8342936906

Name of the course: MATHEMATICAL ANALYSIS						Course codę: 14.3.111.71 AI05 15
Name of the unit giving the course: Department of Econometrics and Statistics
Name of the field of Study: ECONOMICS AND IT APPLICATIONS
Form of studies: Full-time Bachelor			Education profile: academic			Specialization:
Year / semester 1/1			Course/module status: Field of study			Course/module language: English
Form of the course	lecture	exercises		laboratories	conyers.		seminar	other
Number of hours	15	30

Course/module coordinator

dr Barbara Batog, [e-mail]. 91 4441978

Course deals with differential and integral calculus for single and many variable Goal of the course/module    functions; elements of this course will be used in other courses (for example

economics, statistics and econometrics)

Course reguirements

Knowledge: student knows mathematics on the high school level Skills: student is able to solve mathematical problems on the high school level Social competencies: student studies systematically

Number of hours

Course content

Form of the course - lecture

1. Cartesian product. Definition and propertiesof functions: injection, surjection, bijection, monotonicity, inverse functions, cyclometric functions, function composition. Elementary functions. Examples of countable and uncountable sets

2. Metric space. Neighborhood and punctured neighborhood, open and closed set, bounded set. Limits of the seguences, conyergent and diyergent seguences, Euler's number e, indeterminate forms_

3. Definition and properties of limits and continuity

4. Difference quotient, definition and properties of derivative of single variable function, properties of differentiable function, derivatives of elementary functions; rules for finding the derivatives, differential, higher-order derivatives. Derivatives in geometry and economics

5.    Lagrange’s and Rolle’s theorems. Application of derivatives to analyze single variable functions:

necessary and sufficient conditions of existing of local and global extrema, monotonicity, inflection points, curyature. L'Hópital*s rule. Asymptotes._

6.    Indefinite integrals, integration by substitution and by parts.

7. Riemann definite integral, fundamental theorem of integral calculus. Improper integrals. Relationship between definite integral and area._

8. Differentiability, partial derivatives and local extrema of many variable functions

Form of the course - exercises

1. Cartesian product. Definition and propertiesof functions: injection, surjection, bijection, monotonicity, inyerse functions, cyclometric functions, function composition. Elementary functions.

2. Limits of the seguences, conyergent and diyergent seguences, Euler's number e, indeterminate forms.

3. Limits and continuity of functions.