Monologická (výklad, přednáška, instruktáž), Metody samostatných akcí, Nácvik dovedností

Course title Course code

Linear Algebra FEI/ILALG

Type of course

Lecture + Lesson

Level of course

Bc.

Year of study Semester Number of credits Language

0 LS 4 CZ

Name of lecturer * Urban Zbyněk, Mgr. * Vozáb Jaroslav, Mgr. * Seibert Jaroslav, doc. RNDr. CSc.

Objective The aim of the course is to provide the students with basic acquirements to use the selected knowledge from the linear algebra and the analytic geometry. A student acquires a satisfactory view of some topics of the linear algebra. The obtained knowledge enable students to use the mathematical appliance in various areas of mathematics and in special courses of their specialization.

Prerequisities Course contents null

Teaching methods Monologická (výklad, přednáška, instruktáž), Metody samostatných akcí, Nácvik dovedností

Assesment methods Písemná zkouška, Posouzení zadané práce, Rozbor produktů pracovní činnosti studenta

Recommended reading * Abidar,K.M., Magnáš,J.R. Matrix algebra. Cabridge 2005.. * Coufal,J. a kol. Učebnice matematiky pro ekonomické fakulty. Victoria Publishing, Praha 1996.. * Freidberg,S.H. a kol. Linear algebra. Prentice Hall 2003.. * Kolda, S., Černá,M. Matematika - Úvod do lineární algebry a geometrie. Univerzita Pardubice, 2004. * Prachař,O., Cabrnochová,R. Průvodce předmětem Matematika. 3.část. Univerzita Pardubice, 2002. * Rachůnek, J. Algebra a teoretická aritmetika I. UP Olomouc, 1992. * Slovák, J. Lineární algebra. Učební texty.. Brno Masarykova univerzita, 1998.


Mathematics I FEI/IMA1E

Type of course

Lecture + Lesson

Level of course

Bc.


0 ZS 6 CZ

Name of lecturer * Zahrádka Jaromír, RNDr. Ph.D. * Urban Zbyněk, Mgr. * Svoboda Martin, RNDr.

Objective Students will gain knowledge in elementary mathematical terms, linear algebra, analytical geometry, differential and integral calculus function of one's variable. The module should increase logical and mathematical skills of the students. Students will be able to understand mathematical conceptions, definitions and operations from this area. They also will gain mathematical skills in such a level that they will be able to apply these skills to following subjects in a particular field of their future study. (electrical and communication technology, microprocessor technology etc.) Students active use mathematical equipment, are able of logical thinking and are able active to use mathematicel skills in subjects informatics and electrical technology.


Teaching methods Monologická (výklad, přednáška, instruktáž), Projekce, Nácvik dovedností

Assesment methods Písemná zkouška

Recommended reading * Cabrnochová, R. ,Prachař, O. Průvodce předmětem Matematika I (druhá část) - Úlohy z diferenciálního a integrálního počtu. Pardubice, 2004. ISBN 80-7194-694-X. * Coufal, J., Klůfa, J. Matematika I pro VŠE. Praha, 1994. * Kolda, S., Černá, M. Matematika - Úvod do lineární algebry a analytické geometrie. Pardubice, 1995. * Machačová, L. Matematika (Základy diferenciálního a integrálního počtu), skriptum. Pardubice, 2005. ISBN 80-7194-577-3. * Machačová, L.-Prachař, O.-Kolda, S. Cvičebnice z matematiky I/1. Pardubice, 1997. * Prachař, O., Cabrnochová, R. Průvodce předmětem Matematika I (třetí část) - Úlohy z lineární algebry, analytické geometrie a z nekonečných řad. Pardubice, 2000. ISBN 80-7194-694-X.


Mathematics II FEI/IMA2E

Type of course

Lecture + Lesson

Level of course

Bc.


0 LS 6 CZ

Name of lecturer * Marek Jaroslav, Mgr. Ph.D. * Zahrádka Jaromír, RNDr. Ph.D.

Objective The aim of the module is to introduce students to the area of infinite numeral and functional sequences, differential equations and differential and integral calculus of more variables. The module should increase logical and mathematical skills of the students. Students will be able to understand mathematical conceptions, definitions and operations from this area. They also will gain mathematical skills in such a level that they will be able to apply these skills to following subjects in a particular field of their future study. (electrical and communication technology, microprocessor technology etc.)

Students active use mathematical equipment, are able of logical thinking and are able active to use mathematicel skills in subjects informatics and electrical technology.


Teaching methods Monologická (výklad, přednáška, instruktáž), Nácvik dovedností


Recommended reading * Kolda,S.-Machačová,L. Matematika II (skriptum). Pardubice, 2007. ISBN 80-7194-931-2. * Kolda,S.-Machačová,L.-Prachař,0. Cvičebnice z Matematiky II. Pardubice, 2007. ISBN 80-7194-932-9. * Machačová,L. Matematika - Základy diferenciálního a integrálního počtu. Pardubice, 2005. ISBN 80-7194557-3. * Prachař,O., Cabrnochová,R. Průvodce předmětem MATEMATIKA I (třetí část). Pardubice, 2004. ISBN 807194-715-6. * Prachař,O. Písemné návody ke studiu předmětu Matematika II (xeroxovaný učební text). Pardubice, 1999.


Mathematics III FEI/IMA3E

Type of course

Lecture + Lesson

Level of course

Bc.


0 ZS 6 CZ

Name of lecturer * Seibert Jaroslav, doc. RNDr. CSc. * Svoboda Martin, RNDr.

Objective The aim of the course is to acquaint the students with mathematical appliance so that they will be able to use acquired knowledge in solving concrete exercises within their study specialization. A student acquires a satisfactory view of some topics of the mathematical analysis and numerical mathematics. The obtained knowledge enable students to use the mathematical appliance in various areas of mathematics and in special courses of their specialization.

Prerequisities Course contents 1. Sequences and series of functions. Uniform convergence. Special tests for uniform convergence of sequences and series of functions. Power series. Differentiation and integration of power series. Expansion of functions in power series, Taylor series. Some important power series and their using to the approximative computations. 2. Fourier series Ortogonal functions, the proof for the set in the interval . Fourier expansion corresponding to a function, derivation of its coefficients. Sufficient conditions for convergence of Fourier series. 3. Systems of differentional equations The elimination method of solution of systems of differentional equaitons. Homogeneous and non-homogeneous systems of linear ordinary differentional equations. 4. Functions of a complex variable Basic properties of complex numbers. A single - valued and a multiple - valued function. Limits, continuity and derivatives of single - valued functions. Cauchy - Riemann conditions, analytic functions. Elementary functions, Euler relations. Logarithmic function. The integral of a function of a complex variable. Cauchy´s theorem and its conclusions. Cauchy´s integral formulas. Taylor series representation of a function. 5. Laplace transform The Laplace transform as a special form of an integral transform Basic properties of the Laplace transform and rules of operations. The inverse Laplace transform, a convolution. Using of the Laplace transform to solve differential and integral equations. 6. Introduction to the numerical mathematics. The solution of an ordinary differentional equation in the form of Taylor series. Euler method. The numerical solution of equations with one variable. Separation of roots. The general iterated method and its geometrical interpretation,

fixed point theorem. The method regula - falsi, Newton method. Polynomial approximation. The Newton and Lagrange interpolation polynomial.


Assesment methods Písemná zkouška, Analýza výkonu studenta, Rozbor produktů pracovní činnosti studenta

Recommended reading * Davies,B. Integral transform and their applications. Springer, New York 2002.. * Kwok,Y.K. Applied complex variables for scientists and engineers. Cambridge University Press 2002.. * Seibert,J. Matematika III. Univerzita Pardubice 2007.. * Skrášek,J., Tichý, Z. Základy aplikované matematiky II, řada vydání, např. SNTL Praha 1986.. * Widder,D.V. Advanced calculus. Dover Publications, Inc., New York 1989..


