457-0512/01 – Mathematical analysis II (MA2)

Gurantor departmentDepartment of Applied MathematicsCredits4
Subject guarantordoc. Ing. Petr Beremlijski, Ph.D.Subject version guarantordoc. Ing. Petr Beremlijski, Ph.D.
Study levelundergraduate or graduateRequirementCompulsory
Year2Semesterwinter
Study languageCzech
Year of introduction1960/1961Year of cancellation2009/2010
Intended for the facultiesFEIIntended for study typesBachelor
Instruction secured by
LoginNameTuitorTeacher giving lectures
BER95 doc. Ing. Petr Beremlijski, Ph.D.
KRA04 Mgr. Bohumil Krajc, Ph.D.
SAD015 Ing. Marie Sadowská, Ph.D.
SIN29 RNDr. Libor Šindel
SOK038 Ing. Vojtěch Sokol
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

The main task of this subject is to learn the basic knowledge and to gain practical skill concerning integral calculus of real function of one real variable. Furthermore, student will be able to solve ordinary differential equations of the first order and to analyze behaviour of functions of n real variables.

Teaching methods

Lectures
Tutorials

Summary

The subject consists of three parts: integral calculus of real function of one real variable, ordinary differential equations of the first order, differential calculus of functions of n real variables.

Compulsory literature:

James Stewart: Calculus, Brooks Cole Publishing Company, 1986

Recommended literature:

Way of continuous check of knowledge in the course of semester

Průběžná kontrola studia: Studenti v průběhu semestru budou psát písemné testy. Za testy lze získat maximálně 30 bodů. Podmínky udělení zápočtu: Zápočet bude udělen, pokud student získá alespoň 10 bodů.

E-learning

Další požadavky na studenta

Prerequisities

Subject has no prerequisities.

Co-requisities

Subject has no co-requisities.

Subject syllabus:

Přednášky: Integrální počet funkcí jedné proměnné (primitivní funkce, neurčitý integrál, metody výpočtu neurčitého integrálu, Riemannův integrál, aplikace, nevlastní integrál) Obyčejné diferenciální rovnice prvního řádu (rovnice se separovanými proměnnými, lineární diferenciální rovnice prvního řádu, aplikace) Diferenciální počet funkcí více proměnných (funkce více proměnných, parciální derivace, derivace ve směru, gradient, diferenciál, Taylorův polynom, extrémy funkcí více proměnných, aplikace) Cvičení: Řešení příkladů z integrálního počtu pomocí metody per partes a substitučních metod. Řešení úloh o rozkladu racionální lomené funkce na parciální zlomky. Procvičování speciálních substitucí při integraci některých tříd funkcí. Výpočet určitého integrálu. Aplikace. Výpočty nevlastních integrálů. Použití kritérií konvergence nevlastních integrálů. Řešení obyčejných diferenciálních rovnic 1. řádu metodou separace proměnných, řešení lineární diferenciální rovnice. Aplikace. Metrické a topologické vlastnosti eukleidovských prostorů. Určování definičních oborů funkcí více proměnných. Určování vrstevnic. Grafy funkcí dvou proměnných. Vyšetřování spojitosti, řešení jednoduchých úloh na limity pro funkce dvou a více reálných proměnných. Výpočty derivací ve směru, parciálních derivací, totálního diferenciálu a gradientu. Použití Taylorovy věty. Hledání extrémů funkcí několika proměnných.

Conditions for subject completion

Combined form (validity from: 1960/1961 Summer semester, validity until: 2008/2009 Winter semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of points
Exercises evaluation and Examination Credit and Examination 100 (145) 51
        Examination Examination 100  0
        Exercises evaluation Credit 45  0
Mandatory attendence parzicipation:

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Occurrence in study plans

Academic yearProgrammeField of studySpec.FormStudy language Tut. centreYearWSType of duty
2009/2010 (B2645) Electrical Engineering, Communication and Computer Systems (3907R001) Electrical Power Engineering P Czech Ostrava 2 Compulsory study plan
2009/2010 (B2645) Electrical Engineering, Communication and Computer Systems (2612R041) Control and Information Systems P Czech Ostrava 2 Compulsory study plan
2009/2010 (B2645) Electrical Engineering, Communication and Computer Systems (2642R004) Electrical Machines Apparatus and Drives P Czech Ostrava 2 Compulsory study plan
2009/2010 (B2649) Electrical Engineering (2601R004) Measurement and Control Engineering P Czech Ostrava 2 Compulsory study plan
2009/2010 (B2649) Electrical Engineering (3907R001) Electrical Power Engineering P Czech Ostrava 2 Compulsory study plan
2009/2010 (B2649) Electrical Engineering (2602R014) Applied and Commercial Electronics P Czech Ostrava 2 Compulsory study plan
2009/2010 (B2648) Designing of Electric Devices P Czech Ostrava 2 Compulsory study plan
2009/2010 (B2649) Electrical Engineering (3901R039) Biomedical Technician P Czech Ostrava 2 Compulsory study plan
2009/2010 (B2645) Electrical Engineering, Communication and Computer Systems (2642R004) Electrical Machines Apparatus and Drives K Czech Ostrava 2 Compulsory study plan
2009/2010 (B2645) Electrical Engineering, Communication and Computer Systems (2612R041) Control and Information Systems K Czech Ostrava 2 Compulsory study plan
2009/2010 (B2645) Electrical Engineering, Communication and Computer Systems (3907R001) Electrical Power Engineering K Czech Ostrava 2 Compulsory study plan
2009/2010 (B2649) Electrical Engineering (2601R004) Measurement and Control Engineering K Czech Ostrava 2 Compulsory study plan
2009/2010 (B2649) Electrical Engineering (3907R001) Electrical Power Engineering K Czech Ostrava 2 Compulsory study plan
2009/2010 (B2649) Electrical Engineering (2602R014) Applied and Commercial Electronics K Czech Ostrava 2 Compulsory study plan
2009/2010 (B2648) Designing of Electric Devices K Czech Ostrava 2 Compulsory study plan
2009/2010 (B3943) Mechatronics P Czech Ostrava 2 Compulsory study plan
2009/2010 (B3943) Mechatronics K Czech Ostrava 2 Compulsory study plan
2008/2009 (B2645) Electrical Engineering, Communication and Computer Systems (3907R001) Electrical Power Engineering P Czech Ostrava 2 Compulsory study plan
2008/2009 (B2645) Electrical Engineering, Communication and Computer Systems (2612R041) Control and Information Systems P Czech Ostrava 2 Compulsory study plan
2008/2009 (B2645) Electrical Engineering, Communication and Computer Systems (2642R004) Electrical Machines Apparatus and Drives P Czech Ostrava 2 Compulsory study plan
2008/2009 (B2645) Electrical Engineering, Communication and Computer Systems (2642R004) Electrical Machines Apparatus and Drives K Czech Ostrava 2 Compulsory study plan
2008/2009 (B2645) Electrical Engineering, Communication and Computer Systems (2612R041) Control and Information Systems K Czech Ostrava 2 Compulsory study plan
2008/2009 (B2645) Electrical Engineering, Communication and Computer Systems (3907R001) Electrical Power Engineering K Czech Ostrava 2 Compulsory study plan
2008/2009 (B2649) Electrical Engineering (2601R004) Measurement and Control Engineering P Czech Ostrava 2 Compulsory study plan
2008/2009 (B2649) Electrical Engineering (2601R004) Measurement and Control Engineering K Czech Šumperk 2 Compulsory study plan
2008/2009 (B2649) Electrical Engineering (2601R004) Measurement and Control Engineering K Czech Ostrava 2 Compulsory study plan
2008/2009 (B2649) Electrical Engineering (3907R001) Electrical Power Engineering P Czech Ostrava 2 Compulsory study plan
2008/2009 (B2649) Electrical Engineering (3907R001) Electrical Power Engineering K Czech Ostrava 2 Compulsory study plan
2008/2009 (B2649) Electrical Engineering (2602R014) Applied and Commercial Electronics P Czech Ostrava 2 Compulsory study plan
2008/2009 (B2649) Electrical Engineering (2602R014) Applied and Commercial Electronics P Czech Rožnov pod Radhoštěm 2 Compulsory study plan
2008/2009 (B2649) Electrical Engineering K Czech Šumperk 2 Compulsory study plan
2008/2009 (B2649) Electrical Engineering (2602R014) Applied and Commercial Electronics K Czech Ostrava 2 Compulsory study plan
2008/2009 (B2648) Designing of Electric Devices P Czech Ostrava 2 Compulsory study plan
2008/2009 (B2648) Designing of Electric Devices K Czech Ostrava 2 Compulsory study plan
2008/2009 (B2649) Electrical Engineering (3901R039) Biomedical Technician P Czech Ostrava 2 Compulsory study plan
2008/2009 (B3943) Mechatronics P Czech Ostrava 2 Compulsory study plan
2008/2009 (B3943) Mechatronics K Czech Ostrava 2 Compulsory study plan
2007/2008 (B2645) Electrical Engineering, Communication and Computer Systems (3907R001) Electrical Power Engineering P Czech Ostrava 2 Compulsory study plan
2007/2008 (B2645) Electrical Engineering, Communication and Computer Systems (2612R041) Control and Information Systems P Czech Ostrava 2 Compulsory study plan
2007/2008 (B2645) Electrical Engineering, Communication and Computer Systems (2642R004) Electrical Machines Apparatus and Drives P Czech Ostrava 2 Compulsory study plan
2007/2008 (B2645) Electrical Engineering, Communication and Computer Systems (2642R004) Electrical Machines Apparatus and Drives K Czech Ostrava 2 Compulsory study plan
2007/2008 (B2645) Electrical Engineering, Communication and Computer Systems (2612R041) Control and Information Systems K Czech Ostrava 2 Compulsory study plan
2007/2008 (B2645) Electrical Engineering, Communication and Computer Systems (3907R001) Electrical Power Engineering K Czech Ostrava 2 Compulsory study plan
2007/2008 (B2649) Electrical Engineering (2601R004) Measurement and Control Engineering P Czech Ostrava 2 Compulsory study plan
2007/2008 (B2649) Electrical Engineering (2601R004) Measurement and Control Engineering K Czech Ostrava 2 Compulsory study plan
2007/2008 (B2649) Electrical Engineering (3907R001) Electrical Power Engineering P Czech Ostrava 2 Compulsory study plan
2007/2008 (B2649) Electrical Engineering (3907R001) Electrical Power Engineering K Czech Ostrava 2 Compulsory study plan
2007/2008 (B2649) Electrical Engineering (2602R014) Applied and Commercial Electronics P Czech Ostrava 2 Compulsory study plan
2007/2008 (B2649) Electrical Engineering (2602R014) Applied and Commercial Electronics K Czech Ostrava 2 Compulsory study plan
2007/2008 (B2648) Designing of Electric Devices (2648R999) Společné studium P Czech Ostrava 2 Compulsory study plan
2007/2008 (B2648) Designing of Electric Devices (2648R999) Společné studium K Czech Ostrava 2 Compulsory study plan
2007/2008 (B2649) Electrical Engineering (3901R039) Biomedical Technician P Czech Ostrava 2 Compulsory study plan
2006/2007 (B2645) Electrical Engineering, Communication and Computer Systems (3907R001) Electrical Power Engineering P Czech Ostrava 2 Compulsory study plan
2006/2007 (B2645) Electrical Engineering, Communication and Computer Systems (2612R041) Control and Information Systems P Czech Ostrava 2 Compulsory study plan
2006/2007 (N2645) Electrical Engineerong, Communication and Computer Systems (2642T004) Electrical Machines Apparatus and Drives P Czech Ostrava 1 Choice-compulsory study plan
2006/2007 (N2645) Electrical Engineerong, Communication and Computer Systems (3907T001) Electrical Power Engineering P Czech Ostrava 1 Choice-compulsory study plan
2006/2007 (B2645) Electrical Engineering, Communication and Computer Systems (2642R004) Electrical Machines Apparatus and Drives P Czech Ostrava 2 Compulsory study plan
2006/2007 (B2645) Electrical Engineering, Communication and Computer Systems (2642R004) Electrical Machines Apparatus and Drives K Czech Ostrava 2 Compulsory study plan
2006/2007 (B2645) Electrical Engineering, Communication and Computer Systems (2612R041) Control and Information Systems K Czech Ostrava 2 Compulsory study plan
2006/2007 (B2645) Electrical Engineering, Communication and Computer Systems (3907R001) Electrical Power Engineering K Czech Ostrava 2 Compulsory study plan
2006/2007 (N2645) Electrical Engineerong, Communication and Computer Systems (2642T004) Electrical Machines Apparatus and Drives K Czech Ostrava 1 Choice-compulsory study plan
2006/2007 (N2645) Electrical Engineerong, Communication and Computer Systems (3907T001) Electrical Power Engineering K Czech Ostrava 1 Choice-compulsory study plan
2005/2006 (B2645) Electrical Engineering, Communication and Computer Systems (3907R001) Electrical Power Engineering P Czech Ostrava 2 Compulsory study plan
2005/2006 (B2645) Electrical Engineering, Communication and Computer Systems (2612R041) Control and Information Systems P Czech Ostrava 2 Compulsory study plan
2005/2006 (N2645) Electrical Engineerong, Communication and Computer Systems (2642T004) Electrical Machines Apparatus and Drives P Czech Ostrava 1 Choice-compulsory study plan
2005/2006 (N2645) Electrical Engineerong, Communication and Computer Systems (3907T001) Electrical Power Engineering P Czech Ostrava 1 Choice-compulsory study plan
2005/2006 (B2645) Electrical Engineering, Communication and Computer Systems (2642R004) Electrical Machines Apparatus and Drives P Czech Ostrava 2 Compulsory study plan
2005/2006 (B2645) Electrical Engineering, Communication and Computer Systems (2642R004) Electrical Machines Apparatus and Drives K Czech Ostrava 2 Compulsory study plan
2005/2006 (B2645) Electrical Engineering, Communication and Computer Systems (2612R041) Control and Information Systems K Czech Ostrava 2 Compulsory study plan
2005/2006 (B2645) Electrical Engineering, Communication and Computer Systems (3907R001) Electrical Power Engineering K Czech Ostrava 2 Compulsory study plan
2005/2006 (N2645) Electrical Engineerong, Communication and Computer Systems (2642T004) Electrical Machines Apparatus and Drives K Czech Ostrava 1 Choice-compulsory study plan
2005/2006 (N2645) Electrical Engineerong, Communication and Computer Systems (3907T001) Electrical Power Engineering K Czech Ostrava 1 Choice-compulsory study plan
2004/2005 (B2645) Electrical Engineering, Communication and Computer Systems (3907R001) Electrical Power Engineering P Czech Ostrava 2 Compulsory study plan
2004/2005 (B2645) Electrical Engineering, Communication and Computer Systems (2612R041) Control and Information Systems P Czech Ostrava 2 Compulsory study plan
2004/2005 (N2645) Electrical Engineerong, Communication and Computer Systems (2642T004) Electrical Machines Apparatus and Drives P Czech Ostrava 1 Choice-compulsory study plan
2004/2005 (N2645) Electrical Engineerong, Communication and Computer Systems (3907T001) Electrical Power Engineering P Czech Ostrava 1 Choice-compulsory study plan
2004/2005 (B2645) Electrical Engineering, Communication and Computer Systems (2642R004) Electrical Machines Apparatus and Drives P Czech Ostrava 2 Compulsory study plan
2004/2005 (B2645) Electrical Engineering, Communication and Computer Systems (2642R004) Electrical Machines Apparatus and Drives K Czech Ostrava 2 Compulsory study plan
2004/2005 (B2645) Electrical Engineering, Communication and Computer Systems (2612R041) Control and Information Systems K Czech Ostrava 2 Compulsory study plan
2004/2005 (B2645) Electrical Engineering, Communication and Computer Systems (3907R001) Electrical Power Engineering K Czech Ostrava 2 Compulsory study plan
2004/2005 (N2645) Electrical Engineerong, Communication and Computer Systems (2642T004) Electrical Machines Apparatus and Drives K Czech Ostrava 1 Choice-compulsory study plan
2004/2005 (N2645) Electrical Engineerong, Communication and Computer Systems (3907T001) Electrical Power Engineering K Czech Ostrava 1 Choice-compulsory study plan
2003/2004 (N2646) Information Technology (2612T025) Computer Science and Technology P Czech Ostrava 1 Optional study plan
2003/2004 (B2646) Information Technology (1103R021) Computation Mathematics P Czech Ostrava 2 Compulsory study plan
2003/2004 (B2645) Electrical Engineering, Communication and Computer Systems (3907R001) Electrical Power Engineering P Czech Ostrava 2 Compulsory study plan
2003/2004 (B2646) Information Technology (2612R025) Computer Science and Technology P Czech Ostrava 2 Optional study plan
2003/2004 (N2646) Information Technology (2612T025) Computer Science and Technology P Czech Ostrava 2 Compulsory study plan
2003/2004 (B2645) Electrical Engineering, Communication and Computer Systems (2612R041) Control and Information Systems P Czech Ostrava 2 Compulsory study plan
2003/2004 (N2645) Electrical Engineerong, Communication and Computer Systems (2642T004) Electrical Machines Apparatus and Drives P Czech Ostrava 1 Choice-compulsory study plan
2003/2004 (N2646) Information Technology (1103T021) Computational Mathematics P Czech Ostrava 1 Compulsory study plan
2003/2004 (N2645) Electrical Engineerong, Communication and Computer Systems (3907T001) Electrical Power Engineering P Czech Ostrava 1 Compulsory study plan
2003/2004 (B2645) Electrical Engineering, Communication and Computer Systems (2642R004) Electrical Machines Apparatus and Drives P Czech Ostrava 2 Compulsory study plan
2003/2004 (B2645) Electrical Engineering, Communication and Computer Systems (2642R004) Electrical Machines Apparatus and Drives K Czech Ostrava 2 Compulsory study plan
2003/2004 (B2645) Electrical Engineering, Communication and Computer Systems (2612R041) Control and Information Systems K Czech Ostrava 2 Compulsory study plan
2003/2004 (B2645) Electrical Engineering, Communication and Computer Systems (3907R001) Electrical Power Engineering K Czech Ostrava 2 Compulsory study plan
2003/2004 (B2646) Information Technology (2612R025) Computer Science and Technology K Czech Ostrava 2 Optional study plan
2003/2004 (B2646) Information Technology (1103R021) Computation Mathematics K Czech Ostrava 2 Compulsory study plan
2003/2004 (N2645) Electrical Engineerong, Communication and Computer Systems (2642T004) Electrical Machines Apparatus and Drives K Czech Ostrava 1 Choice-compulsory study plan
2003/2004 (N2645) Electrical Engineerong, Communication and Computer Systems (3907T001) Electrical Power Engineering K Czech Ostrava 1 Compulsory study plan
2003/2004 (N2646) Information Technology (2612T025) Computer Science and Technology K Czech Ostrava 1 Optional study plan
2003/2004 (N2646) Information Technology (2612T025) Computer Science and Technology K Czech Ostrava 2 Compulsory study plan
2003/2004 (N2646) Information Technology (1103T021) Computational Mathematics K Czech Ostrava 1 Compulsory study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner