230-0403/02 – Special Topics in Mathematics (VKM)

Gurantor departmentDepartment of MathematicsCredits5
Subject guarantordoc. Ing. Martin Čermák, Ph.D.Subject version guarantordoc. Ing. Martin Čermák, Ph.D.
Study levelundergraduate or graduateRequirementCompulsory
Year1Semesterwinter
Study languageCzech
Year of introduction2019/2020Year of cancellation
Intended for the facultiesHGFIntended for study typesFollow-up Master
Instruction secured by
LoginNameTuitorTeacher giving lectures
CER365 doc. Ing. Martin Čermák, Ph.D.
DLO44 Mgr. Dagmar Dlouhá, Ph.D.
DUB02 RNDr. Viktor Dubovský, Ph.D.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
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:

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

Recommended literature:

Škrášek, J. - Tichý, Z.: Základy aplikované matematiky I, II, III, SNTL, Praha 1990. Burda, P., Doležalová, J.: Cvičení z matematiky IV. Skriptum VŠB-TUO, Ostrava 2002, ISBN 80-248-0028-4. James, G.: Modern Engineering Mathematics, Addison-Wesley, 1992, 0-201-1805456. Doležalová, Jarmila: Mathematics I, VŠB - TUO, Ostrava 2005, 80-248-0796-3.

Way of continuous check of knowledge in the course of semester

Tests and credits ================= Exercises: completion of programs, max. 20 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

They are no other requests for students.

Prerequisities

Subject has no prerequisities.

Co-requisities

Subject has no co-requisities.

Subject syllabus:

Program of lectures ------------------- 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

Combined form (validity from: 2019/2020 Winter semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of points
Credit and Examination Credit and Examination 100 (100) 51
        Credit Credit 20  5
        Examination Examination 80 (80) 30
                Písemná zkouška Written examination 60  25
                Ústní zkouška Oral examination 20  5
Mandatory attendence parzicipation: At least 70% attendance at the exercises. Absence, up to a maximum of 30%, must be excused and the apology must be accepted by the teacher (the teacher decides to recognize the reason for the excuse).

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Occurrence in special blocks

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