The aim of studying and bibliography

The main aim of study: Skills calculating limits, derivatives and their use in the testing process functions. The ability of calculating definite integrals, improper, and their application using computer techniques. Using the power and trigonometric series.

The general information about the module: Mathematical analysis allows to learn contemporary mathematical terminology and basic research methods that find application in other fields of science.

Bibliography required to complete the module

Bibliography used during lectures

1	F. Leja	Rachunek różniczkowy i całkowy	PWN, Warszawa.	2016.
2	S. Banach	Rachunek różniczkowy i całkowy, t.1, t.2	PWN, Warszawa.	1955.
3	W. Żakowski, G. Decewicz	Analiza matematyczna, t. 1.	WNT, Warszawa.	2010.
4	W. Krysicki, L. Włodarski	Analiza matematyczna w zadaniach, t.1, t.2.	PWN, Warszawa.	2015.
5	M. Gewert, Z. Skoczylas	Analiza matematyczna 1. Przykłady i zadania.	GiS, Wrocław.	2016.

Basic requirements in category knowledge/skills/social competences

Formal requirements: Knowledge and skills in mathematics at school and computer skills. The student satisfies the formal requirements set out in the study regulations.

Basic requirements in category knowledge: Knowledge and skills in mathematics at school and computer skills.

Basic requirements in category skills: Thoughts.

Basic requirements in category social competences: Can behave and cooperate in a group.

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	He can calculate the limits of the function. He can calculate derivatives and use them to calculate boundaries, study the monotonicity of functions or extremes of a function.	lectures, exercises.	colloquium, exam	K_W01+ K_W02+ K_U01+ K_U25+ K_K01+	P6S_KK P6S_UU P6S_UW P6S_WG
02	He can calculate integrals and apply them. He uses the power and trigonometric series.	lecture, exercises	colloquium, exam	K_W01+ K_W02+ K_U01+ K_U25+ K_K01+	P6S_KK P6S_UU P6S_UW P6S_WG
03	He can solve the algebraic equations, systems of equations, generate function graphs, calculate integrals in practical problems in CAS Maxima.	laboratory	Practical Examination - written tests using Maxima CAS package.	K_W02+ K_U01+ K_K05+	P6S_KO 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
1	TK01	Real numbers. Logic.	W1, C1	MEK01
1	TK02	Cyclometric functions. Polynomials.	W2, C2	MEK01
1	TK03	Infinity. Induction.	W3, C3	MEK01
1	TK04	Limit of number sequences. Number e	W4, C4	MEK01 MEK03
1	TK05	Limit of function. Continuity of functions.	W5, C5	MEK01 MEK03
1	TK06	Derivative. Integral.	W6, C6	MEK01 MEK02 MEK03
1	TK07	Integration methods.	W7, C7	MEK01 MEK02 MEK03
1	TK08	Sets and continuous functions.	W8, C8	MEK01 MEK03
1	TK09	Applications of derivatives.	W9, C9	MEK01 MEK03
1	TK10	Riemann integral.	W10, C10	MEK01
1	TK11	Series.	W11, C11	MEK01
1	TK12	Sequences of functions. Power series.	W12, C12	MEK01 MEK02 MEK03
1	TK13	Improper integrals. Gamma function.	W13, C13	MEK02 MEK03
1	TK14	Fourier series.	W14, C14	MEK02 MEK03
1	TK15	Weierstrass approximation.	W15, C15	MEK01 MEK02 MEK03

The student's effort

The type of classes	The work before classes	The participation in classes	The work after classes
Lecture (sem. 1)		contact hours: 45.00 hours/sem.	complementing/reading through notes: 5.00 hours/sem. Studying the recommended bibliography: 10.00 hours/sem.
Class (sem. 1)	The preparation for a Class: 2.00 hours/sem. The preparation for a test: 8.00 hours/sem.	contact hours: 30.00 hours/sem.	Finishing/Studying tasks: 6.00 hours/sem.
Laboratory (sem. 1)	The preparation for a Laboratory: 1.00 hours/sem. The preparation for a test: 4.00 hours/sem.	contact hours: 15.00 hours/sem.	Finishing/Making the report: 2.00 hours/sem.
Advice (sem. 1)	The preparation for Advice: 1.00 hours/sem.	The participation in Advice: 2.00 hours/sem.
Exam (sem. 1)	The preparation for an Exam: 15.00 hours/sem.	The written exam: 4.00 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	Only students who passed the laboratory and obtained at least 50 points during the classes can take part in the exam. At the written exam without the use of computer techniques, the student may receive 0 - 50 points.
Class	In the case of two written colloquia, the student may receive 0-100 points.
Laboratory	Practical test (laboratory) using the CAS Maxima package.
The final grade	The final grade is the grade from the written exam. The written exam consists of 5 problems. You can get 0-50 points on the exam. Final score: [25.30) rating E, [30.35) rating D, [35.40) rating C, [40.45) rating B, [45.50] rating A.

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