470-2111/12 – Mathematical Analysis 2 (MA2)

Gurantor departmentDepartment of Applied MathematicsCredits4
Subject guarantordoc. Mgr. Petr Vodstrčil, Ph.D.Subject version guarantordoc. Mgr. Petr Vodstrčil, Ph.D.
Study levelundergraduate or graduate
Study languageEnglish
Year of introduction2023/2024Year of cancellation
Intended for the facultiesFEIIntended for study typesBachelor
Instruction secured by
LoginNameTuitorTeacher 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 studyWay of compl.Extent
Full-time Graded credit 2+2
Part-time Graded credit 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.

Additional study materials

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

Full-time form (validity from: 2023/2024 Winter semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of pointsMax. počet pokusů
Graded credit Graded credit 100  51 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.

Show history
Part-time form (validity from: 2023/2024 Winter semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of pointsMax. počet pokusů
Graded credit Graded credit 100  51 3
Mandatory attendence participation: participation at all exercises is obligatory, absence of 20% can be excused participation at all lectures is expected

Show history

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

Show history

Occurrence in study plans

Academic yearProgrammeBranch/spec.Spec.ZaměřeníFormStudy language Tut. centreYearWSType of duty
2025/2026 (B0613A140010) Computer Science TZI P English Ostrava 2 Compulsory study plan
2024/2025 (B0613A140010) Computer Science TZI P English Ostrava 2 Compulsory study plan
2023/2024 (B0613A140010) Computer Science TZI P English Ostrava 2 Compulsory study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner
ECTS - bc. 2025/2026 Full-time English Optional 401 - Study Office stu. block

Assessment of instruction

Předmět neobsahuje žádné hodnocení.