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Lecturer(s)
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Bílek Jiřina, doc. RNDr. CSc.
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Course content
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Content: 1st week: Revision of concept of mathematical logic. Basic types of proves. 2nd week: Sequences as a model of discrete system. Examples. Sequence notation. Graphical interpretation. Sequence attributes. 3rd week: Geometric sequence ? (...), monotone, convergence and divergence. Theorems about convergent sequences. 4th week: Proves of elemental attributes. Analysis of divergent sequence and (...). 5th week: Number series, convergence and divergence. 6th week: Elemental attributes of function, monotone, injection, inverse function, graphs. 7th week: Limit and continuous function. Examples. 8th week: Derivative, finding derivative, relation to continuity. 9th ? 10th week: Use of derivative for finding extremes and monotone intervals of function. 11th week: Higher order derivatives and differentials. Taylor?s theorem. 12th week: Primitive function. Integration per partes, substitution. 13th week: Rational function integration.
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Learning activities and teaching methods
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Individual study, Seminar
- Contact hours
- 26 hours per semester
- Preparation for formative assessments (2-20)
- 30 hours per semester
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| prerequisite |
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| Knowledge |
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| Assumptions Student: - identifies a type of propositional formula, - illustrates the concept of a propositional form and distinguishes a propositional form from a proposition, - applies theoretical knowledge of sets, set operations and Venn diagrams in solving word problems, - uses basic rules for counting real and complex numbers and for algebraic expression transformation, - chooses effective way of solving equations and inequalities, - applies the concept of matrix and rules for operating with them, - understands principles of analytic expression of linear objects, curves and elementary surfaces, is able to express a linear object with a proper equation, - determines a number of permutations, variations and combinations, - understands basics of experimental and theoretical probability. |
| learning outcomes |
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| Learning outcomes and gained competencies: Students are able to apply basic knowledge of elementary functions of elementary proof of simple statements, handle simple calculations in the field of mathematical analysis. |
| teaching methods |
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| Seminar |
| Individual study |
| assessment methods |
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| Test |
| Skills demonstration during practicum |
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Recommended literature
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Drábek, Jaroslav; Hora, Jaroslav. Algebra. Polynomy a rovnice. 1. vyd. Plzeň : Západočeská univerzita, 2001. ISBN 80-7082-787-4.
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Hora, Jaroslav. Matematická analýza : pomocný učební text pro studenty 1. ročníku.
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Hora, Jaroslav. Matematická analýza : pomocný učební text pro studenty 1. ročníku. 5. upr. vyd. Plzeň : Západočeská univerzita, 2004. ISBN 80-7043-298-5.
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