470-2111/02 – Mathematical Analysis 2 (MA2)

Gurantor department	Department of Applied Mathematics	Credits	4
Subject guarantor	doc. Mgr. Petr Vodstrčil, Ph.D.	Subject version guarantor	doc. Mgr. Petr Vodstrčil, Ph.D.
Study level	undergraduate or graduate	Requirement	Compulsory
Year	1	Semester	summer
		Study language	English
Year of introduction	2015/2016	Year of cancellation	2021/2022
Intended for the faculties	FEI	Intended for study types	Bachelor

Instruction secured by
Login	Name	Tuitor	Teacher giving lectures
KRA04	Mgr. Bohumil Krajc, Ph.D.
LAM05	prof. RNDr. Marek Lampart, Ph.D.
SAD015	Ing. Marie Sadowská, Ph.D.

Extent of instruction for forms of study
Form of study	Way of compl.	Extent
Full-time	Credit and Examination	2+2
Part-time	Credit and Examination	10+10

Subject aims expressed by acquired skills and competences

Students will learn about differential calculus of more-variable real functions. In the second part students will get the basic practical skills for working with fundamental concepts, methods and applications of integral calculus of more-variable real functions.

Teaching methods

Lectures
Tutorials

Summary

This subject contains following topics: ----------------------------------- differential calculus of two and more-variable real functions, integral calculus of more-variable real functions or differential equations (according to the version)

Compulsory literature:

BOUCHALA, Jiří; KRAJC, Bohumil. Introduction to Differential Calculus of Several Variables, 2022 http://am.vsb.cz/bouchala BOUCHALA, Jiří; VODSTRČIL, Petr; ULČÁK, David. Integral Calculus of Multivariate Functions, 2022 http://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

During the semester we will write two tests.

E-learning

Other requirements

There are not defined other requirements for student.

Prerequisities

Subject has no prerequisities.

Co-requisities

Subject has no co-requisities.

Subject syllabus:

Lectures: - More-variable real functions. Partial and directional derivatives, differential and gradient. - Taylor's theorem. - Extremes of more-variable real functions. - Definition of double integral, basic properties. Fubini theorems for double integral. - Transformation of double integral, aplications of double integral. - Definition of triple integral, basic properties. Fubini theorems for triple integral. - Transformation of triple integral, aplications of triple integral. Exercises: - More-variable real functions. Partial and directional derivatives, differential and gradient. - Taylor's theorem. - Extremes of more-variable real functions. - Definition of double integral, basic properties. Fubini theorems for double integral. - Transformation of double integral, aplications of double integral. - Definition of triple integral, basic properties. Fubini theorems for triple integral. - Transformation of triple integral, aplications of triple integral.

Conditions for subject completion

Part-time form (validity from: 2015/2016 Winter semester, validity until: 2021/2022 Summer 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 (30)	10
Test 1	Written test	15	0
Test 2	Written test	15	0
Examination	Examination	70	21	3

Mandatory attendence participation: participation at all exercises is obligatory, absence of 20% can be excused participation at all 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	Form	Study language	Tut. centre	Year	Type of duty
2020/2021	(B2647) Information and Communication Technology	P	English	Ostrava	1	Compulsory	study plan
2019/2020	(B2647) Information and Communication Technology	P	English	Ostrava	1	Compulsory	study plan
2019/2020	(B2647) Information and Communication Technology	K	English	Ostrava	1	Compulsory	study plan
2018/2019	(B2647) Information and Communication Technology	P	English	Ostrava	1	Compulsory	study plan
2018/2019	(B2647) Information and Communication Technology	K	English	Ostrava	1	Compulsory	study plan
2017/2018	(B2647) Information and Communication Technology	P	English	Ostrava	1	Compulsory	study plan
2017/2018	(B2647) Information and Communication Technology	K	English	Ostrava	1	Compulsory	study plan
2016/2017	(B2647) Information and Communication Technology	P	English	Ostrava	1	Compulsory	study plan
2016/2017	(B2647) Information and Communication Technology	K	English	Ostrava	1	Compulsory	study plan
2015/2016	(B2647) Information and Communication Technology	P	English	Ostrava	1	Compulsory	study plan
2015/2016	(B2647) Information and Communication Technology	K	English	Ostrava	1	Compulsory	study plan

Occurrence in special blocks

Block name	Academic year	Form of study	Study language	Type of block	Block owner
V - ECTS - bc.	2019/2020	Full-time	English	Optional	401 - Study Office	stu. block
V - ECTS - bc.	2018/2019	Full-time	English	Optional	401 - Study Office	stu. block
V - ECTS - bc.	2017/2018	Full-time	English	Optional	401 - Study Office	stu. block
V - ECTS - bc.	2016/2017	Full-time	English	Optional	401 - Study Office	stu. block

Assessment of instruction

2018/2019 Summer

2015/2016 Summer