151-0400/05 – Mathematics A (MatKomb)
| 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 | Czech |
| Year of introduction | 2010/2011 | 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.
• 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.
Teaching methods
Lectures
Individual consultations
Other activities
Summary
Taught in Czech only. It contains the following topics:
1. Linear algebra – matrices, determinant, rank.
2. Linear algebra – the inverse of the matrix, linear equations.
3. Functions of one real variable – definition, properties, graphs, inverse
functions.
4. The limit of function – properties of limits, limits to infinity, one sided
limits, definition of continuit, sequences, limits
of sequences.
5. An introduction to the derivation – slope of a tangent line at a point,
6. Higher order derivations, l´Hospital´s rule.
7. Additional applications of derivation.
Compulsory literature:
[1] Hoy, M., Livernois, J., McKenna, Ch., Rees, R., Stengos, T. Mathematics for Economics. The MIT Press, London, 2011.
[2] Tan, T.S. Calculus: Early Transcendentals. Brooks/Cole Cengage Learning, Belmont, 2011.
Recommended literature:
[1] Larson, R., Falvo, C.D. Elementary Linear Algebra. Houghton Mifflin, Boston, New York, 2008.
[2] Luderer, B., Nollau, V., Vetters, K. Mathematical Formulas for Economists. Springer Verlag, third edition, 2007.
[3] Simon, C.P., Blume, L. Mathematics for Economists. W.W. Norton & Company, New York-London, 2005.
Way of continuous check of knowledge in the course of semester
Odevzdání korespondenčních úkolů v elektronické podobě (viz LMS MOODLE na EkF VŠB-TUO) a vykonání písemky podle pokynů vyučujícícho. Z maximálního počtu bodů je nutno získat alespoň 50%.
E-learning
Other requirements
Credit requirements:
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
1. Fulfiling of all task assigned by a teacher
2. Familiarity with lecture topics and ability to solve assigned problems
Prerequisities
Subject has no prerequisities.
Co-requisities
Subject has no co-requisities.
Subject syllabus:
Témata výkladu zpracovaných v podobě multimediálních studijních opor:
1. Linear algebra – linear dependence of vectors, linear independence of vectors, matrices, addition and multiplication of matrices, determinant, the inverse of the matrix, matrix equations.
2. Functions of one real variable – definition, domain and range, classification, graphs, even and odd functions, monotonic functions (strictly increasing, strictly decreasing), inverse functions, composition of functions.
3. The limits of functions – properties of limits, limits to infinity, one sided limits, definition of continuity, continuity on an interval.
4. An introduction to the differential calculus – 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.
5. Course of a function – local and global extrema, intervals of monotonicity, points of inflection, convexity, concavity, asymptotic lines.
Problems are solved offline (individually, under the supervision of a tutor with the aid of supportive materials).
Conditions for subject completion
Conditions for completion are defined only for particular subject version and form of study
Occurrence in study plans
Occurrence in special blocks