457-0511/01 – 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 Czech Year of introduction 1999/2000 Year of cancellation 2009/2010 Intended for the faculties FEI Intended for study types Bachelor
Instruction secured by
HEN50 RNDr. Ctibor Henzl, Ph.D.
KAB002 Ing. Pavla Hrušková, Ph.D.
KOT237 Ing. Petr Kotas
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
Combined Credit and Examination 10+10
Lifelong 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.

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: 1960/1961 Summer semester)
Min. number of points
Exercises evaluation and Examination Credit and Examination 100 (100) 51
Examination Examination 70  0
Exercises evaluation Credit 30 (30) 10
Testy 1 Written test 15  0
Testy 2 Written test 15  0
Mandatory attendence parzicipation:

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Occurrence in study plans

Academic yearProgrammeField of studySpec.ZaměřeníFormStudy language Tut. centreYearWSType of duty
2009/2010 (B2649) Electrical Engineering (3901R039) Biomedical Technician P Czech Ostrava 1 Compulsory study plan
2009/2010 (B2648) Designing of Electric Devices P Czech Ostrava 1 Compulsory study plan
2009/2010 (B2649) Electrical Engineering (2601R004) Measurement and Control Engineering P Czech Ostrava 1 Compulsory study plan
2009/2010 (B2649) Electrical Engineering (2602R014) Applied and Commercial Electronics P Czech Ostrava 1 Compulsory study plan
2009/2010 (B2649) Electrical Engineering (3907R001) Electrical Power Engineering P Czech Ostrava 1 Compulsory study plan
2009/2010 (B2649) Electrical Engineering P Czech Ostrava 1 Compulsory study plan
2009/2010 (B2648) Designing of Electric Devices K Czech Ostrava 1 Compulsory study plan
2009/2010 (B2649) Electrical Engineering (2601R004) Measurement and Control Engineering K Czech Ostrava 1 Compulsory study plan
2009/2010 (B2649) Electrical Engineering (2602R014) Applied and Commercial Electronics K Czech Ostrava 1 Compulsory study plan
2009/2010 (B2649) Electrical Engineering (3907R001) Electrical Power Engineering K Czech Ostrava 1 Compulsory study plan
2009/2010 (B2649) Electrical Engineering K Czech Ostrava 1 Compulsory study plan
2009/2010 (B3943) Mechatronics P Czech Ostrava 1 Compulsory study plan
2009/2010 (B3943) Mechatronics K Czech Ostrava 1 Compulsory study plan
2009/2010 (B2649) Electrical Engineering C Czech Ostrava 1 Compulsory study plan
2008/2009 (B2645) Electrical Engineering, Communication and Computer Systems (2608R004) Commercial Electrical Engineering P Czech Ostrava 1 Compulsory study plan
2008/2009 (B2645) Electrical Engineering, Communication and Computer Systems (2612R018) Electronics and Communication Technology P Czech Ostrava 1 Compulsory study plan
2008/2009 (B2645) Electrical Engineering, Communication and Computer Systems (2612R041) Control and Information Systems P Czech Ostrava 1 Compulsory study plan
2008/2009 (B2645) Electrical Engineering, Communication and Computer Systems (2642R004) Electrical Machines Apparatus and Drives P Czech Ostrava 1 Compulsory study plan
2008/2009 (B2645) Electrical Engineering, Communication and Computer Systems (3907R001) Electrical Power Engineering P Czech Ostrava 1 Compulsory study plan
2008/2009 (B2645) Electrical Engineering, Communication and Computer Systems (2608R004) Commercial Electrical Engineering K Czech Ostrava 1 Compulsory study plan
2008/2009 (B2645) Electrical Engineering, Communication and Computer Systems (2612R018) Electronics and Communication Technology K Czech Ostrava 1 Compulsory study plan
2008/2009 (B2645) Electrical Engineering, Communication and Computer Systems (2612R041) Control and Information Systems K Czech Ostrava 1 Compulsory study plan
