151-0801 – Mathematics A (MA Cžv)
| Gurantor department | Department of Mathematical Methods in Economics |
| Subject guarantor | Ing. Orlando Arencibia Montero, Ph.D. |
| Study level | undergraduate or graduate |
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 – Euclidean space, matrices, determinant.
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:
[4] Hoy M., Livernois J., McKenna Ch., Rees R., Stengos T. Mathematics for Economics. The MIT Press, London, 2011.
[5] Tan T.S. Calculus: Early Transcendentals. Brooks/Cole Cengage Learning, Belmont, 2011.
Recommended literature:
[4] Larson R., Falvo C.D. Elementary Linear Algebra. Houghton Mifflin, Boston, New York, 2008.
[5] Luderer B., Nollau V., Vetters K. Mathematical Formulas for Economists. Springer Verlag, third edition, 2007.
[6] Simon C.P., Blume L. Mathematics for Economists. W.W. Norton & Company, New York-London, 2005.
Prerequisities
Subject has no prerequisities.
Co-requisities
Subject has no co-requisities.