457-0526/02 – Mathematical Analysis for IT (MAIT)

Gurantor departmentDepartment of Applied MathematicsCredits7
Subject guarantorprof. RNDr. Jiří Bouchala, Ph.D.Subject version guarantorprof. RNDr. Jiří Bouchala, Ph.D.
Study levelundergraduate or graduateRequirementCompulsory
Year1Semestersummer
Study languageCzech
Year of introduction2006/2007Year of cancellation2009/2010
Intended for the facultiesFEIIntended for study typesBachelor
Instruction secured by
LoginNameTuitorTeacher giving lectures
BER95 doc. Ing. Petr Beremlijski, Ph.D.
BOU10 prof. RNDr. Jiří Bouchala, Ph.D.
CER365 doc. Ing. Martin Čermák, Ph.D.
HOR33 doc. Ing. David Horák, Ph.D.
KAB002 Ing. Pavla Hrušková, Ph.D.
JAH02 RNDr. Pavel Jahoda, Ph.D.
DOM033 Ing. Marta Jarošová, Ph.D.
KOV16 doc. Mgr. Petr Kovář, Ph.D.
KRA04 Mgr. Bohumil Krajc, Ph.D.
KRA557 Ing. Martin Kramář
KUB59 RNDr. Michael Kubesa, Ph.D.
LAM05 doc. RNDr. Marek Lampart, Ph.D.
LUK76 doc. Ing. Dalibor Lukáš, Ph.D.
MEN060 Ing. Martin Menšík
MOC017 Ing. Lukáš Mocek
SAD015 Ing. Marie Sadowská, Ph.D.
SIN29 RNDr. Libor Šindel
SOK038 Ing. Vojtěch Sokol
VLA04 Ing. Oldřich Vlach, 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 3+3
Combined Credit and Examination 15+15

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
Project work

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 (www.am.vsb.cz/bouchala)

Recommended literature:

L. Gillman, R. H. McDowell: Calculus, New York, W.W. Norton & Comp. Inc. 1973 J. Stewart: Calculus, Belmont, California, Brooks/Cole Pub. Comp. 1987 (anglicky).

Way of continuous check of knowledge in the course of semester

Průběžná kontrola studia: Studenti v průběhu semestru budou psát písemné testy a vypracují zadaný projekt. Za testy lze získat maximálně 24 body, za projekt 6 bodů. Podmínky udělení zápočtu: K získání zápočtu je nutné získat minimálně 10 bodů.

E-learning

Další požadavky na studenta

Prerequisities

Subject has no prerequisities.

Co-requisities

Subject has no co-requisities.

Subject syllabus:

Přednášky: Reálná čísla. Supremum a infimum. Reálné funkce jedné reálné proměnné. Elementární funkce. Posloupnosti reálných čísel. Limita posloupnosti. Limita funkce. Spojitost funkce. Diferenciál a derivace funkce. Základní věty diferenciálního počtu. Taylorův polynom. Vyšetřování průběhu funkcí. Primitivní funkce a neurčitý integrál. Metody integrace (per partes, substituce, rozklad na parciální zlomky). Integrace speciálních tříd funkcí. Riemannův integrál. Integrál s proměnnou horní mezí. Výpočet určitého integrálu. Aplikace. Nevlastní integrály. Cvičení: Zkratky a termíny výrokové logiky. Aplikace principu matematické indukce. Identifikace suprema a infima u různých typů množin. Zadání funkce. Funkce rostoucí, klesající, periodické,... Prosté funkce, hledání inverzní funkce. Znázornění grafu funkce. Aplikace vlastností elementárních funkcí při řešení rovnic a nerovnic a dalších úlohách. Výpočty limit posloupností, diskuze pojmu limita funkce. Techniky výpočtu limit funkcí. Výpočet derivace a diferenciálu funkce. Konstrukce Taylorova polynomu a odhady zbytku po aproximaci funkce. Aplikace derivace, diferenciálu a Taylorova polynomu ve fyzice, geometrii a numerické matematice. Řešení příkladů na průběh funkce. 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. Projekty: Projekty zadávané studentům obsahují standardní úlohy k procvičení látky.

Conditions for subject completion

Combined form (validity from: 1960/1961 Summer 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
        Examination Examination 70  0
        Exercises evaluation Credit 30  10
Mandatory attendence parzicipation:

Show history

Occurrence in study plans

Academic yearProgrammeField of studySpec.FormStudy language Tut. centreYearWSType of duty
2009/2010 (B2647) Information and Communication Technology (1103R031) Computational Mathematics P Czech Ostrava 1 Compulsory study plan
2009/2010 (B2647) Information and Communication Technology (2601R013) Telecommunication Technology P Czech Ostrava 1 Compulsory study plan
2009/2010 (B2647) Information and Communication Technology (2612R025) Computer Science and Technology P Czech Ostrava 1 Compulsory study plan
2009/2010 (B2647) Information and Communication Technology (2612R059) Mobile Technology P Czech Ostrava 1 Compulsory study plan
2009/2010 (B2647) Information and Communication Technology P Czech Ostrava 1 Compulsory study plan
2009/2010 (B2647) Information and Communication Technology (1103R031) Computational Mathematics K Czech Ostrava 1 Compulsory study plan
2009/2010 (B2647) Information and Communication Technology (2601R013) Telecommunication Technology K Czech Ostrava 1 Compulsory study plan
2009/2010 (B2647) Information and Communication Technology (2612R025) Computer Science and Technology K Czech Ostrava 1 Compulsory study plan
2009/2010 (B2647) Information and Communication Technology (2612R059) Mobile Technology K Czech Ostrava 1 Compulsory study plan
2009/2010 (B2647) Information and Communication Technology K Czech Ostrava 1 Compulsory study plan
2008/2009 (B2647) Information and Communication Technology (1103R031) Computational Mathematics P Czech Ostrava 1 Compulsory study plan
2008/2009 (B2647) Information and Communication Technology (2601R013) Telecommunication Technology P Czech Ostrava 1 Compulsory study plan
2008/2009 (B2647) Information and Communication Technology (2612R025) Computer Science and Technology P Czech Ostrava 1 Compulsory study plan
2008/2009 (B2647) Information and Communication Technology (2612R059) Mobile Technology P Czech Ostrava 1 Compulsory study plan
2008/2009 (B2647) Information and Communication Technology P Czech Ostrava 1 Compulsory study plan
2008/2009 (B2647) Information and Communication Technology (1103R031) Computational Mathematics K Czech Ostrava 1 Compulsory study plan
2008/2009 (B2647) Information and Communication Technology (2601R013) Telecommunication Technology K Czech Ostrava 1 Compulsory study plan
2008/2009 (B2647) Information and Communication Technology (2612R025) Computer Science and Technology K Czech Ostrava 1 Compulsory study plan
2008/2009 (B2647) Information and Communication Technology (2612R059) Mobile Technology K Czech Ostrava 1 Compulsory study plan
2008/2009 (B2647) Information and Communication Technology K Czech Ostrava 1 Compulsory study plan
2007/2008 (B2647) Information and Communication Technology (1103R031) Computational Mathematics P Czech Ostrava 1 Compulsory study plan
2007/2008 (B2647) Information and Communication Technology (2601R013) Telecommunication Technology P Czech Ostrava 1 Compulsory study plan
2007/2008 (B2647) Information and Communication Technology (2612R025) Computer Science and Technology P Czech Ostrava 1 Compulsory study plan
2007/2008 (B2647) Information and Communication Technology (2612R059) Mobile Technology P Czech Ostrava 1 Compulsory study plan
2007/2008 (B2647) Information and Communication Technology (1103R031) Computational Mathematics K Czech Ostrava 1 Compulsory study plan
2007/2008 (B2647) Information and Communication Technology (2601R013) Telecommunication Technology K Czech Ostrava 1 Compulsory study plan
2007/2008 (B2647) Information and Communication Technology (2612R025) Computer Science and Technology K Czech Ostrava 1 Compulsory study plan
2007/2008 (B2647) Information and Communication Technology (2612R059) Mobile Technology K Czech Ostrava 1 Compulsory study plan
2006/2007 (B2647) Information and Communication Technology (1103R031) Computational Mathematics P Czech Ostrava 1 Compulsory study plan
2006/2007 (B2647) Information and Communication Technology (2601R013) Telecommunication Technology P Czech Ostrava 1 Compulsory study plan
2006/2007 (B2647) Information and Communication Technology (2612R025) Computer Science and Technology P Czech Ostrava 1 Compulsory study plan
2006/2007 (B2647) Information and Communication Technology (2612R059) Mobile Technology P Czech Ostrava 1 Compulsory study plan
2006/2007 (B2647) Information and Communication Technology (1103R031) Computational Mathematics K Czech Ostrava 1 Compulsory study plan
2006/2007 (B2647) Information and Communication Technology (2601R013) Telecommunication Technology K Czech Ostrava 1 Compulsory study plan
2006/2007 (B2647) Information and Communication Technology (2612R025) Computer Science and Technology K Czech Ostrava 1 Compulsory study plan
2006/2007 (B2647) Information and Communication Technology (2612R059) Mobile Technology K Czech Ostrava 1 Compulsory study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner