MATHEMATICS I - LECTURES
doc. RNDr. Daniela Velichová, CSc.
1. Lecture - Introduction to linear algebra - Matrices
2. Lecture - Systems of linear equations I
3. Lecture - Systems of linear equations II
4. Lecture - Determinants
5. Lecture - Number sequences, limit of a sequence
6. Lecture - Number series, convergence and sum
7. Lecture - Real function of real variable
8. Lecture - Elementary functions
9. Lecture - Limit of a function
10. Lecture - Continuity of a function, asymptotes to the graph
11. Lecture - Derivative of a function, rules for derivation
12. Lecture - Derivatives of elementary functions
13. Lecture - Derivatives of higher orders, Taylor polynomial, L´Hospital rule
14. Lecture - Basic theorems of differentiable calculus
15. Lecture - Monotonicity of a function, function extrema
16. Lecture - Convexity and concavity, point of inflexion, investigation of function behaviour
17. Lecture - Antiderivatives, Indefinite integrals, Methods of integration
18. Lecture - Integration fo special functions
19. Lecture - Definite integrals, Newton-Leibniz formula
20. Lecture - Methods of calculation of definite integrals
21. Lecture - Geometric and physical applications of definite integrals
22. Lecture - Improper integrals