151-0400/06 – 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 | 2018/2019 | Year of cancellation | |
| 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:
1. Real sequences – definition, properties, graphs, arithmetic sequence, geometric sequence, summation.
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.
1. Linear algebra – matrices, addition and multiplication of matrices, rank of a matrix, determinant, the inverse of the matrix, matrix equations.
Problems are solved offline (individually, under the supervision of a tutor with the aid of supportive materials).
Conditions for subject completion
Occurrence in study plans
Occurrence in special blocks