Course: Mathematics II

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Course title Mathematics II
Course code UMKM/PMAT2
Organizational form of instruction Lecture + Lesson
Level of course Bachelor
Year of study not specified
Semester Summer
Number of ECTS credits 5
Language of instruction Czech
Status of course Compulsory
Form of instruction Face-to-face
Work placements This is not an internship
Recommended optional programme components None
Lecturer(s)
  • Pacáková Viera, prof. RNDr. Ph.D.
  • Seinerová Kateřina, Ing.
  • Seibert Jaroslav, doc. RNDr. CSc.
  • Jindrová Pavla, Mgr. Ph.D.
  • Brebera Jan, RNDr.
  • Brebera David, Mgr.
  • Papoušková Monika, Ing.
  • Koudela Libor, Mgr. Ph.D.
  • Gogola Ján, RNDr. Ph.D.
Course content
Function series, convergence range, total series. Power series, radius and interval of convergence. Taylor's series. Use of series. Geometrical vectors. Euclidean space. Scalar, vector and mixed product in three-dimensional Euclidean space. Analytical geometry of linear systems in a space. Analysis of incidence and metric problems. Differential functions with more variables. Mapping and function in k-dimensional space. Partial derivation and its geometrical importance. Differentiable function, total differential of a function and its use. Implicit function and its derivation. Local extremes of a function, constrained extremes, absolute extremes and its determination. Usual differential equations and methods of solution. The solution of usual differential equations of the first order - separate, homogenous, linear equation. Elementary methods in analysis of differential equations of higher-order. Integral calculus of functions with more variables. Riemann's multidimensional integral in a compact interval and in a measurable set, Fubini's theorem, calculation of double integrals. Substitution in double integral. Transformation into polar coordinates in E2. Application of double integrals.

Learning activities and teaching methods
Monologic (reading, lecture, briefing), Methods of individual activities, Skills training
Learning outcomes
The course is designed to acquaint students with basics of infinite function series, differential and integral calculus of functions of several real variables and theory of ordinary differential equations and to develop their ability to find and use appropriate mathematical methods to solve problems of various economic and technical disciplines.
Students will be able to apply obtained skills in solving concrete mathematical, technical and economic problems.
Prerequisites
Supposes examination from subject PMAT1.

Assessment methods and criteria
Written examination, Home assignment evaluation, Didactic test

Assignment - active participation in seminars and elaboration of engaged tasks. Passing written test with evaluation at least 40%. Examination - passing written test with evaluation at least 50%%. The test consists of 4 calculus tasks and 5 theoretic questions.
Recommended literature
  • Lineární diferenciální rovnice 1.řádu - Přímočarý pohyb ( k dispozici ve studovně Univerzitní knihovny)..
  • Výukové videoprogramy: Diferenciální rovnice 1. řádu, Diferenciální rovnice vyšších řádů, Diferenciální rovnice - příklady.
  • Kolda S. - Černá M. Úvod do lineární algebry a analytické geometrie. null. Pardubice, 2007. ISBN null.
  • Kolda S.- Machačová L. Matematika II, skriptum. Pardubice, 2007.
  • Kolda S.-Machačová L.-Prachař O. Cvičebnice z Matematiky II.. Pardubice, 2007.
  • Prachař O. - Jelínková J. : Průvodce předmětem MATEMATIKA II (pátá část) -Úlohy z obyčejných diferenciálních rovnic.. Pardubice, 2008.
  • Prachař O. - Jelínková J. Průvodce předmětem MATEMATIKA II (šestá část) -Úlohy z vícerozměrného a křivkového integrálu.. Pardubice, 2007.
  • Prachař O.-Cabrnochová R. Průvodce předmětem MATEMATIKA (třetí část)- Úlohy z lineární algebry, analytické geometrie a z nekonečných řad. Pardubice, 2007.
  • Prachař, Otakar. Průvodce předmětem matematika II.. Pardubice: Univerzita Pardubice, 2004. ISBN 80-7194-655-9.


Study plans that include the course
Faculty Study plan (Version) Branch of study Category Recommended year of study Recommended semester
Faculty of Economics and Administration Security Management in Enterprises (2016) Economy 1 Summer
Faculty of Economics and Administration Enterprise Management (2016) Economy 1 Summer
Faculty of Economics and Administration Enterprise Management (2015) Economy 1 Summer
Faculty of Economics and Administration Enterprise Management (2014) Economy 1 Summer
Faculty of Economics and Administration Enterprise Management (2014) Economy 1 Summer
Faculty of Economics and Administration Economics and Operation in Enterprises (2016) Economy 1 Summer
Faculty of Economics and Administration Economics and Operation in Enterprises (2013) Economy 1 Summer
Faculty of Economics and Administration Public Economics and Administration (2013) Economy 1 Summer
Faculty of Economics and Administration Security Management in Enterprises (2014) Economy 1 Summer
Faculty of Economics and Administration Security Management in Enterprises (2013) Economy 1 Summer
Faculty of Economics and Administration Public Economics and Administration (2014) Economy 1 Summer
Faculty of Economics and Administration Public Economics and Administration (2014) Economy 1 Summer
Faculty of Economics and Administration Enterprise Management (2016) Economy 1 Summer
Faculty of Economics and Administration Economics and Operation in Enterprises (2015) Economy 1 Summer
Faculty of Economics and Administration Economics and Operation in Enterprises (2014) Economy 1 Summer
Faculty of Economics and Administration Public Economics and Administration (2015) Economy 1 Summer
Faculty of Economics and Administration Public Economics and Administration (2015) Economy 1 Summer
Faculty of Economics and Administration Enterprise Management (2013) Economy 1 Summer
Faculty of Economics and Administration Enterprise Management (2015) Economy 1 Summer
Faculty of Economics and Administration Enterprise Management (2013) Economy 1 Summer
Faculty of Economics and Administration Public Economics and Administration (2013) Economy 1 Summer
Faculty of Economics and Administration Security Management in Enterprises (2015) Economy 1 Summer