151-0340/01 – Mathematics E (Mat E)
| 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 | winter |
| | 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 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.
• Order knowledge about vectors in the plain.
• Identify the types of matrices.
• Solve the system of linear equations.
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.
• Express knowledge of vectors to the space.
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.
• Apply knowledge of linear algebra in economics, e.g. traffic problems, structural analysis.
• Solve basic problems of linear programming.
Analysis
• Analyse mathematical principle of some economic terms and properties.
• Appraise the trends of economic values.
Teaching methods
Summary
The subject is built on the university level of mathematics.
It 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 as well as the ability to enunciate
thoughts accurately and to give the correct argumentation
when solving the practical problems. This is being done
especially by mathematization of the real 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 study
of economic 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
Subject has no prerequisities.
Co-requisities
Subject has no co-requisities.
Subject syllabus:
1.Functions of one real variable – definition, domain and range,
classification, graph, even and odd functions, monotonic functions
(strictly increasing, strictly decreasing). Inverse functions.
2.The limits of functions – properties of limits, limits to infinity,
one sided limits, definition of continuity, continuity on an interval,
sequences, limits of sequences.
3.An introduction to the derivate – 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, higher order derivations,
l´Hospital´s rule.
4.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.
5.Linear algebra – matrices, addition and multiplication
of matrices, determinant, the inverse of the matrix,
matrix equations.
6.Linear algebra – system of linear equations, Gauss
elimination method.
Conditions for subject completion
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction
Předmět neobsahuje žádné hodnocení.