# 230-0403/03 – Special Topics in Mathematics (VKM)

 Gurantor department Department of Mathematics Credits 5 Subject guarantor doc. Ing. Martin Čermák, Ph.D. Subject version guarantor doc. Ing. Martin Čermák, Ph.D. Study level undergraduate or graduate Requirement Compulsory Year 1 Semester winter Study language English Year of introduction 2019/2020 Year of cancellation Intended for the faculties HGF Intended for study types Follow-up Master
Instruction secured by
CER365 doc. Ing. Martin Čermák, Ph.D.
DLO44 Mgr. Dagmar Dlouhá, Ph.D.
DUB02 RNDr. Viktor Dubovský, 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

### 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:

JAMES, G.: Modern Engineering Mathematics, Addison-Wesley, 1992, 0-201-1805456. DOLEŽALOVÁ, Jarmila: Mathematics I, VŠB - TUO, Ostrava 2005, 80-248-0796-3. MOORE,C: Math quations and inequalities, Science & Nature, 2014. JAMES, G.: Modern Engineering Mathematics. Addison – Wesley Publishing Company, Wokingham, 1994, ISBN 0-201-18504-5.

### 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, 0-14 CP - completion of two programs, 6 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.

### Other requirements

There are no other requirements on students.

### Prerequisities

Subject has no prerequisities.

### 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: 2019/2020 Winter semester)
Min. number of pointsMax. počet pokusů
Credit and Examination Credit and Examination 100 (100) 51
Credit Credit 20  5
Examination Examination 80 (80) 30 3
Písemná zkouška Written examination 60  25
Ústní zkouška Oral examination 20  5
Mandatory attendence participation: 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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Conditions for subject completion and attendance at the exercises within ISP: Mandatory participation in the course is not required. Other conditions for subject completion will respect the individual needs of the student.

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### Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner