151-0500/01 – Mathematics A (Math A)
| Gurantor department | Department of Mathematical Methods in Economics | Credits | 4 |
| Subject guarantor | RNDr. Pavel Rucki, Ph.D. | Subject version guarantor | PaedDr. Renata Majovská, PhD. |
| Study level | undergraduate or graduate | Requirement | Compulsory |
| Year | 1 | Semester | winter |
| | Study language | English |
| Year of introduction | 2004/2005 | Year of cancellation | 2009/2010 |
| Intended for the faculties | | Intended for study types | Bachelor |
Subject aims expressed by acquired skills and competences
Knowledge
• Define the function of one variable.
• Find the domain and range and basic properties.
• Draw graphs of elementary functions.
• Compute limits and derivates of functions.
• Find the properties of no elementary functions a draw theirs graphs.
• Obtain easier imagine about economic functions.
Comprehension
• Express economic dependences using a mathematical function.
• Explain the slope of a function.
• Restate the terms “concavity” and “convexity” into the “degressive” and “progressive”.
• Generalise the functions on the dependences in the real live.
Applications
• Relate economic and mathematical functions.
• Discover the tools suitable for describing of dependences in economics and other sciences.
• Develop the technique of graphs drawing.
Teaching methods
Lectures
Individual consultations
Tutorials
Other activities
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 real world. This is being
done especially by mathematization of the practical as well as theoretical
economic problems. This subject supplies the students’ education with realms of
higher Mathematics which is applicable namely to the creation and investigation
of economic models.
Compulsory literature:
Recommended literature:
Way of continuous check of knowledge in the course of semester
E-learning
Other requirements
Prerequisities
Subject has no prerequisities.
Co-requisities
Subject has no co-requisities.
Subject syllabus:
1. Linear algebra – Euclidean space, matrices, addition and multiplication of
matrices, determinant.
2. Linear algebra – the inverse of the matrix, matrix equations, input-output
analysis. System of linear equations, Gauss elimination method.
3. Functions of one real variable – definition, domain and range,
classification, graphs, even and odd functions, monotonic functions (strictly
increasing, strictly decreasing), inverse functions.
4. The limit of function – properties of limits, limits to infinity, one sided
limits, definition of continuity, continuity on an interval, sequences, limits
of sequences.
5. An introduction to the derivation – slope of a tangent line at a point,
derivative, equation of a tangent line and normal line to a curve at a point,
techniques of differentiation.
6. Higher order derivations, l´Hospital´s rule.
7. Additional applications of derivative – extreme values of a continuous
function, intervals of increase and decrease, the second-derivative test for
concavity, the second-derivative test for relative extreme, asymptotes.
Conditions for subject completion
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction
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