Mathematics 1 FEI/IMAT1

Type of course

Lecture + Lesson

Level of course

Bc.


0 ZS 6 CZ

Name of lecturer * Zahrádka Jaromír, RNDr. Ph.D. * Urban Zbyněk, Mgr. * Marek Jaroslav, Mgr. Ph.D. * Vozáb Jaroslav, Mgr. * Kordek David, Mgr.

Objective The module is focused to introduce students to the area of elementary mathematical terms, differential and integral calculus function of one's variable and theory of numeral and functional sequences.The module should increase logical and mathematical skills of the students. Students will be able to understand mathematical conceptions, definitions and operations from this area. They also will gain mathematical skills in such a level that they will be able to apply these skills to following subjects in a particular field of their future study. (electrical and communication technology, microprocessor technology etc.) Students active use mathematical equipment, are able of logical thinking and are able active to use mathematicel skills in subjects informatics and electrical technology.




Recommended reading * Cabrnochová, R. - Prachař, O. Průvodce předmětem Matematika I (druhá část) - Úlohy z diferenciálního a integrálního počtu. Pardubice, 2004. ISBN 80-7194-694-X. * Coufal, J., Klůfa, J. Matematika I pro VŠE. Praha, 1994. * Machačová, L. - Prachař, O. - Kolda, S. Cvičebnice z matematiky I/1. Pardubice, 1997. * Machačová, L. Matematika (Základy diferenciálního a integrálního počtu). Pardubice, 2005. ISBN 80-7194577-3. * Prachař, O. - Cabrnochová, R. Průvodce předmětem Matematika (třetí část) - Úlohy z lineární algebry, analytické geometrie a z nekonečných řad.. Pardubice, 2007. ISBN 80-7194-715-6. * zrušeno. zrušeno.


Mathematics 2 FEI/IMAT2

Type of course

Lecture + Lesson

Level of course

Bc.


0 LS 6 CZ

Name of lecturer * Marek Jaroslav, Mgr. Ph.D. * Svoboda Martin, RNDr. * Vozáb Jaroslav, Mgr. * Zahrádka Jaromír, RNDr. Ph.D.

Objective The subject Mathematics II includes the following topics: infinite sequences, infinite series, power sets mappings, a differential and integral calculus of functions of more real variables, vector functions, differential equations.

Students active use mathematical equipment, are able of logical thinking and are able active to use mathematicel skills in subjects informatics and electrical technology.




Recommended reading * Kolda, S. - Machačová, L. - Prachař, 0. Cvičebnice z Matematiky II. Pardubice, 2007. ISBN 80-7194-932-9. * Kolda, S. - Machačová, L. Matematika II (skriptum). Pardubice, 2007. ISBN 80-7194-931-2. * Machačová, L. Matematika - Základy diferenciálního a integrálního počtu. Pardubice, 2005. ISBN 80-7194577-3. * Prachař, O. - Cabrnochová, R. Průvodce předmětem MATEMATIKA I (třetí část). Pardubice, 2007. ISBN 807194-715-6. * Prachař O. - Jelínková J. Průvodce předmětem MATEMATIKA II (čtvrtá část) -Úlohy z diferenciálního počtu funkcí více reálných proměnných. Pardubice, 2007. ISBN 80-7194-655-9. * Prachař O. - Jelínková J. Průvodce předmětem MATEMATIKA II (šestá část) - Úlohy z vícerozměrného a křivkového integrálu. Pardubice, 2008. ISBN 80-7194-557-9.


Mathematic Seminar I FEI/IMS1E

Type of course

Lesson

Level of course

Bc.


0 ZS 1 CZ

Name of lecturer * Zahrádka Jaromír, RNDr. Ph.D. * Kordek David, Mgr.

Objective The module is focused to improve and enlarge mathematical skills from module Mathematic I in the field of elementary mathematic conceptions, linear algebra, analytical geometry and differential and integral calculus function of one's variable. The module should increase logical and mathematical skills of the students. Students will be able to understand mathematical conceptions, definitions and operations from this area. They also will gain mathematical skills in such a level that they will be able to apply these skills to following subjects in a particular field of their future study. (electrical and communication technology, microprocessor technology etc.)

Students will be able to solve independently all problems concerning the topics covered by the course Mathematics I. Students active use mathematical equipment, are able of logical thinking and are able active to use mathematicel skills in subjects informatics and electrical technology. Students will be able to solve independently all problems concerning the topics covered by the course Mathematics I. Students active use mathematical equipment, are able of logical thinking and are able active to use mathematicel skills in subjects informatics and electrical technology.

Prerequisities

Course contents null

Teaching methods Metody samostatných akcí, Nácvik dovedností

Assesment methods Rozbor produktů pracovní činnosti studenta

Recommended reading * Cabrnochová,R. - Prachař,O. Průvodce předmětem Matematika I (druhá část) - Úlohy z diferenciálního a integrálního počtu. Pardubice, 1999. * Coufal,J., - Klůfa,J. Matematika I pro VŠE. Praha, 1994. * Kolda,S.-Černá,M. Matematika - Úvod do lineární algebry a analytické geometrie. Pardubice, 2007. * Machačová,L. Matematika (Základy diferenciálního a integrálního počtu), skriptum. Pardubice, 2005. ISBN

80-7194-577-3. * Machačová,L.-Prachař,O.-Kolda,S. Cvičebnice z matematiky I/1. Pardubice, 1997. * Prachař,O. - Cabrnochová,R. Průvodce předmětem Matematika (třetí část) - Úlohy z lineární algebry,analytické geometrie a z nekonečných řad. Pardubice, 2000. * Seibert,J. - Kolda,S. Úvod do studia matematiky na univerzitě v Pardubicích, skriptum. Pardubice, 1996.


Mathematic Seminar II FEI/IMS2E

Type of course

Lesson

Level of course

Bc.


0 LS 1 CZ

Name of lecturer * Svoboda Martin, RNDr. * Zahrádka Jaromír, RNDr. Ph.D.

Objective The module is focused to improve and enlarge mathematical skills from module Mathematic II in the area of infinite numeral and functional sequences, differential equations and differential and integral calculus of more variables.The module should increase logical and mathematical skills of the students. Students will be able to understand mathematical conceptions, definitions and operations from this area. They also will gain mathematical skills in such a level that they will be able to apply these skills to following subjects in a particular field of their future study. (electrical and communication technology, microprocessor technology etc.)

Students will be able to solve independently all problems concerning the topics covered by the course Mathematics I. Students active use mathematical equipment, are able of logical thinking and are able active to use mathematicel skills in subjects informatics and electrical technology.


Teaching methods Metody samostatných akcí, Nácvik dovedností

Assesment methods Rozbor produktů pracovní činnosti studenta

Recommended reading

* Kolda,S.-Machačová,L. Matematika II (skriptum). Pardubice, 2001. * Kolda,S.-Machačová,L.--Prachař,0. Cvičebnice z Matematiky II. Pardubice, 2001. * Machačová,L. Matematika - Základy diferenciálního a integrálního počtu. Pardubice, 2007. * Prachař,O. - Cabrnochová,R. Průvodce předmětem MATEMATIKA (třetí část). Pardubice, 2000.


Matrix Algebra FEI/INMAE

Type of course

Lecture + Lesson

Level of course

Mgr.


0 LS 5 CZ

Name of lecturer * Urban Zbyněk, Mgr. * Linda Bohdan, doc. RNDr. CSc.

Objective To afford students more remarkable knowledge on vector spaces, matrix theory and their use in practices. Students will obtain survey of the linear algebra which unable them to home study new trends in their professional field in future.



Assesment methods Písemná zkouška, Rozhovor, Systematické pozorování

Recommended reading * Abadir, K.M., Magnus, J.,R. Matrix Algebra. Cambridge, 2005. * Blažek, J. a kol. Algebra a teoretická aritmetika I.. SPN Praha, 1985. * Friedberg,S.H., Insel,A.J.,Spence,L.E. Linear Algebra. Prentice Hall, 2003. * Nicholson, K.W. Linear algebra with aplications. Washington, 1990.


Statistics FEI/ISTAT

Type of course

Lecture + Lesson

Level of course

Bc.


0 ZS 5 CZ

Name of lecturer * Čenčík Petr, Mgr. * Marek Jaroslav, Mgr. Ph.D.

Objective The goal is to get the students familiar with the fundamental terms of the theory of probability and the principles of statistical data analysis.

Capability of statistical data evaluation and interpretation of results.

Prerequisities Course contents Statistics - summary Probability theory Random events and elementary event space. Probability. Axiomatic, classical, geometrical and statistical definition of probability. Conditional probability, independent random events. The complete probability. One-dimensional and multi-dimensional random variable. Continues and discrete random variable. Probability function, probability density function, distribution function. Marginal and conditional distribution. Moments, measures of position and measures of dispersion of one-dimensional and two-dimensional random distribution. Selected distributions of discrete and continuous one-dimensional random variables : two point, binomial, Poisson distribution, uniform, exponential, normal distribution, Chi-square, t, F distribution. Chebyshev theorem, central limit theorem. Statistical methods Population and random sample. Empirical distribution. Sample moments, sample arithmetic mean, sample variation. Estimation methods.Point estimation. Interval estimation. Confidence intervals for expected value and for variance . Lower and upper control limits. Statistical hypothesis testing.A null hypothesis, an alternative hypothesis, the level of significance of the test, the critical region, one-sided tests, two-sided tests. Testing the hypothesis concerning the expected value of the normal distribution, testing the hypothesis concerning the variance of the normal random variable. The u-test, t-test, F-test.

Non-parametric hypothesis testing. The sign test, Wilcoxon test. The chi-square test for goodness of fit. The least square method. Linear regression model by the least square method. Testing significance of regression coefficient and intercept. Confidence intervals of regression coefficient and intercept. Correlation. Measures of dependence. Study of significance of correlations.

Teaching methods Monologická (výklad, přednáška, instruktáž), Nácvik dovedností, Aktivizující (simulace, hry, dramatizace)

Assesment methods Písemná zkouška, Analýza výkonu studenta, Rozbor produktů pracovní činnosti studenta

Recommended reading * Anděl, J. Matematická statistika. SNTL&ALFA, Praha, 1978. * Cyhelský, L., Kahounová, J., Hindls, R. Elementární statistická analýza. Praha: Management Press, 1996. ISBN 80-85943-18-2. * Hátle, J., Likeš, J. Základy počtu pravděpodobnosti a matematické statistiky. Praha: SNTL, 1974. ISBN 04311-74. * Kolda,S. Úvod do počtu pravděpodobnosti a matematické statistiky. VŠCHT, Pardubice, 1980. * Kubanová J. Statistické metody pro ekonomickou a technickou praxi. Statis Bratislava, 2004. ISBN 8085659-379. * Kubanová,J. Linda,B. Sbírka příkladů z pravděpodobnosti. Statis Bratislava, 2004. ISBN 80-85659-36-0. * Kubanová,J. Teorie pravděpodobnosti. Univerzita Pardubice, 1999. ISBN 80-7194-193-X.

Monologická (výklad, přednáška, instruktáž), Metody samostatných akcí, Nácvik dovedností

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