470-2110/07 – Mathematical Analysis 1 (MA1)

Gurantor department	Department of Applied Mathematics	Credits	6
Subject guarantor	prof. RNDr. Jiří Bouchala, Ph.D.	Subject version guarantor	prof. RNDr. Jiří Bouchala, Ph.D.
Study level	undergraduate or graduate	Requirement	Compulsory
Year	1	Semester	winter
		Study language	Czech
Year of introduction	2024/2025	Year of cancellation
Intended for the faculties	FMT, FEI	Intended for study types	Bachelor

Instruction secured by
Login	Name	Tuitor	Teacher giving lectures
BOU10	prof. RNDr. Jiří Bouchala, Ph.D.
SAD015	Ing. Marie Sadowská, Ph.D.
S1A64	RNDr. Petra Vondráková, Ph.D.

Extent of instruction for forms of study
Form of study	Way of compl.	Extent
Full-time	Credit and Examination	3+3
Part-time	Credit and Examination	15+15

Subject aims expressed by acquired skills and competences

Students will get basic practical skills for work with fundamental concepts, methods and applications of differential and integral calculus of one-variable real functions.

Teaching methods

Lectures
Tutorials
Project work

Summary

In the first part of this subject, there are fundamental properties of the set of real numbers mentioned. Further, basic properties of elementary functions are recalled. Then limit of sequence, limit of function, and continuity of function are defined and their basic properties are studied. Differential and integral calculus of one-variable real functions is essence of this course.

Compulsory literature:

BOUCHALA, Jiří; SADOWSKÁ, Marie. Mathematical Analysis I, 2007. http://www.am.vsb.cz/bouchala

Recommended literature:

ANTON, Howard; BIVENS, Irl a DAVIS, Stephen. Calculus. 8th ed. Hoboken: Wiley, c2005. ISBN 0-471-48273-0.

Way of continuous check of knowledge in the course of semester

Průběžná kontrola studia: Studenti v průběhu semestru budou psát písemné testy a vypracují zadané projekty. Za testy lze získat maximálně 24 body, za projekty 6 bodů. Podmínky udělení zápočtu: K získání zápočtu je nutné získat minimálně 10 bodů. Zkouška je písemná.

E-learning

Other requirements

No additional requirements are imposed on the student.

Prerequisities

Subject has no prerequisities.

Co-requisities

Subject has no co-requisities.

Subject syllabus:

Real Number System. Real Functions of a Single Real Variable. Elementary Functions. Sequences of Real Numbers. Limit and Continuity of a Function. Differential and Derivative of a Function. Basic Theorems of Differential Calculus. Function Behaviour. Approximation of a Function by a Polynomial. Antiderivative (Indefinite Integral). Riemann’s (Definite) Integral.

Conditions for subject completion

Full-time form (validity from: 2024/2025 Winter semester)

Task name	Type of task	Max. number of points (act. for subtasks)	Min. number of points	Max. počet pokusů
Credit and Examination	Credit and Examination	100 (100)	51
Credit	Credit	30	10
Examination	Examination	70	21	3

Mandatory attendence participation: Obligatory participation in 80% of the exercises. Attendance at lectures is expected.

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Conditions for subject completion and attendance at the exercises within ISP: Completion of all mandatory tasks within individually agreed deadlines.

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Occurrence in study plans

Academic year	Programme	Branch/spec.	Spec.	Zaměření	Form	Study language	Tut. centre	Year	W	S	Type of duty
2024/2025	(B0533A110023) Applied Physics				P	Czech	Ostrava	1			Compulsory	study plan

Occurrence in special blocks

Block name	Academic year	Form of study	Study language	Year	W	S	Type of block	Block owner

Assessment of instruction

Předmět neobsahuje žádné hodnocení.