Předměty(verze: 954)

Mathematics - AB501094
Anglický název: Mathematics Ústav ekonomiky a managementu (837) Celoškolská pracoviště VŠCHT Praha od 2022 oba 8 8 3/4, Z+Zk [HT] zimní:neurčen / neurčen (neurčen) letní:neurčen / neurčen (neurčen) neomezen vyučován angličtina prezenční prezenční předmět je možno zapsat mimo plánpovolen pro zápis po webupředmět lze zapsat v ZS i LS
Garant: Vozárová Pavla Ing. Mgr. Ph.D., M.A.Romanenko Viktoriia doc. Ph.D.
 Literatura - angličtina

Sydsæter, K., Strøm, A., & Berck, P. (2005). Economists' mathematical manual (Vol. 3). Berlin: Springer.

Dowling, E. T. (2001). THEORY AND PROBLEMS OF INTRODUCTION TO MATHEMATICAL ECONOMICS 3rd ed. MC Graw Hill Education.

Sydsæter, K., & Hammond, P. J. (2008). Essential mathematics for economic analysis. Pearson Education.

Bronshtein, I. N., & Semendyayev, K. A. (2013). Handbook of mathematics. Springer Science & Business Media.

Vinogradov V. (1999). A Cook-book of Mathematics. CERGE-EI.

Poslední úprava: Cibulková Jana (19.12.2022)
 Sylabus - angličtina

1. High school mathematics revision.

2. Mathematical logic and notation.

3. Linear algebra (1) Matrices and matrix operations. Determinants. Eigenvalues. Positive and negative definite matrices.

4. Linear algebra (2) Singular and regular matrices, inverse matrices, systems of linear equations. Frobenius theorem, Gaussian elimination, Cramer's rule.

5. Linear algebra (3) Vector space, linear independence, basis and dimension.

6. Functions of one variable (1) Domain of definition, range. Properties of functions. Limit and continuity.

7. Functions of one variable (2) Elementary functions, their properties and graphs. Complex functions. Bijective and inverse functions.

8. Functions of one variable (3) Derivative – definition and meaning. Rules for calculating the derivative. Derivatives of complex and inverse functions. Derivatives of higher orders.

9. Functions of one variable (4) Monotonicity and local extrema. Global extrema. Convexity, concavity, inflection points.

10. Functions of one variable (5) L'Hospital's rule. Taylor’s polynomial. Tangent to graph of a function.

11. Functions of one variable (6) Asymptotes. Sketching the graph of a function.

12. Functions of multiple variables (1) Domain, limit and continuity. Visualisation using the section method.

13. Functions of multiple variables (2) Differential calculus, partial derivatives. Gradient, directional derivative. Total differential.

14. Functions of multiple variables (3) Implicitly specified functions of multiple variables and their derivatives. Derivatives of higher orders, convex and concave functions, quasi-convex and quasi-concave functions.

Poslední úprava: Cibulková Jana (19.12.2022)
 Podmínky zakončení předmětu (Další požadavky na studenta) - angličtina

Requirements for assessment: A combined result of three tests written during the semester of at least 50%, conditional on the teaching assistant agreement to grant credit on the basis of active participation during exercies sessions.

Exam requirements: The grade will be awarded based on the result of the written exam followed by an oral discussion.

Poslední úprava: Cibulková Jana (19.12.2022)
 Zátěž studenta Činnost Kredity Hodiny Účast na přednáškách 1.5 42 Příprava na přednášky, semináře, laboratoře, exkurzi nebo praxi 3.5 98 Příprava na zkoušku a její absolvování 1 28 Účast na seminářích 2 56 8 / 8 224 / 224

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