470-2102/02 – Mathematical Analysis I (MA 1)

 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 2020/2021 Intended for the faculties USP, FEI Intended for study types Bachelor
Instruction secured by
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
Part-time Credit and Examination 10+10

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.

Lectures
Tutorials

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:

J. Bouchala, M. Sadowská: Mathematical Analysis I, VŠB-TUO.

Recommended literature:

L. Gillman, R. H. McDowell: Calculus, New York, W.W. Norton & Comp. Inc. 1973.

Way of continuous check of knowledge in the course of semester

During the semester we will write 6 tests.

Other requirements

No additional requirements are imposed on the student.

Prerequisities

Subject has no prerequisities.

Co-requisities

Subject has no co-requisities.

Subject syllabus:

Lectures: Real numbers. Supremum and infimum. Principle of mathematical induction. Real one-variable functions and their basic properties. Elementary functions. Sequences of real numbers. Limit of sequence. Theorems on limit of sequences, calculation of limits. Limit of a function. Theorems on limits. Continuity of a function. Theorems on limits and continuity of composite function. Derivative and differential of a function. Calculation of derivatives. Basic theorems of differential calculus. L'Hospital rule. Intervals of monotony of a function. Local extremes of a function. Convexity and concavity. Asymptotes of graphs. Course of a function. Global extremes of a function. Weierstrass-theorem. Taylor's theorem. Fundamental principles of integral calculus. Exercises: Application of principle of mathematical induction. Supremum and infimum of various sets. Functions and their properties. Graph of a function. Functions with absolute value. Elementary functions. Calculation of inverse function. Finding domain of definition of a function. Arithmetic and geometric sequence. Calculation of limits of sequences. Calculation of limits of functions. Limits of functions. Continuity of a function. Calculation of derivatives. Tangent and normal line. L'Hospital rule. Monotony of a function. Local extremes. Convexity and concavity, asymptotes. Course of a function. Global extremes of a function. Taylor's polynom and error estimation. Calculation of antiderivatives and Riemann integrals.

Conditions for subject completion

Full-time form (validity from: 2015/2016 Winter semester, validity until: 2020/2021 Summer semester)
Min. number of pointsMax. počet pokusů
Credit and Examination Credit and Examination 100 (100) 51
Credit Credit 30 (30) 15
Tests 1 Written test 15  0
Tests 2 Written test 15  0
Examination Examination 70  21 3
Mandatory attendence participation: participation at all exercises is obligatory, 2 apologies are accepted participation at all lectures is expected

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Conditions for subject completion and attendance at the exercises within ISP:

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Occurrence in study plans

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2018/2019 (B2660) Computer Systems for the Industry of the 21st. Century P English Ostrava 1 Compulsory study plan
2018/2019 (B3973) Automotive Electronic Systems P English Ostrava 1 Compulsory study plan
2018/2019 (B2649) Electrical Engineering P English Ostrava 1 Compulsory study plan
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2017/2018 (B2649) Electrical Engineering P English Ostrava 1 Compulsory study plan
2017/2018 (B2649) Electrical Engineering K English Ostrava 1 Compulsory study plan
2017/2018 (B2660) Computer Systems for the Industry of the 21st. Century P English Ostrava 1 Compulsory study plan
2017/2018 (B3973) Automotive Electronic Systems P English Ostrava 1 Compulsory study plan
2016/2017 (B2649) Electrical Engineering P English Ostrava 1 Compulsory study plan
2016/2017 (B2649) Electrical Engineering K English Ostrava 1 Compulsory study plan
2016/2017 (B2660) Computer Systems for the Industry of the 21st. Century P English Ostrava 1 Compulsory study plan
2015/2016 (B2649) Electrical Engineering P English Ostrava 1 Compulsory study plan
2015/2016 (B2649) Electrical Engineering K English Ostrava 1 Compulsory study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner

Assessment of instruction

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