The aim of studying and bibliography

The main aim of study: To acquaint the students with the selected topics of higher mathematics. The students will choose one of the two moduli given before the end of the second semester.

The general information about the module: The module is implemented in the second semester in the form of lectures (30 hours) and exercises (15 hours).

Bibliography required to complete the module

Bibliography used during lectures

1	M. Gewert, Z. Skoczylas	Analiza matematyczna 2. Definicje, twierdzenia, wzory	Oficyna Wydawnicza GiS, Wrocław.	2005
2	M. Gewert, Z. Skoczylas	Analiza matematyczna 2. Przykłady i zadania	Oficyna Wydawnicza GiS, Wrocław.	2005
3	W. Żakowski, W. Kołodziej	Matematyka, część II	WNT, Warszawa.	2003

Bibliography used during classes/laboratories/others

1	J. Banaś, S. Wędrychowicz	Zbiór zadań z analizy matematycznej	WNT, Warszawa.	2004
2	M. Gewert, Z. Skoczylas	Analiza matematyczna 2. Przykłady i zadania	Oficyna Wydawnicza GiS, Wrocław.	2005
3	W. Krysicki, L. Włodarski	Analiza matematyczna w zadaniach cz. 1 i cz. 2	PWN, Warszawa.	2004

Basic requirements in category knowledge/skills/social competences

Formal requirements: Knowledge of the basics of mathematical analysis (completed Mathematical analysis 1 and Mathematical analysis 2) and of linear algebra (module Linear algebra with geometry). The student satisfies the

Basic requirements in category knowledge: A student has mathematical knowledge which allows him/her to understand the lectured material.

Basic requirements in category skills: Ability to use the knowledge obtained during previous education at university.

Basic requirements in category social competences: A student is prepared to undertake substantiated mathematical operations in order to solve a task and has the ability to extend his/her knowledge independently.

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
01	knows how to examine pointwise or uniform convergence of function series	lecture, exercises	test	K_W01++ K_U01++ K_U25+ K_K01+	P6S_KK P6S_UU P6S_UW P6S_WG
02	knows how to expand a function to power series	lecture, exercises	test	K_W01++ K_U01++ K_U25+ K_K01+	P6S_KK P6S_UU P6S_UW P6S_WG
03	knows how to expand a function to Fourier series	lecture, exercises	test	K_W01++ K_U01++ K_U25+ K_K01+	P6S_KK P6S_UU P6S_UW P6S_WG

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).

The syllabus of the module

Sem.	TK	The content	realized in	MEK
4	TK01	Sequence and series of numbers - reminder.	W01-W04, C01-C02	MEK01 MEK02
4	TK02	Function sequences and function series: pointwise and uniform convergence, Weierstrass test and Dirichlet test for convergence of function series, continuity and differentiability of limit of function sequence and function series, differentiation and integration of series term-by-term, power series, radius of convergence and Hadamard theorem, expanding a function to Taylor and Maclaurin series, an example of continuous and nowhere differentiable function, approximation of continuous function by polynomials.	W05-W20, C03-C09	MEK01 MEK02
4	TK03	Fourier trigonometric series: Dirichlet theorem, expanding a function to Fourier series.	W21-W30, C10-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.
Class (sem. 4)	The preparation for a Class: 10.00 hours/sem.	contact hours: 15.00 hours/sem.	Finishing/Studying tasks: 5.00 hours/sem.
Advice (sem. 4)	The preparation for Advice: 2.00 hours/sem.	The participation in Advice: 2.00 hours/sem.
Credit (sem. 4)	The preparation for a Credit: 10.00 hours/sem.	The written credit: 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	A credit for the lecture is based on attendance at the lectures.
Class	A credit for the exercises is based on the result of tests and oral answers.
The final grade	The final grade is a credit for the exercises.

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: no