Course unit code:
N424M3_4B
Course unit title:
Mathematics I
Mode of completion and Number of ECTS credits:
Exm (9 credits)
Course supervisor:
doc. RNDr. Milan Jasem, CSc.
Name of lecturer(s):
V. Baláž, M. Gall, Ľ. Horanská, P. Jánoš, M. Jasem, N. Krivoňáková, M. Langerová, Z. Ontkovičová, Z. Takáč, P. Viceník, T. Visnyai (2022/2023 – Winter)
V. Baláž, M. Gall, Ľ. Horanská, P. Jánoš, M. Jasem, N. Krivoňáková, M. Langerová, S. Pavlíková, P. Viceník, T. Visnyai (2021/2022 – Winter)
V. Baláž, M. Gall, Ľ. Horanská, M. Jasem, M. Langerová, M. Nehéz, S. Pavlíková, P. Viceník, T. Visnyai (2020/2021 – Winter)
V. Baláž, Š. Boor, M. Gall, Ľ. Horanská, M. Jasem, A. Maťašovský, M. Nehéz, S. Pavlíková, P. Viceník, T. Visnyai (2019/2020 – Winter)
V. Baláž, Š. Boor, M. Gall, Ľ. Horanská, M. Jasem, A. Maťašovský, M. Nehéz, S. Pavlíková, P. Viceník, T. Visnyai (2018/2019 – Winter)
V. Baláž, Š. Boor, M. Gall, Ľ. Horanská, M. Jasem, N. Krivoňáková, A. Maťašovský, M. Nehéz, S. Pavlíková, M. Šabo, P. Viceník, T. Visnyai (2017/2018 – Winter)
V. Baláž, Š. Boor, M. Gall, Ľ. Horanská, K. Chudá, M. Jasem, N. Krivoňáková, A. Maťašovský, M. Nehéz, S. Pavlíková, M. Šabo, P. Viceník, T. Visnyai (2016/2017 – Winter)
V. Baláž, Ľ. Balko, M. Gall, I. Garaj, Ľ. Horanská, K. Chudá, M. Jasem, N. Krivoňáková, C. Krommerová, P. Letavaj, M. Nehéz, S. Pavlíková, J. Poljovka, M. Šabo, Z. Takáč, T. Visnyai, M. Žitňanská (2015/2016 – Winter)
Learning outcomes of the course unit:
Students have acquired basic knowledge of linear algebra, differential and integral calculus of real functions needed for their further study.
Prerequisites for registration:
none
Course contents:

The subject is divided into four main parts. The first one is devoted to selected topics in algebra. The second part deals with real functions of one variable. The third part is devoted to differential calculus of functions of one variable. The final part deals with integral calculus of functions of one variable.


I.

1. week: Notion of a vector, linear dependence and independence of vectors. Matrices. Properties of matrices. Operations with matrices.

2. week: Rank of a matrix. Systems of linear equations.

3. week: Determinants, definition and properties. Cramer's rule. Inverse of a matrix. Matrix equations.

4. week: Complex numbers. Polynomials and algebraic equations.

II.

5. week: Real fuctions. Properties of real functions. Composite and inverse functions. Exponential and logarithmic function. Cyclometric functions.

6. week: Sequences. Limit of a sequence. Limit and continuity of a function.

III.

7. week: Derivative of a function. Derivative of composite and inverse functions. Higher order derivatives. L' Hospital's rule. Differential.

8. week: Taylor polynomial. Properties of functions with a derivative. Asymptotes.

IV.

9. week: Indefinite integral, definition. Basic properties and formulas. Integration by substitution. Integration by parts.

10. week: Decomposition into partial fractions. Integration of rational and other functions.

11. week: Definite integral, definition and properties. Newton-Leibniz formula. The mean value theorem. Calculation methods.

12. week: Applications of definite integral. Planar area calculation.

13. week: Length of plane curves. Volume of rotating solids.

Recommended or required reading:
Basic:
  • ŠABO, M. Matematika 1. Bratislava: STU, 2009. 195 s.
  • JASEM, M. – HORANSKÁ, Ľ. Matematika I, Zbierka úloh. Bratislava : STU v Bratislave, 2009. 134 s. ISBN 978-80-227-3136-2.
Recommended:
  • Franklin Demana, Bert K. Waits, Stanley R. Clemens: College Algebra & Trigonometry: A Graphing Approach. Addison - Wesley Publishing Company, 1992. ISBN 0201562944.
  • Sherman K. Stein: Calculus and analytic geometry. McGraw-Hill Book company, 1987. ISBN 0-07-061159-9.
Planned learning activities and teaching methods:
Contact teaching: lectures 52h, exercises 52h, consultation 12h Contactless teaching: preparation for lectures 26h, preparation for exercises and elaboration of home assignments 83h
Assesment methods and criteria:
Evalution is based 20% on work during the semester, 80% on final exam. The rating is based on the standard FCHPT scale.
Language of instruction:
Slovak, English
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