2008/2009 (B2645) Electrical Engineering, Communication and Computer Systems (2642R004) Electrical Machines Apparatus and Drives K Czech Ostrava 1 Compulsory study plan
2008/2009 (B2645) Electrical Engineering, Communication and Computer Systems (3907R001) Electrical Power Engineering K Czech Ostrava 1 Compulsory study plan
2008/2009 (B2649) Electrical Engineering (3901R039) Biomedical Technician P Czech Ostrava 1 Compulsory study plan
2008/2009 (B3943) Mechatronics P Czech Ostrava 1 Compulsory study plan
2008/2009 (B2648) Designing of Electric Devices P Czech Ostrava 1 Compulsory study plan
2008/2009 (B2649) Electrical Engineering (2601R004) Measurement and Control Engineering P Czech Ostrava 1 Compulsory study plan
2008/2009 (B2649) Electrical Engineering (2602R014) Applied and Commercial Electronics P Czech Ostrava 1 Compulsory study plan
2008/2009 (B2649) Electrical Engineering (3907R001) Electrical Power Engineering P Czech Ostrava 1 Compulsory study plan
2008/2009 (B2649) Electrical Engineering P Czech Ostrava 1 Compulsory study plan
2008/2009 (B2649) Electrical Engineering (2602R014) Applied and Commercial Electronics P Czech Rožnov pod Radhoštěm 1 Compulsory study plan
2008/2009 (B2648) Designing of Electric Devices K Czech Ostrava 1 Compulsory study plan
2008/2009 (B2649) Electrical Engineering (2601R004) Measurement and Control Engineering K Czech Šumperk 1 Compulsory study plan
2008/2009 (B2649) Electrical Engineering (2601R004) Measurement and Control Engineering K Czech Ostrava 1 Compulsory study plan
2008/2009 (B2649) Electrical Engineering K Czech Šumperk 1 Compulsory study plan
2008/2009 (B2649) Electrical Engineering (2602R014) Applied and Commercial Electronics K Czech Ostrava 1 Compulsory study plan
2008/2009 (B2649) Electrical Engineering (3907R001) Electrical Power Engineering K Czech Ostrava 1 Compulsory study plan
2008/2009 (B2649) Electrical Engineering K Czech Ostrava 1 Compulsory study plan
2008/2009 (B3943) Mechatronics K Czech Ostrava 1 Compulsory study plan
2007/2008 (B2645) Electrical Engineering, Communication and Computer Systems (2608R004) Commercial Electrical Engineering P Czech Ostrava 1 Compulsory study plan
2007/2008 (B2645) Electrical Engineering, Communication and Computer Systems (2612R018) Electronics and Communication Technology P Czech Ostrava 1 Compulsory study plan
2007/2008 (B2645) Electrical Engineering, Communication and Computer Systems (2612R041) Control and Information Systems P Czech Ostrava 1 Compulsory study plan
2007/2008 (B2645) Electrical Engineering, Communication and Computer Systems (2642R004) Electrical Machines Apparatus and Drives P Czech Ostrava 1 Compulsory study plan
2007/2008 (B2645) Electrical Engineering, Communication and Computer Systems (3907R001) Electrical Power Engineering P Czech Ostrava 1 Compulsory study plan
2007/2008 (B2645) Electrical Engineering, Communication and Computer Systems (2608R004) Commercial Electrical Engineering K Czech Ostrava 1 Compulsory study plan
2007/2008 (B2645) Electrical Engineering, Communication and Computer Systems (2612R018) Electronics and Communication Technology K Czech Ostrava 1 Compulsory study plan
2007/2008 (B2645) Electrical Engineering, Communication and Computer Systems (2612R041) Control and Information Systems K Czech Ostrava 1 Compulsory study plan
2007/2008 (B2645) Electrical Engineering, Communication and Computer Systems (2642R004) Electrical Machines Apparatus and Drives K Czech Ostrava 1 Compulsory study plan
2007/2008 (B2645) Electrical Engineering, Communication and Computer Systems (3907R001) Electrical Power Engineering K Czech Ostrava 1 Compulsory study plan
2007/2008 (B3943) Mechatronics (3906R999) Společné studium oboru Automobilová elektronika, Mechatronické systémy P Czech Ostrava 1 Compulsory study plan
2007/2008 (B2648) Designing of Electric Devices (2648R999) Společné studium P Czech Ostrava 1 Compulsory study plan
2007/2008 (B2649) Electrical Engineering (2601R004) Measurement and Control Engineering P Czech Ostrava 1 Compulsory study plan
2007/2008 (B2649) Electrical Engineering (2602R014) Applied and Commercial Electronics P Czech Ostrava 1 Compulsory study plan
2007/2008 (B2649) Electrical Engineering (3907R001) Electrical Power Engineering P Czech Ostrava 1 Compulsory study plan
2007/2008 (B2648) Designing of Electric Devices (2648R999) Společné studium K Czech Ostrava 1 Compulsory study plan
2007/2008 (B2649) Electrical Engineering (2601R004) Measurement and Control Engineering K Czech Ostrava 1 Compulsory study plan
2007/2008 (B2649) Electrical Engineering (2602R014) Applied and Commercial Electronics K Czech Ostrava 1 Compulsory study plan
2007/2008 (B2649) Electrical Engineering (3907R001) Electrical Power Engineering K Czech Ostrava 1 Compulsory study plan
2007/2008 (B2649) Electrical Engineering (3901R039) Biomedical Technician P Czech Ostrava 1 Compulsory study plan
2006/2007 (B2645) Electrical Engineering, Communication and Computer Systems (2608R004) Commercial Electrical Engineering P Czech Ostrava 1 Compulsory study plan
2006/2007 (B2645) Electrical Engineering, Communication and Computer Systems (2612R018) Electronics and Communication Technology P Czech Ostrava 1 Compulsory study plan
2006/2007 (B2645) Electrical Engineering, Communication and Computer Systems (2612R041) Control and Information Systems P Czech Ostrava 1 Compulsory study plan
2006/2007 (B2645) Electrical Engineering, Communication and Computer Systems (2642R004) Electrical Machines Apparatus and Drives P Czech Ostrava 1 Compulsory study plan
2006/2007 (B2645) Electrical Engineering, Communication and Computer Systems (3907R001) Electrical Power Engineering P Czech Ostrava 1 Compulsory study plan
2006/2007 (B2645) Electrical Engineering, Communication and Computer Systems (2608R004) Commercial Electrical Engineering K Czech Ostrava 1 Compulsory study plan
2006/2007 (B2645) Electrical Engineering, Communication and Computer Systems (2612R018) Electronics and Communication Technology K Czech Ostrava 1 Compulsory study plan
2006/2007 (B2645) Electrical Engineering, Communication and Computer Systems (2612R041) Control and Information Systems K Czech Ostrava 1 Compulsory study plan
2006/2007 (B2645) Electrical Engineering, Communication and Computer Systems (2642R004) Electrical Machines Apparatus and Drives K Czech Ostrava 1 Compulsory study plan
2006/2007 (B2645) Electrical Engineering, Communication and Computer Systems (3907R001) Electrical Power Engineering K Czech Ostrava 1 Compulsory study plan
2005/2006 (B2645) Electrical Engineering, Communication and Computer Systems (2608R004) Commercial Electrical Engineering P Czech Ostrava 1 Compulsory study plan
2005/2006 (B2645) Electrical Engineering, Communication and Computer Systems (2612R018) Electronics and Communication Technology P Czech Ostrava 1 Compulsory study plan
2005/2006 (B2645) Electrical Engineering, Communication and Computer Systems (2612R041) Control and Information Systems P Czech Ostrava 1 Compulsory study plan
2005/2006 (B2645) Electrical Engineering, Communication and Computer Systems (2642R004) Electrical Machines Apparatus and Drives P Czech Ostrava 1 Compulsory study plan
2005/2006 (B2645) Electrical Engineering, Communication and Computer Systems (3907R001) Electrical Power Engineering P Czech Ostrava 1 Compulsory study plan
2005/2006 (B2645) Electrical Engineering, Communication and Computer Systems (2608R004) Commercial Electrical Engineering K Czech Ostrava 1 Compulsory study plan
