470-2112/01 – Repetition of Mathematical Analysis (RMA)

Gurantor departmentDepartment of Applied MathematicsCredits8
Subject guarantorprof. RNDr. Jiří Bouchala, Ph.D.Subject version guarantorprof. RNDr. Jiří Bouchala, Ph.D.
Study levelundergraduate or graduateRequirementCompulsory
Year2Semesterwinter
Study languageCzech
Year of introduction2015/2016Year of cancellation
Intended for the facultiesFEIIntended for study typesBachelor
Instruction secured by
LoginNameTuitorTeacher giving lectures
BOU10 prof. RNDr. Jiří Bouchala, Ph.D.
DOM0015 Ing. Simona Domesová
KRA04 Mgr. Bohumil Krajc, Ph.D.
VOD03 Mgr. Petr Vodstrčil, Ph.D.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 3+3
Combined Credit and Examination 15+15

Subject aims expressed by acquired skills and competences

The main objective of the course is to deepen knowledge and understanding of the basics of differential and integral calculus of real functions of one and more variables.

Teaching methods

Lectures
Tutorials
Project work

Summary

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

Compulsory literature:

J. Bouchala, M. Sadowská: Mathematical Analysis I, http://am.vsb.cz/bouchala W. Rudin: Principles of Mathematical Analysis, McGraw-Hill, Inc.

Recommended literature:

H. Anton, I. Bivens, S. Davis: Calculus, John Wiley & sons, Inc.

Way of continuous check of knowledge in the course of semester

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.

E-learning

Další požadavky na studenta

No additional requirements are imposed on the student.

Prerequisities

Subject has no prerequisities.

Co-requisities

Subject has no co-requisities.

Subject syllabus:

Lectures: 1. Basic ideas of set theory. 2. Cardinality of sets. 3. Real numbers. 4. Sequences, limit of sequence. 5. Infinite series, criteria for convergence. 6. Exponential function, goniometric functions. 7. Sequence of functions, convergence. 8. Continuities of functions. 9. Differentiation of function . Implicit function theorem. 10. Extremes of function. 11. Weierstrass theorem . 12. Taylor´s polynomial. 13. Riemann integral. 14. Integration of functions of several real variables.

Conditions for subject completion

Combined form (validity from: 2015/2016 Winter semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of points
Credit and Examination Credit and Examination 100 (100) 51
        Credit Credit 30  10
        Examination Examination 70  21
Mandatory attendence parzicipation:

Show history

Occurrence in study plans

Academic yearProgrammeField of studySpec.FormStudy language Tut. centreYearWSType of duty
2019/2020 (B2647) Information and Communication Technology (1103R031) Computational Mathematics P Czech Ostrava 2 Compulsory study plan
2019/2020 (B2647) Information and Communication Technology (1103R031) Computational Mathematics K Czech Ostrava 2 Compulsory study plan
2018/2019 (B2647) Information and Communication Technology (1103R031) Computational Mathematics P Czech Ostrava 2 Compulsory study plan
2018/2019 (B2647) Information and Communication Technology (1103R031) Computational Mathematics K Czech Ostrava 2 Compulsory study plan
2017/2018 (B2647) Information and Communication Technology (1103R031) Computational Mathematics K Czech Ostrava 2 Compulsory study plan
2017/2018 (B2647) Information and Communication Technology (1103R031) Computational Mathematics P Czech Ostrava 2 Compulsory study plan
2016/2017 (B2647) Information and Communication Technology (1103R031) Computational Mathematics K Czech Ostrava 2 Compulsory study plan
2016/2017 (B2647) Information and Communication Technology (1103R031) Computational Mathematics P Czech Ostrava 2 Compulsory study plan
2015/2016 (B2647) Information and Communication Technology (1103R031) Computational Mathematics K Czech Ostrava 2 Compulsory study plan
2015/2016 (B2647) Information and Communication Technology (1103R031) Computational Mathematics P Czech Ostrava 2 Compulsory study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner