714-0503/01 – Mathematics III (M III)

Gurantor departmentDepartment of Mathematics and Descriptive GeometryCredits4
Subject guarantordoc. RNDr. Radim Havelek, Ph.D.Subject version guarantordoc. RNDr. Radim Havelek, Ph.D.
Study levelundergraduate or graduateRequirementCompulsory
Year2Semesterwinter
Study languageCzech
Year of introduction1999/2000Year of cancellation2005/2006
Intended for the facultiesHGFIntended for study typesMaster
Instruction secured by
LoginNameTuitorTeacher giving lectures
BUR30 doc. RNDr. Pavel Burda, CSc.
HAV10 doc. RNDr. Radim Havelek, Ph.D.
HRA20 RNDr. Radoslava Hradecká
JED20 Mgr. Lumír Jedelský
S1E60 RNDr.Ing. Zdeněk Ševčík, CSc.
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 16+0

Subject aims expressed by acquired skills and competences

This course is closed.

Teaching methods

Summary

Probability: probability of random events, independence of events, random variables, mean and variance, important distributions. Functions of several variables: partial differentiation, extremal values. Integral calculus of functions of two variables and its application. Line integral and its applications.

Compulsory literature:

Škrášek, J. - Tichý, Z.: Základy aplikované matematiky I, II, III, SNTL, Praha 1990 Doležalová, J., Pavelka, L.: Pravděpodobnost a statistika, skriptum VŠB – TU, Ostrava. Burda, P., Doležalová, J.: Cvičení z matematiky IV, skriptum VŠB – TU, Ostrava.

Recommended literature:

Additional study materials

Way of continuous check of knowledge in the course of semester

E-learning

Other requirements

Prerequisities

Subject has no prerequisities.

Co-requisities

Subject has no co-requisities.

Subject syllabus:

Úvod do počtu pravděpodobnosti Základní pojmy z kombinatoriky, náhodný pokus a náhodný jev, definice pravděpodobnosti, nezávislé jevy a jejich pravděpodobnost, pojem náhodné veličiny, diskrétní náhodná veličina, pravděpodobnostní funkce a distribuční funkce diskrétní náhodné veličiny, spojitá náhodná veličina, hustota pravděpodobnosti a distribuční funkce, střední hodnota, rozptyl, rozdělení alternativní, binomické, Poissonovo, rovnoměrné, exponenciální, normální. Diferenciální počet funkcí dvou a více proměnných Plochy 2. stupně. Funkce více proměnných: definiční obory, limita a spojitost funkce více proměnných, parciální derivace a totální diferenciály funkcí více proměnných, rovnice tečné roviny a normály k ploše, funkce dané implicitně a jejich derivace, lokální, vázané a absolutní extrémy funkcí více proměnných. Dvojrozměrné integrály Dvojrozměrný integrál v obdélníku, dvojrozměrný integrál v obecné uzavřené oblasti, transformace dvojrozměrných integrálů, použití dvojrozměrných integrálů. Křivkový integrál Křivky v prostoru E3, pojem křivkového integrálu I., II. druhu, vlastnosti křivkových integrálů, Greenova věta, nezávislost křivkového integrálu na integrační cestě, integrace totálního diferenciálu, exaktní diferenciální rovnice, použití křivkových integrálů.

Conditions for subject completion

Full-time form (validity from: 1960/1961 Summer semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of pointsMax. počet pokusů
Exercises evaluation and Examination Credit and Examination 100 (100) 51 3
        Exercises evaluation Credit 20 (20) 0 3
                Written exam Written test 15  0 3
                Other task type Other task type 5  0 3
        Examination Examination 80 (80) 0 3
                Written examination Written examination 60  0 3
                Oral Oral examination 20  0 3
Mandatory attendence participation:

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Conditions for subject completion and attendance at the exercises within ISP:

