151-0341/01 – Mathematics F (Mat F)
| Gurantor department | Department of Mathematical Methods in Economics | Credits | 6 |
| Subject guarantor | PaedDr. Renata Majovská, PhD. | Subject version guarantor | PaedDr. Renata Majovská, PhD. |
| Study level | undergraduate or graduate | Requirement | Compulsory |
| Year | 1 | Semester | summer |
| | Study language | Czech |
| Year of introduction | 2006/2007 | Year of cancellation | 2009/2010 |
| Intended for the faculties | EKF | Intended for study types | Bachelor |
Subject aims expressed by acquired skills and competences
Knowledge
• Define basic integration rules.
• Define indefinite and definite integral.
• Relate properties of indefinite and definite integral.
• Define the function of two variables.
• Find the domain and range.
• Describe basic properties.
• Compute partial derivates of functions.
• Order knowledge about first-ordered differential equations.
• Identify the types of differential equations.
• Solve differential equations.
Comprehension
• Select suitable integral methods.
• Solve integrals of rational functions by the method of partial fractions.
• Solve integrals of some irrational functions and trigonometric functions.
• Extend knowledge about economic dependences using a mathematical function.
• Generalise the functions on the dependences in the real live.
• Express knowledge about equation solving.
Applications
• Apply integration methods in economics.
• Obtain easier imagine about economic functions of utility.
• Discover the tools suitable for describing of dynamical models.
Analysis
• Analyse mathematical principle of some economic terms and properties.
• Appraise the trends of economic values.
Teaching methods
Summary
The subject continues fulfilling general methodical and professional
goals of mathematics, i.e. to train the rational thinking and
the ability to conceive and work with quantitative information
concerning the outer world. Students get knowledge of several
mathematical techniques which are necessary to understand
economic relationships and models.
Compulsory literature:
Recommended literature:
Way of continuous check of knowledge in the course of semester
Validation tests using CMS Moodle.
E-learning
Other requirements
Prerequisities
Co-requisities
Subject has no co-requisities.
Subject syllabus:
1. The indefinite integral – definition and properties, basic integration rules, methods of integration: integration by parts, integration by substitution.
2. The indefinite integral – integrals of rational functions, the method of partial fractions, integrals of some irrational functions, integrals of some trigonometric functions.
3. The definite integral – definition and properties, Riemann sums, the Newton-Leibniz formula, application of the definite integral: area between curves, capital stock, improper integral.
4. Functions of two variables – introduction and terminology, domain, range, graph, partial derivatives, higher-order partial derivatives.
5. Equation of a tangent plane and a normal of a surface, extreme of functions of two variables: local extreme, extreme with a condition.
6. Ordinary differential equation – first-order differential equations, introduction and terminology, general solution, particular solution, separable differential equation, homogeneous differential equation.
7. Linear differential equation.
Conditions for subject completion
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction
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