer Science, Applications of Mathematics in Economics
The position in the studies teaching programme: sem: 1 / W30 C30 / 6 ECTS / E
The language of the lecture: Polish
The name of the coordinator: Lucyna Trojnar-Spelina, PhD
office hours of the coordinator: Terminy podane na stronie https://lucynatrojnar-spelina.v.prz.edu.pl/
The main aim of study: Get aequitancedwith the theory of complex functions, undestanding some analogues and differences with the theory of real functions of one and two variable. Make the easy using the cocepts of complex analysis.
The general information about the module: The scope of the material concerns the introduction of the concept of the complex function of a real variable and its interpretation and application, complex function of a complex variable, its limits, continuity and derivatives and the concept of holomorphic function and meromorphic function and their properties
1 | Franciszek Leja | Funkcje zespolone | PWN Warszawa. | 2008 |
2 | J. Chądzyński | Wstęp do analizy zespolonej | Wydawnictwo Naukowe PWN. | 2000 |
1 | J. Krzyż | Zbiór zadań z funkcji analitycznych | Wydawnictwo Naukowe PWN. | 2005 |
2 | Bolesław Szafnicki | Zadania z funkcji zespolonych | PWN Warszawa, Kraków. | 1971 |
1 | A. Ganczar | Analiza Matematyczna w zadaniach | Wydawnictwo Naukowe PWN. | 2010 |
Formal requirements: First year of supplementary stuies in the field of mathematics
Basic requirements in category knowledge: Basic knowledge of differential calculus of functions of real variables. Basic knowledge of algebra and geometry.
Basic requirements in category skills: Ability to calculate derivatives and integrals of real functions of one and several variables.
Basic requirements in category social competences: Awareness of the level of knowledge and skills in mathematics, particularly in complex analysis and the tendency of its widening.
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 OEK |
---|---|---|---|---|---|
01 | Knows the basic transformation of the complex plane, can describe conics on the complex plane. Knows concept of the sequence and series of complex numbers, including power series. Student can compute limit of the sequence and examine the convergence of the series | lectures, tutorials, | written test |
K_W01+ K_W04++ K_K07+ |
X2A_W02 X2A_K06 |
02 | knows the concept of derivative and formal derivative of complex functions, can provide some elementary functions in a power series | lectures, exercises | written test |
K_W02++ K_W07+ K_U01+ |
X2A_W02 X2A_W03+ X2A_U01 X2A_U02 X2A_U05 |
03 | Knows the concept of analytic function and holomorphic function and knows their basic properties. It can determine whether the function is analytic or holomorphic | lectures, exercises | written or oral exam |
K_W01+ K_W05++ K_U02+ K_U03+ K_U04+ K_U05+ K_U13+ |
X2A_W02 X2A_U01++ X2A_U02 X2A_U03 X2A_U05 |
04 | Knows the notion of a meromorphic function, and singular points and residues of functions. Can determine a type of singularity of the selected point. | lectures, exercises | written or oral exam |
K_W01+ K_W03+ K_U05+ |
X2A_W01 X2A_W06 X2A_U01+ |
Attention: Depending on the epidemic situation, verification of the achieved learning outcomes specified in the study program, in particular credits and examinations at the end of specific classes, can be implemented remotely (real-time meetings).
Sem. | TK | The content | realized in | MEK |
---|---|---|---|---|
1 | TK01 | W01-W15, C01-C15 | MEK01 | |
1 | TK02 | W01-W15, C01-C15 | MEK02 | |
1 | TK03 | W01-W15, C01-C15 | MEK03 | |
1 | TK04 | W01-W15, C01-C15 | MEK04 |
The type of classes | The work before classes | The participation in classes | The work after classes |
---|---|---|---|
Lecture (sem. 1) | The preparation for a test:
15.00 hours/sem. |
contact hours:
30.00 hours/sem. |
complementing/reading through notes:
10.00 hours/sem. Studying the recommended bibliography: 15.00 hours/sem. |
Class (sem. 1) | The preparation for a Class:
15.00 hours/sem. The preparation for a test: 10.00 hours/sem. |
contact hours:
30.00 hours/sem. |
Finishing/Studying tasks:
15.00 hours/sem. Others: 10.00 hours/sem. |
Advice (sem. 1) | The preparation for Advice:
10.00 hours/sem. |
The participation in Advice:
5.00 hours/sem. |
|
Exam (sem. 1) |
The type of classes | The way of giving the final grade |
---|---|
Lecture | The basis for passing the lecture is attendance. |
Class | To pass classes student should participate in exercise classes. The grade of classes is the arithmetic mean of positive marks of two written tests. It can be increased by 1/2 degree after taking into account the activity of the classes. Each of the tests includes basic tasks, associated with the effect of modular training (I test - MEK01, II test - MEK02) and additional tasks that can be associated with other educational content, implemented in the classroom. The solution of additional tasks allows to get higher than 3.0 mark of the written test. |
The final grade | Final mark, after completing all the MEKs is the arithmetic mean of marks of the exercices and exam rounded to the nearest mark permitted by the regulations of studies. Written or oral exam includes basic tasks related to MEK03 and MEK04 and additional tasks that can be associated with other educational content, implemented in the classroom. Solutions of the additional tasks is the basis for obtaining the mark of the exam, higher than 3.0. |
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