Mathematics IV

* Exchange students do not have to consider this information when selecting suitable courses for an exchange stay.

Course Unit Code714-0369/01
Number of ECTS Credits Allocated5 ECTS credits
Type of Course Unit *Compulsory
Level of Course Unit *Second Cycle
Year of Study *First Year
Semester when the Course Unit is deliveredWinter Semester
Mode of DeliveryFace-to-face
Language of InstructionCzech, English
Prerequisites and Co-Requisites There are no prerequisites or co-requisites for this course unit
Name of Lecturer(s)Personal IDName
DOL30doc. RNDr. Jarmila Doležalová, CSc.
Summary
Systems of n ordinary linear differential equations of the first order for n
functions: definition, representation at matrix form, methods of solution of
systems of 2 equations for 2 functions, Euler method for homogeneous systems of
n equations for n functions. Integral calculus of functions of several
independent variables: two-dimensional integrals, three-dimensional integrals,
vector analysis, line integral of the first and the second kind, surface
integral of the first and second kind. Infinite series: number series, series
of functions, power series.
Learning Outcomes of the Course Unit
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.
Course Contents
Syllabus of lecture
1 Systems of n ordinary linear differential equations of the first order for n functions: definition, representation at matrix form, methods of solution of systems of 2 equations for 2 functions
2 Euler method for homogeneous systems of n equations for n functions
3 Integral calculus of functions of several independent variables: two-dimensional integrals on coordinate rectangle, on bounded subset of R2
4 Transformation - polar coordinates, geometrical and physical applications
5 Three-dimensional integrals on coordinate cube, on bounded subset of R3
6 Transformation - cylindrical and spherical coordinates, geometrical and physical applications
7 Vector analysis, gradient
8 Divergence, rotation
9 Line integral of the first and of the second kind
10 Green´s theorem, potential
11 Geometrical and physical applications
12 Infinite number series
13 Infinite series of functions, power series

Syllabus of tutorial
1 Systems of n ordinary linear differential equations of the first order for n functions: definition, representation at matrix form, methods of solution of systems of 2 equations for 2 functions
2 Euler method for homogeneous systems of n equations for n functions
3 Euler method for homogeneous systems of n equations for n functions, test
4 Integral calculus of functions of several independent variables: two-dimensional integrals on coordinate rectangle, on bounded subset of R2
5 Transformation - polar coordinates
6 Geometrical and physical applications
7 Three-dimensional integrals on coordinate cube, on bounded subset of R3
8 Transformation - cylindrical and spherical coordinates
9 Geometrical and physical applications, test
10 Vector analysis, gradient
11 Divergence, rotation
12 Line integral of the first kind
13 Line integral of the second kind, test
14 Geometrical and physical applications
Recommended or Required Reading
Required Reading:
Harshbarger, R.J.-Reynolds, J.J.: Calculus with Applications.
D.C.Heath and Company, Lexington1990, ISBN 0-669-21145-1
James, G.: Modern Engineering Mathematics. Addison-Wesley, 1992.
ISBN 0-201-1805456
http://www.studopory.vsb.cz
Burda, P. - Doležalová, J.: Integrální počet funkcí více proměnných – Matematika IIIb. Skriptum VŠB, Ostrava 2003. ISBN 80-248-0454-9.
Burda, P. - Doležalová, J.: Cvičení z matematiky IV. Skriptum VŠB, Ostrava
2002. ISBN 80-248-0028-4.
Vlček, J. – Vrbický, J.: Řady – Matematika VI. Skriptum VŠB-TU, Ostrava 2000.
ISBN 80-7078-775-9.
Recommended Reading:
Harshbarger, R.J.-Reynolds, J.J.: Calculus with Applications.
D.C.Heath and Company, Lexington1990, ISBN 0-669-21145-1
James, G.: Modern Engineering Mathematics. Addison-Wesley, 1992.
ISBN 0-201-1805456
James, G.: Advanced Modern Engineering Mathematics. Addison-Wesley, 1993.
ISBN 0-201-56519-6
Častová, N. a kol.: Cvičení z matematiky III. Skriptum VŠB, Ostrava 1988
Škrášek, J.-Tichý, Z.: Základy aplikované matematiky II. SNTL Praha, 1986
http://mdg.vsb.cz/M
Planned learning activities and teaching methods
Lectures, Individual consultations, Tutorials, Other activities
Assesment methods and criteria
Task TitleTask TypeMaximum Number of Points
(Act. for Subtasks)
Minimum Number of Points for Task Passing
Exercises evaluation and ExaminationCredit and Examination100 (100)51
        Exercises evaluationCredit20 5
        ExaminationExamination80 (80)31
                written exam Written examination60 25
                Oral examination Oral examination20 5