2005/2006 (B2645) Electrical Engineering, Communication and Computer Systems (2612R018) Electronics and Communication Technology K Czech Ostrava 1 Compulsory study plan
2005/2006 (B2645) Electrical Engineering, Communication and Computer Systems (2612R041) Control and Information Systems K Czech Ostrava 1 Compulsory study plan
2005/2006 (B2645) Electrical Engineering, Communication and Computer Systems (2642R004) Electrical Machines Apparatus and Drives K Czech Ostrava 1 Compulsory study plan
2005/2006 (B2645) Electrical Engineering, Communication and Computer Systems (3907R001) Electrical Power Engineering K Czech Ostrava 1 Compulsory study plan
2004/2005 (B2645) Electrical Engineering, Communication and Computer Systems (2608R004) Commercial Electrical Engineering P Czech Ostrava 1 Compulsory study plan
2004/2005 (B2645) Electrical Engineering, Communication and Computer Systems (2612R018) Electronics and Communication Technology P Czech Ostrava 1 Compulsory study plan
2004/2005 (B2645) Electrical Engineering, Communication and Computer Systems (2612R041) Control and Information Systems P Czech Ostrava 1 Compulsory study plan
2004/2005 (B2645) Electrical Engineering, Communication and Computer Systems (2642R004) Electrical Machines Apparatus and Drives P Czech Ostrava 1 Compulsory study plan
2004/2005 (B2645) Electrical Engineering, Communication and Computer Systems (3907R001) Electrical Power Engineering P Czech Ostrava 1 Compulsory study plan
2004/2005 (B2645) Electrical Engineering, Communication and Computer Systems (2608R004) Commercial Electrical Engineering K Czech Ostrava 1 Compulsory study plan
2004/2005 (B2645) Electrical Engineering, Communication and Computer Systems (2612R018) Electronics and Communication Technology K Czech Ostrava 1 Compulsory study plan
2004/2005 (B2645) Electrical Engineering, Communication and Computer Systems (2612R041) Control and Information Systems K Czech Ostrava 1 Compulsory study plan
2004/2005 (B2645) Electrical Engineering, Communication and Computer Systems (2642R004) Electrical Machines Apparatus and Drives K Czech Ostrava 1 Compulsory study plan
2004/2005 (B2645) Electrical Engineering, Communication and Computer Systems (3907R001) Electrical Power Engineering K Czech Ostrava 1 Compulsory study plan
2003/2004 (B2645) Electrical Engineering, Communication and Computer Systems (2612R018) Electronics and Communication Technology P Czech Ostrava 1 Choice-compulsory study plan
2003/2004 (B2645) Electrical Engineering, Communication and Computer Systems (2612R041) Control and Information Systems P Czech Ostrava 1 Choice-compulsory study plan
2003/2004 (B2645) Electrical Engineering, Communication and Computer Systems (2642R004) Electrical Machines Apparatus and Drives P Czech Ostrava 1 Choice-compulsory study plan
2003/2004 (B2645) Electrical Engineering, Communication and Computer Systems (3907R001) Electrical Power Engineering P Czech Ostrava 1 Choice-compulsory study plan
2003/2004 (B2645) Electrical Engineering, Communication and Computer Systems (2612R018) Electronics and Communication Technology K Czech Ostrava 1 Choice-compulsory study plan
2003/2004 (B2645) Electrical Engineering, Communication and Computer Systems (2612R041) Control and Information Systems K Czech Ostrava 1 Choice-compulsory study plan
2003/2004 (B2645) Electrical Engineering, Communication and Computer Systems (2642R004) Electrical Machines Apparatus and Drives K Czech Ostrava 1 Choice-compulsory study plan
2003/2004 (B2645) Electrical Engineering, Communication and Computer Systems (3907R001) Electrical Power Engineering K Czech Ostrava 1 Choice-compulsory study plan

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