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Lecturer(s)
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Řezníčková Jana, Mgr. Ph.D.
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Prokop Roman, prof. Ing. CSc.
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Fajkus Martin, RNDr. Ph.D.
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Martinek Pavel, Ing. Ph.D.
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Course content
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I. In the winter semester, students must choose one of two areas: A. Differential Equations, or B. Graph Theory. II. In the summer semester, all students must choose the Statistics ============================================== CONTENT: I.A. - Differential Equations 1. The concept of a differential equation. The initial value problem. 2. First order ordinary differential equations. Solutions of separable and linear first order ordinary differential equations. 3. Linear higher order ordinary differential equations with constant coefficients and their solutions. 4. The Laplace transform and its application to solving ordinary differential equations. 5. Selected applications of ordinary differential equations. I.B. - Graph Theory - The concept of a graph - Graph connectivity - Distance and metrics in graphs - Trees and forests, minimum spanning tree - Network flows - Selected NP-complete problems in graph theory ------------------------------------------------------------------------------------------------------------------- II. - Statistics - Brief review of combinatorics and elementary probability. - Introduction to probability theory, random event, properties of probability, conditional probability, law of total probability, Bayes' theorem - Random variable, probability and cumulative distribution functions - Random vector, marginal functions - Numerical characteristics of random variables and random vectors - Distributions of selected discrete variables - Distributions of selected continuous variables - Law of large numbers and central limit theorem - Types of variables and their characteristics - Descriptive statistics; random sample and its processing; ungrouped and grouped frequency distributions - Point and interval estimations - Normality testing and parametric tests - Goodness-of-fit test and non-parametric tests - Qualitative data analysis - Fundamentals of correlation and regression analysis
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Learning activities and teaching methods
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Methods for working with texts (Textbook, book), Individual work of students
- Preparation for examination
- 270 hours per semester
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| prerequisite |
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| Knowledge |
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| . |
| . |
| learning outcomes |
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| define basic concepts of theory of differential equations: a differential equation, a general solution and a particular solution of the differential equation, an initial value problem |
| define basic concepts of theory of differential equations: a differential equation, a general solution and a particular solution of the differential equation, an initial value problem |
| recognize a separable differential equation |
| recognize a separable differential equation |
| explain the concept of a linear first order ordinary differential equation |
| explain the concept of a linear first order ordinary differential equation |
| define a homogeneous and a nonhomogeneous linear higher order ordinary differential equation |
| define a homogeneous and a nonhomogeneous linear higher order ordinary differential equation |
| describe basic methods of solving linear higher order ordinary differential equations with constant coefficients |
| describe basic methods of solving linear higher order ordinary differential equations with constant coefficients |
| Skills |
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| apply a method of separating variables in solving separable differential equations |
| apply a method of separating variables in solving separable differential equations |
| solve a linear first order ordinary differential equation using the method of variation of a parameter |
| solve a linear first order ordinary differential equation using the method of variation of a parameter |
| use a suitable method in solving higher order linear ordinary differential equations with constant coefficients |
| use a suitable method in solving higher order linear ordinary differential equations with constant coefficients |
| solve an initial value problem for the given differential equation |
| solve an initial value problem for the given differential equation |
| teaching methods |
|---|
| Knowledge |
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| Individual work of students |
| Individual work of students |
| Methods for working with texts (Textbook, book) |
| Methods for working with texts (Textbook, book) |
| assessment methods |
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| Composite examination (Written part + oral part) |
| Composite examination (Written part + oral part) |
| Grade (Using a grade system) |
| Grade (Using a grade system) |
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Recommended literature
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BRONSON R., COSTA B. G. Schaum's outline of differential equations. New York: McGraw-Hill, 2006. ISBN 0-07-145687-2.
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Budíková M. Popisná statistika. Brno, 2001. ISBN 8021018313.
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Budíková M. Průvodce základními statistickými metodami. Praha, 2010. ISBN 978-80-247-3243-5.
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CODDINGTON, E.A., LEVINSON, N. Theory of Ordinary Differential Equations. New York: McGraw-Hill, 1955. ISBN 0070115427.
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Černý J. Základní grafové algoritmy.
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Demel J. Grafy a jejich aplikace. Praha, 2002.
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Diestel J. Graph Theory. 2005.
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Gruska J. Foundations of computing. International Thompson Computer Press, 1997. ISBN 978-1850322436.
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Hliněný P. Základy teorie grafů. Brno, 2010.
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Jaroš F. Pravděpodobnost a statistika. Praha, 2002. ISBN 80-7080-474-2.
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Jungnickel D. Graphs, networks and algorithms. 2013.
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Kalas J., Ráb M. Obyčejné diferenciální rovnice. Brno, 2001. ISBN 80-210-2589-1.
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Kučera L. Kombinatorické algoritmy. Praha, 1989.
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Matoušek J., Nešetřil J. Kapitoly z diskrétní matematiky. Praha, 2010.
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Nagy, J. Stabilita řešení obyčejných diferenciálních rovnic. Praha: SNTL, 1980.
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Řezníčková J. Diferenciální rovnice - učební text. Zlín, 2015.
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Sipser M. Introduction to the theory of computation. Boston, 1997.
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Veit J. Integrální transformace. Praha, 1979.
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