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

Gurantor departmentDepartment of Applied MathematicsCredits4
Subject guarantordoc. Mgr. Petr Vodstrčil, Ph.D.Subject version guarantordoc. Mgr. Petr Vodstrčil, Ph.D.
Study levelundergraduate or graduateRequirementCompulsory
Year1Semestersummer
Study languageEnglish
Year of introduction2015/2016Year of cancellation2020/2021
Intended for the facultiesUSP, FEIIntended for study typesBachelor
Instruction secured by
LoginNameTuitorTeacher giving lectures
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.

Teaching methods

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.

E-learning

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

Conditions for completion are defined only for particular subject version and form of study

Occurrence in study plans

Academic yearProgrammeBranch/spec.Spec.ZaměřeníFormStudy language Tut. centreYearWSType of duty
2020/2021 (B2660) Computer Systems for the Industry of the 21st. Century P English Ostrava 1 Compulsory study plan
2019/2020 (B2660) Computer Systems for the Industry of the 21st. Century P English Ostrava 1 Compulsory study plan
2019/2020 (B2649) Electrical Engineering P English Ostrava 1 Compulsory study plan
2019/2020 (B2649) Electrical Engineering K English Ostrava 1 Compulsory study plan
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
2018/2019 (B2649) Electrical Engineering K English Ostrava 1 Compulsory study plan
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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