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Lecturer(s)
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Valentová Ivana, doc. Ing. Ph.D.
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Course content
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1. Sequence as a model of a discrete system - recurrence and difference equation. Sequence as a mathematical object - algebra and properties, convergence and divergence. Sequence of partial sums - infinite sums. Sequences in finance, biology and social sciences. 2. Function as a model of a continuous system - basic functions, graphs, diagrams. Function operations, continuity, composed function. Local properties. Function as a tool of description of natural and economic quantities and dependences. 3. Fundaments of differential calculus - difference, differential, derivative. Methods of differentiation. Modeling of changes in natural sciences, economy and social sciences. 4. Methods of differential calculus - basic optimization, formulation of basic natural laws. Primitive function and methods of solving simple differential equations. Potential. 5. Definite integral as a model of a balance principle. Properties and methods of calculations. Integral sum - geometric and physical interpretation. 6. Local polynomial approximation of a function - Taylor formula, derivatives and differentials of higher orders, simple approximate calculations.
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Learning activities and teaching methods
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Multimedia supported teaching, Task-based study method, Lecture, Practicum
- Contact hours
- 65 hours per semester
- Preparation for an examination (30-60)
- 30 hours per semester
- Preparation for formative assessments (2-20)
- 20 hours per semester
- Preparation for comprehensive test (10-40)
- 25 hours per semester
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| prerequisite |
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| Knowledge |
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| There is no prerequisite for this course. Students should be familiar with a high school algebra and trigonometry. |
| learning outcomes |
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| The student is able to understand and to describe the basic laws in nature sciences by mathematical tools. |
| teaching methods |
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| Lecture |
| Practicum |
| Multimedia supported teaching |
| Task-based study method |
| assessment methods |
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| Combined exam |
| Test |
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Recommended literature
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Drábek, Pavel; Míka, Stanislav. Matematická analýza I. 1. vyd. Plzeň : Západočeská univerzita, 1995. ISBN 80-7082-217-1.
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Gillman, Leonard; McDowell, Robert H. Matematická analýza. 1. vyd. Praha : SNTL, 1980.
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Míka, S. Speciální učební texty. Systém TRIAL, KMA ZCU.
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