# 470-8723/02 – Mathematical Analysis II (MA2AVAT)

 Gurantor department Department of Applied Mathematics Credits 4 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 summer Study language English Year of introduction 2019/2020 Year of cancellation Intended for the faculties FS, USP Intended for study types Bachelor
Instruction secured by
BOU10 prof. RNDr. Jiří Bouchala, Ph.D.
KRA04 Mgr. Bohumil Krajc, Ph.D.
VOD03 doc. Mgr. Petr Vodstrčil, Ph.D.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 2+2

### 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 multivariable functions.

Lectures
Tutorials

### Summary

This subject contains 2 basic themes: differential and integral calculus of multivariable real functions.

### Compulsory literature:

J. Stewart: Calculus, 2008 Thomson

### Recommended literature:

W. Rudin: Principles of Mathematical Analysis. McGraw-Hill Book Company, New York 1964

### Way of continuous check of knowledge in the course of semester

Tests, individual work.

### Other requirements

Additional requirements for students are not.

### Prerequisities

Subject has no prerequisities.

### Co-requisities

Subject has no co-requisities.

### Subject syllabus:

1. Differential calculus of multivariable functions Real functions of several variables. Limits and continuity. Partial derivative, gradient and directional derivative, total differential. Differentials of higher orders, Taylor polynomials, Taylor's theorem. Implicit function theorem. Local, constrained and global extrema. Lagrange multipliers method. 2. Integration of multivariable functions Riemann double and triple integrals. Fubini theorem. Substitution theorem for double and triple integrals. Applications of double and triple integrals.

### Conditions for subject completion

Full-time form (validity from: 2019/2020 Winter semester)
Min. number of points
Credit and Examination Credit and Examination 100 (100) 51
Credit Credit 30  10
Examination Examination 70  21
Mandatory attendence parzicipation: Participation at all exercises is obligatory, 2 apologies are accepted. Participation at all lectures is expected.

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### Occurrence in study plans

Academic yearProgrammeField of studySpec.ZaměřeníFormStudy language Tut. centreYearWSType of duty
2021/2022 (B0588A170002) Applied Sciences and Technologies MAT P English Ostrava 1 Compulsory study plan
2020/2021 (B0588A170002) Applied Sciences and Technologies MAT P English Ostrava 1 Compulsory study plan
2019/2020 (B0588A170002) Applied Sciences and Technologies MAT P English Ostrava 1 Compulsory study plan

### Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner