470-2102/01 – Mathematical Analysis I (MA 1)

Gurantor departmentDepartment of Applied MathematicsCredits4
Subject guarantorMgr. Petr Vodstrčil, Ph.D.Subject version guarantorMgr. Petr Vodstrčil, Ph.D.
Study levelundergraduate or graduateRequirementCompulsory
Year1Semestersummer
Study languageCzech
Year of introduction2010/2011Year of cancellation
Intended for the facultiesUSP, FEI, FSIntended for study typesBachelor
Instruction secured by
LoginNameTuitorTeacher giving lectures
JAH02 RNDr. Pavel Jahoda, Ph.D.
VOD03 Mgr. Petr Vodstrčil, Ph.D.
S1A64 RNDr. Petra Vondráková, Ph.D.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 2+2
Combined 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

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: 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

Combined form (validity from: 2012/2013 Winter semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of points
Exercises evaluation and Examination Credit and Examination 100 (100) 51
        Exercises evaluation Credit 30 (30) 10
                Homework Other task type 15  0
                Test Written test 15  0
        Examination Examination 70  21
Mandatory attendence parzicipation: participation at all exercises is obligatory, absence of 20% can be excused participation at all lectures is expected

Show history

Occurrence in study plans

Academic yearProgrammeField of studySpec.FormStudy language Tut. centreYearWSType of duty
2019/2020 (B2660) Computer Systems for the Industry of the 21st. Century P Czech Ostrava 1 Compulsory study plan
2019/2020 (B2648) Designing of Electric Devices P Czech Ostrava 1 Compulsory study plan
2019/2020 (B2649) Electrical Engineering (3901R039) Biomedical Technician P Czech Ostrava 1 Compulsory study plan
2019/2020 (B2649) Electrical Engineering P Czech Ostrava 1 Compulsory study plan
2019/2020 (B2648) Designing of Electric Devices K Czech Ostrava 1 Compulsory study plan
2019/2020 (B2649) Electrical Engineering K Czech Ostrava 1 Compulsory study plan
2019/2020 (B3943) Mechatronics (3906R006) Mechatronics Systems P Czech Ostrava 1 Compulsory study plan
2019/2020 (B3943) Mechatronics (3906R006) Mechatronics Systems K Czech Ostrava 1 Compulsory study plan
2019/2020 (B0714A270002) Mechatronics P Czech Ostrava 1 Compulsory study plan
2019/2020 (B0714A270002) Mechatronics K Czech Ostrava 1 Compulsory study plan
2018/2019 (B2660) Computer Systems for the Industry of the 21st. Century P Czech Ostrava 1 Compulsory study plan
2018/2019 (B3973) Automotive Electronic Systems P Czech Ostrava 1 Compulsory study plan
2018/2019 (B2648) Designing of Electric Devices P Czech Ostrava 1 Compulsory study plan
2018/2019 (B2649) Electrical Engineering (3901R039) Biomedical Technician P Czech Ostrava 1 Compulsory study plan
2018/2019 (B2649) Electrical Engineering P Czech Ostrava 1 Compulsory study plan
2018/2019 (B2648) Designing of Electric Devices K Czech Ostrava 1 Compulsory study plan
2018/2019 (B2649) Electrical Engineering K Czech Ostrava 1 Compulsory study plan
2018/2019 (B3943) Mechatronics P Czech Ostrava 1 Compulsory study plan
2018/2019 (B3943) Mechatronics K Czech Ostrava 1 Compulsory study plan
2017/2018 (B2648) Designing of Electric Devices P Czech Ostrava 1 Compulsory study plan
2017/2018 (B2648) Designing of Electric Devices K Czech Ostrava 1 Compulsory study plan
2017/2018 (B2649) Electrical Engineering (3901R039) Biomedical Technician P Czech Ostrava 1 Compulsory study plan
2017/2018 (B2649) Electrical Engineering P Czech Ostrava 1 Compulsory study plan
2017/2018 (B2649) Electrical Engineering K Czech Ostrava 1 Compulsory study plan
2017/2018 (B2660) Computer Systems for the Industry of the 21st. Century P Czech Ostrava 1 Compulsory study plan
2017/2018 (B3973) Automotive Electronic Systems P Czech Ostrava 1 Compulsory study plan
2017/2018 (B3943) Mechatronics P Czech Ostrava 1 Compulsory study plan
2017/2018 (B3943) Mechatronics K Czech Ostrava 1 Compulsory study plan
2016/2017 (B3943) Mechatronics P Czech Ostrava 1 Compulsory study plan
2016/2017 (B3943) Mechatronics K Czech Ostrava 1 Compulsory study plan
2016/2017 (B2648) Designing of Electric Devices P Czech Ostrava 1 Compulsory study plan
2016/2017 (B2648) Designing of Electric Devices K Czech Ostrava 1 Compulsory study plan
2016/2017 (B2649) Electrical Engineering (3901R039) Biomedical Technician P Czech Ostrava 1 Compulsory study plan
2016/2017 (B2649) Electrical Engineering P Czech Ostrava 1 Compulsory study plan
2016/2017 (B2649) Electrical Engineering K Czech Ostrava 1 Compulsory study plan
2016/2017 (B2660) Computer Systems for the Industry of the 21st. Century P Czech Ostrava 1 Compulsory study plan
2015/2016 (B2648) Designing of Electric Devices K Czech Ostrava 1 Compulsory study plan
2015/2016 (B2648) Designing of Electric Devices P Czech Ostrava 1 Compulsory study plan
2015/2016 (B2649) Electrical Engineering (3901R039) Biomedical Technician P Czech Ostrava 1 Compulsory study plan
2015/2016 (B2649) Electrical Engineering P Czech Ostrava 1 Compulsory study plan
2015/2016 (B2649) Electrical Engineering K Czech Ostrava 1 Compulsory study plan
2015/2016 (B3943) Mechatronics P Czech Ostrava 1 Compulsory study plan
2015/2016 (B3943) Mechatronics K Czech Ostrava 1 Compulsory study plan
2014/2015 (B2648) Designing of Electric Devices K Czech Ostrava 1 Compulsory study plan
2014/2015 (B2648) Designing of Electric Devices P Czech Ostrava 1 Compulsory study plan
2014/2015 (B2649) Electrical Engineering (3901R039) Biomedical Technician P Czech Ostrava 1 Compulsory study plan
2014/2015 (B2649) Electrical Engineering P Czech Ostrava 1 Compulsory study plan
2014/2015 (B2649) Electrical Engineering K Czech Ostrava 1 Compulsory study plan
2014/2015 (B3943) Mechatronics P Czech Ostrava 1 Compulsory study plan
2014/2015 (B3943) Mechatronics K Czech Ostrava 1 Compulsory study plan
2013/2014 (B2648) Designing of Electric Devices K Czech Ostrava 1 Compulsory study plan
2013/2014 (B2648) Designing of Electric Devices P Czech Ostrava 1 Compulsory study plan
2013/2014 (B2649) Electrical Engineering (3901R039) Biomedical Technician P Czech Ostrava 1 Compulsory study plan
2013/2014 (B2649) Electrical Engineering P Czech Ostrava 1 Compulsory study plan
2013/2014 (B2649) Electrical Engineering K Czech Ostrava 1 Compulsory study plan
2013/2014 (B3943) Mechatronics P Czech Ostrava 1 Compulsory study plan
2013/2014 (B3943) Mechatronics K Czech Ostrava 1 Compulsory study plan
2012/2013 (B2648) Designing of Electric Devices K Czech Ostrava 1 Compulsory study plan
2012/2013 (B2648) Designing of Electric Devices P Czech Ostrava 1 Compulsory study plan
2012/2013 (B2649) Electrical Engineering (3901R039) Biomedical Technician P Czech Ostrava 1 Compulsory study plan
2012/2013 (B2649) Electrical Engineering P Czech Ostrava 1 Compulsory study plan
2012/2013 (B2649) Electrical Engineering K Czech Ostrava 1 Compulsory study plan
2012/2013 (B3943) Mechatronics P Czech Ostrava 1 Compulsory study plan
2012/2013 (B3943) Mechatronics K Czech Ostrava 1 Compulsory study plan
2011/2012 (B2649) Electrical Engineering (3901R039) Biomedical Technician P Czech Ostrava 1 Compulsory study plan
2011/2012 (B2649) Electrical Engineering P Czech Ostrava 1 Compulsory study plan
2011/2012 (B2649) Electrical Engineering (2601R004) Measurement and Control Engineering P Czech Ostrava 1 Compulsory study plan
2011/2012 (B2649) Electrical Engineering (3907R001) Electrical Power Engineering P Czech Ostrava 1 Compulsory study plan
2011/2012 (B2649) Electrical Engineering (2602R014) Applied and Commercial Electronics P Czech Ostrava 1 Compulsory study plan
2011/2012 (B2649) Electrical Engineering K Czech Ostrava 1 Compulsory study plan
2011/2012 (B3943) Mechatronics P Czech Ostrava 1 Compulsory study plan
2011/2012 (B3943) Mechatronics K Czech Ostrava 1 Compulsory study plan
2011/2012 (B2648) Designing of Electric Devices K Czech Ostrava 1 Compulsory study plan
2011/2012 (B2648) Designing of Electric Devices P Czech Ostrava 1 Compulsory study plan
2010/2011 (B2649) Electrical Engineering (3901R039) Biomedical Technician P Czech Ostrava 1 Compulsory study plan
2010/2011 (B2649) Electrical Engineering P Czech Ostrava 1 Compulsory study plan
2010/2011 (B2648) Designing of Electric Devices P Czech Ostrava 1 Compulsory study plan
2010/2011 (B2649) Electrical Engineering K Czech Ostrava 1 Compulsory study plan
2010/2011 (B2648) Designing of Electric Devices K Czech Ostrava 1 Compulsory study plan
2010/2011 (B3943) Mechatronics K Czech Ostrava 1 Compulsory study plan
2010/2011 (B3943) Mechatronics P Czech Ostrava 1 Compulsory study plan
2010/2011 (B3943) Mechatronics (3906R007) Automotive Electronics P Czech Ostrava 1 Compulsory study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner