714-0513/01 – Special Topics in Mathematics (VKM)

Gurantor departmentDepartment of Mathematics and Descriptive GeometryCredits5
Subject guarantorprof. RNDr. Radek Kučera, Ph.D.Subject version guarantorprof. RNDr. Radek Kučera, Ph.D.
Study levelundergraduate or graduateRequirementCompulsory
Year2Semesterwinter
Study languageCzech
Year of introduction2006/2007Year of cancellation
Intended for the facultiesHGFIntended for study typesFollow-up Master
Instruction secured by
LoginNameTuitorTeacher giving lectures
DLO44 Mgr. Dagmar Dlouhá, Ph.D.
DUB02 RNDr. Viktor Dubovský, Ph.D.
KUC14 prof. RNDr. Radek Kučera, Ph.D.
STA50 RNDr. Jana Staňková, Ph.D.
URB0186 RNDr. Zbyněk Urban, Ph.D.
VIT0060 Mgr. Aleš Vítek, 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 18+0

Subject aims expressed by acquired skills and competences

Mathematics is essential part of education on technical universities. It should be considered rather the method in the study of technical courses than a goal. Thus the goal of mathematics is train logical reasoning than mere list of mathematical notions, algorithms and methods. Students should learn how to analyze problems, distinguish between important and unimportant, suggest a method of solution, verify each step of a method, generalize achieved results, analyze correctness of achieved results with respect to given conditions, apply these methods while solving technical problems, understand that mathematical methods and theoretical advancements outreach the field mathematics.

Teaching methods

Lectures
Individual consultations
Tutorials
Other activities

Summary

Basics of vector calculus. Functions of several variables: partial differentiation, extremal values. Integral calculus of functions of two variables and its application. Line integral and its applications. Basics of vector fields.

Compulsory literature:

1. Kreml, Pavel: Mathematics II, VŠB – TUO, Ostrava 2005, ISBN 80-248-0798-X. 2. Kučera, Radek: Mathematics III, VŠB – TUO, Ostrava 2005, ISBN 80-248-0802-1. 3. Harshbarger, Ronald; Reynolds, James: Calculus with Applications, D.C. Heath and Company 1990, ISBN 0-669-21145-1.

Recommended literature:

1. Harshbarger, Ronald; Reynolds, James: Calculus with Applications, D.C. Heath and Company 1990, ISBN 0-669-21145-1.

Way of continuous check of knowledge in the course of semester

Tests and credits ================= Exercises --------- Conditions for obtaining credit points (CP): - participation in exercises, 20% can be to apologize - completion of three written tests, 0-15 CP - completion of two programs, 5 CP Exam ---- - written exam 0-60 CP, successful completion at least 25 CP - oral exam 0-20 CP, successful completion at least 5 CP The exam questions are analogous to the program of the lectures.

E-learning

Další požadavky na studenta

There are no other requirements on students.

Prerequisities

Subject codeAbbreviationTitleRequirement
714-0566 BM I Bachelor Mathematics I Recommended
714-0567 BM II Bachelor Mathematics II Recommended

Co-requisities

Subject has no co-requisities.

Subject syllabus:

Week. Lecture ------------- 1st Vector calculus, scalar, cross and triple product, vector functions. 2nd Differential calculus of functions of two or more real variables: domain, graph, limit and continuity. 3rd Partial derivatives, total differential, tangent plane and normal to a surface. 4th Implicit function and its derivatives. 5th Extremes of functions, calculation via derivatives. 6th Constrained extremes, Lagrange's method. 7th Global extremes. Taylor's theorem. 8th Two-dimensional integrals on a rectangle and on a general domain. 9th Calculations of two-dimensional integrals, applications in geometry and physics. 10th Three-dimensional integrals, calculation and application. 11th Line integral of the first and second kind, calculation methods. 12th Applications of curved integrals, Green's theorem, independence of the integration path. 13th Surface integrals and their calculation. 14th Introduction to the field theory: gradient, potential, divergence rotation, Gauss-Ostrogradsky's and Stoke's theorem.

Conditions for subject completion

Full-time form (validity from: 2010/2011 Winter semester, validity until: 2013/2014 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
        Exercises evaluation Credit 20 (20) 5
                Written exam Written test 15  0
                Other task type Other task type 5  5
        Examination Examination 80 (80) 30
                Written examination Written examination 60  25
                Oral Oral examination 20  5
Mandatory attendence parzicipation:

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2008/2009 (N3646) Geodesy and Cartography (3602T004) Mobile Geoinformatics Technology P Czech Ostrava 1 Compulsory study plan
2008/2009 (N3646) Geodesy and Cartography (3602T002) Geoinformatics (10) P Czech Ostrava 1 Compulsory study plan
2008/2009 (N3646) Geodesy and Cartography (3602T002) Geoinformatics (20) P Czech Ostrava 1 Compulsory study plan
2008/2009 (N2110) Geological Engineering (2101T003) Geological Engineering (10) GI P Czech Ostrava 1 Compulsory study plan
2008/2009 (N2110) Geological Engineering (2101T003) Geological Engineering (00) Geologické inženýrství P Czech Ostrava 2 Compulsory study plan
2008/2009 (N2102) Mineral Raw Materials (2102T001) Economics and Management in the Field of Raw Materials K Czech Most 1 Compulsory study plan
2008/2009 (N2102) Mineral Raw Materials (2102T003) Commerce Engineering in Raw Materials Treatment Industry (10) Commerce Engineering in Raw Materials Treatment Industry K Czech Ostrava 1 Compulsory study plan
2007/2008 (N2102) Mineral Raw Materials (3902T033) System Engineering in Raw Materials Industry P Czech Ostrava 1 Compulsory study plan
2007/2008 (N2102) Mineral Raw Materials (3902T033) System Engineering in Raw Materials Industry K Czech Most 1 Compulsory study plan
2007/2008 (N2102) Mineral Raw Materials (6208T031) Environmental Management P Czech Ostrava 1 Compulsory study plan
2007/2008 (N2102) Mineral Raw Materials (2102T003) Commerce Engineering in Raw Materials Treatment Industry (00) Commerce Engineering in Raw Materials Treatment Industry P Czech Ostrava 1 Compulsory study plan
2007/2008 (N2102) Mineral Raw Materials (2102T001) Economics and Management in the Field of Raw Materials P Czech Ostrava 1 Compulsory study plan
2007/2008 (N2102) Mineral Raw Materials (3904T005) Environmental Engineering P Czech Ostrava 1 Compulsory study plan
2007/2008 (N2102) Mineral Raw Materials (3904T022) Waste Treatment and Disposal P Czech Ostrava 1 Compulsory study plan
2007/2008 (N2102) Mineral Raw Materials (2102T006) Water Technologies and Water Management P Czech Ostrava 1 Compulsory study plan
2007/2008 (N2102) Mineral Raw Materials (3901T037) Water - strategic resource P Czech Ostrava 1 Compulsory study plan
2007/2008 (N3646) Geodesy and Cartography (3602T004) Mobile Geoinformatics Technology P Czech Ostrava 1 Compulsory study plan
2007/2008 (N3646) Geodesy and Cartography (3602T002) Geoinformatics (10) P Czech Ostrava 1 Compulsory study plan
2007/2008 (N3646) Geodesy and Cartography (3602T002) Geoinformatics (20) P Czech Ostrava 1 Compulsory study plan
2007/2008 (N2110) Geological Engineering (2101T003) Geological Engineering (10) GI P Czech Ostrava 1 Compulsory study plan
2006/2007 (N2102) Mineral Raw Materials (3904T005) Environmental Engineering K Czech Most 1 Compulsory study plan
2006/2007 (N3646) Geodesy and Cartography (3602T002) Geoinformatics (20) P Czech Ostrava 1 Compulsory study plan
2006/2007 (N2102) Mineral Raw Materials (3902T033) System Engineering in Raw Materials Industry P Czech Ostrava 1 Compulsory study plan
2006/2007 (N3646) Geodesy and Cartography (3602T002) Geoinformatics (20) K Czech Ostrava 1 Compulsory study plan
2006/2007 (N2102) Mineral Raw Materials (3902T033) System Engineering in Raw Materials Industry K Czech Most 1 Compulsory study plan
2006/2007 (N2102) Mineral Raw Materials (6208T031) Environmental Management P Czech Ostrava 1 Compulsory study plan
2006/2007 (N2102) Mineral Raw Materials (6208T031) Environmental Management K Czech Ostrava 1 Compulsory study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner