151-0500/02 – Mathematics A (Math A)
| Gurantor department | Department of Mathematical Methods in Economics | Credits | 5 |
| Subject guarantor | RNDr. Pavel Rucki, Ph.D. | Subject version guarantor | RNDr. Pavel Rucki, Ph.D. |
| Study level | undergraduate or graduate | Requirement | Compulsory |
| Year | 1 | Semester | winter |
| | Study language | English |
| Year of introduction | 2014/2015 | Year of cancellation | 2017/2018 |
| Intended for the faculties | EKF | 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
Credit requirements:
1. Passing the credit test (succes rate - at least 50%)
2. Fulfiling of all task assigned by a teacher
3. Active participation at seminars - at most three absence without leave
4. Familiarity with lecture topics and ability to solve assigned problems
Credit requirements in case of individual study:
It is possible to replace active participation at seminars (req. 3) with written tasks assigned by a teacher. Other requirements remain valid.
E-learning
Other requirements
Credit requirements:
1. Passing the credit test (succes rate - at least 50%)
2. Fulfiling of all tasks assigned by a teacher
3. Active participation at seminars - at most three absence without leave
4. Familiarity with lecture topics and ability to solve assigned problems
Credit requirements in case of individual study:
It is possible to replace active participation at seminars (req. 3) with written tasks assigned by a teacher. Other requirements remain valid.
Prerequisities
Subject has no prerequisities.
Co-requisities
Subject has no co-requisities.
Subject syllabus:
1. Introduction to mathematical logic and set theory - statement, proposition, logical connectives, quantifiers, necessary and sufficient conditions, set operations, number sets, intervals.
2. Real sequences – basic concepts, properties, arithmetic and geometric sequence and their application.
3. Real sequences – limit of a sequence, improper limit of a sequence, definition of Euler's number e.
4. Function of a single real variable – definition, domain and range, classification, graphs, even and odd functions, monotonic functions (strictly increasing, strictly decreasing).
5. Function of a single real variable – inverse functions, elementary functions, graph of a function and its transformation, points of intersection.
6. Function of a single real variable – continuous function, limit of a function at a point, properties of limits, one-sided limits.
7. Function of a single real variable – improper limit of a function, limit of a funciton at infinity, properties of continuous functions.
8. Function of a single real variable – derivative of a function, slope of a tangent line at a point, equation of a tangent line and normal line to a curve at a point, differentiation techniques, higher order derivatives.
9. Function of a single real variable - differential of a function, Rolle's and Lagrange'S Theorem, l'Hospital's Theorem, Taylor and Maclaurin polynomial.
10. Function of a single real variable - monotonoic function, local and global extrema of a function.
11. Function of a single real variable – convex and concave function, inflexion points, asymptotes - horizontal, vertical, oblique.
12. Linear algebra – matrix, matrix operation, rank of a matrix.
13. Linear algebra – determinant of a matrix, properties of determinant, Sarrus' scheme, Laplace's formula, inverse matrix, matrix equations.
14. Linear algebra – vector, vector operation, linearly independent vectors, vector spaces, inner product of vectors, length of a vector.
Conditions for subject completion
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction
Předmět neobsahuje žádné hodnocení.