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Occurrence in study plans

Academic yearProgrammeBranch/spec.Spec.ZaměřeníFormStudy language Tut. centreYearWSType of duty
2004/2005 (M2111) Hornictví (2101T008) Mining Engineering P Czech Ostrava 2 Compulsory study plan
2004/2005 (M2110) Geological Engineering (2101T003) Geological Engineering P Czech Ostrava 2 Compulsory study plan
2004/2005 (M2102) Mineral Raw Materials (3904T005) Environmental Engineering P Czech Ostrava 2 Compulsory study plan
2004/2005 (M2102) Mineral Raw Materials (3904T022) Waste Treatment and Disposal P Czech Ostrava 2 Compulsory study plan
2004/2005 (M2102) Mineral Raw Materials (2102T001) Economics Management in Raw Materials treatment Industry P Czech Ostrava 2 Compulsory study plan
2004/2005 (M2102) Mineral Raw Materials (2102T006) Water Technology and Management P Czech Ostrava 2 Compulsory study plan
2004/2005 (M2102) Mineral Raw Materials (2102T003) Commerce Engineering in Raw Materials Treatment Industry P Czech Ostrava 2 Compulsory study plan
2004/2005 (M3646) Geodézie a kartografie (3646T007) Geodesy Engineering P Czech Ostrava 2 Compulsory study plan
2004/2005 (M2102) Mineral Raw Materials (3902T033) systems Engineering in Raw Materials Treatment Industry P Czech Ostrava 2 Compulsory study plan
2004/2005 (M3646) Geodézie a kartografie (3602T002) Geoinformatics P Czech Ostrava 2 Compulsory study plan
2004/2005 (B3646) Geodesy and Cartography (3646R006) Geoinformatics P Czech Ostrava 2 Compulsory study plan
2004/2005 (M2102) Mineral Raw Materials (3902T006) Automation and Computers in Raw Materials Treatment Industry P Czech Ostrava 2 Compulsory study plan
2004/2005 (M2102) Mineral Raw Materials (2102T012) Utilization of building raw-materials resources P Czech Ostrava 2 Compulsory study plan
2003/2004 (M2111) Hornictví (2101T008) Mining Engineering P Czech Ostrava 2 Compulsory study plan
2003/2004 (M2110) Geological Engineering (2101T003) Geological Engineering P Czech Ostrava 2 Compulsory study plan
2003/2004 (M2102) Mineral Raw Materials (3904T005) Environmental Engineering P Czech Ostrava 2 Compulsory study plan
2003/2004 (M2102) Mineral Raw Materials (3904T022) Waste Treatment and Disposal P Czech Ostrava 2 Compulsory study plan
2003/2004 (M2102) Mineral Raw Materials (2102T012) Utilization of building raw-materials resources P Czech Ostrava 2 Compulsory study plan
2003/2004 (M2102) Mineral Raw Materials (2102T009) Industrial treatment technologies P Czech Ostrava 2 Compulsory study plan
2003/2004 (M2102) Mineral Raw Materials (2102T001) Economics Management in Raw Materials treatment Industry P Czech Ostrava 2 Compulsory study plan
2003/2004 (M2102) Mineral Raw Materials (2102T006) Water Technology and Management P Czech Ostrava 2 Compulsory study plan
2003/2004 (M2102) Mineral Raw Materials (3911T001) Applied Physics of Materials P Czech Ostrava 2 Compulsory study plan
2003/2004 (M2102) Mineral Raw Materials (2102T003) Commerce Engineering in Raw Materials Treatment Industry P Czech Ostrava 2 Compulsory study plan
2003/2004 (M3646) Geodézie a kartografie (3646T007) Geodesy Engineering P Czech Ostrava 2 Compulsory study plan
2003/2004 (M3646) Geodézie a kartografie (3646T001) Mine Surveying P Czech Ostrava 2 Compulsory study plan
2003/2004 (M2102) Mineral Raw Materials (3902T006) Automation and Computers in Raw Materials Treatment Industry P Czech Ostrava 2 Compulsory study plan
2003/2004 (M2102) Mineral Raw Materials (3902T033) systems Engineering in Raw Materials Treatment Industry P Czech Ostrava 2 Compulsory study plan
2003/2004 (M3646) Geodézie a kartografie (3602T002) Geoinformatics P Czech Ostrava 2 Compulsory study plan
2003/2004 (B3646) Geodesy and Cartography (3646R006) Geoinformatics P Czech Ostrava 2 Compulsory study plan
2002/2003 (M2111) Hornictví (2101T008) Mining Engineering P Czech Ostrava 2 Compulsory study plan
2002/2003 (M2110) Geological Engineering (2101T003) Geological Engineering P Czech Ostrava 2 Compulsory study plan
2002/2003 (M2102) Mineral Raw Materials (3904T005) Environmental Engineering P Czech Ostrava 2 Compulsory study plan
2002/2003 (M2102) Mineral Raw Materials (3904T022) Waste Treatment and Disposal P Czech Ostrava 2 Compulsory study plan
2002/2003 (M2102) Mineral Raw Materials (2102T012) Utilization of building raw-materials resources P Czech Ostrava 2 Compulsory study plan
2002/2003 (M2102) Mineral Raw Materials (2102T009) Industrial treatment technologies P Czech Ostrava 2 Compulsory study plan
2002/2003 (M2102) Mineral Raw Materials (3902T006) Automation and Computers in Raw Materials Treatment Industry P Czech Ostrava 2 Compulsory study plan
2002/2003 (M2102) Mineral Raw Materials (2102T001) Economics Management in Raw Materials treatment Industry P Czech Ostrava 2 Compulsory study plan
2002/2003 (M2102) Mineral Raw Materials (2102T006) Water Technology and Management P Czech Ostrava 2 Compulsory study plan
2002/2003 (M2102) Mineral Raw Materials (3902T033) systems Engineering in Raw Materials Treatment Industry P Czech Ostrava 2 Compulsory study plan
2002/2003 (M2102) Mineral Raw Materials (3911T001) Applied Physics of Materials P Czech Ostrava 2 Compulsory study plan
2002/2003 (M2102) Mineral Raw Materials (2102T003) Commerce Engineering in Raw Materials Treatment Industry P Czech Ostrava 2 Compulsory study plan
2002/2003 (B3646) Geodesy and Cartography (3646R006) Geoinformatics P Czech Ostrava 2 Compulsory study plan
2002/2003 (M3646) Geodézie a kartografie (3646T007) Geodesy Engineering P Czech Ostrava 2 Compulsory study plan
2002/2003 (M3646) Geodézie a kartografie (3602T002) Geoinformatics P Czech Ostrava 2 Compulsory study plan
2002/2003 (M3646) Geodézie a kartografie (3646T001) Mine Surveying P Czech Ostrava 2 Compulsory study plan
2002/2003 (M3908) Fire Protection and Industrial Safety (3908T002) Safety Engineering P Czech Ostrava 2 Compulsory study plan
2002/2003 (M3908) Fire Protection and Industrial Safety (3908T006) Fire Protection Engineering and Industrial Safety P Czech Ostrava 2 Compulsory study plan
2001/2002 (M2111) Hornictví (2101T008) Mining Engineering P Czech Ostrava 2 Compulsory study plan
2001/2002 (M2110) Geological Engineering (2101T003) Geological Engineering P Czech Ostrava 2 Compulsory study plan
2001/2002 (M2102) Mineral Raw Materials (3904T005) Environmental Engineering P Czech Ostrava 2 Compulsory study plan
2001/2002 (M2102) Mineral Raw Materials (3904T022) Waste Treatment and Disposal P Czech Ostrava 2 Compulsory study plan
2001/2002 (M2102) Mineral Raw Materials (2102T012) Utilization of building raw-materials resources P Czech Ostrava 2 Compulsory study plan
2001/2002 (M2102) Mineral Raw Materials (3902T006) Automation and Computers in Raw Materials Treatment Industry P Czech Ostrava 2 Compulsory study plan
2001/2002 (M2102) Mineral Raw Materials (2102T001) Economics Management in Raw Materials treatment Industry P Czech Ostrava 2 Compulsory study plan
2001/2002 (M2102) Mineral Raw Materials (2102T006) Water Technology and Management P Czech Ostrava 2 Compulsory study plan
2001/2002 (M2102) Mineral Raw Materials (3902T033) systems Engineering in Raw Materials Treatment Industry P Czech Ostrava 2 Compulsory study plan
2001/2002 (M2102) Mineral Raw Materials (2102T003) Commerce Engineering in Raw Materials Treatment Industry P Czech Ostrava 2 Compulsory study plan
2001/2002 (B3646) Geodesy and Cartography (3646R006) Geoinformatics P Czech Ostrava 2 Compulsory study plan
2001/2002 (M3646) Geodézie a kartografie (3646T007) Geodesy Engineering P Czech Ostrava 2 Compulsory study plan
2001/2002 (M3646) Geodézie a kartografie (3602T002) Geoinformatics P Czech Ostrava 2 Compulsory study plan
2001/2002 (M3908) Požární ochrana a průmyslová bezpečnost (3908T002) Industrial Safety Engineering P Czech Ostrava 2 Compulsory study plan
2001/2002 (M3908) Požární ochrana a průmyslová bezpečnost (3908T006) Fire Protection Engineering and Industrial Safety P Czech Ostrava 2 Compulsory study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner

Assessment of instruction

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