### Mathematics Analysis

#### Mathematics Analysis - B6B01MAA

 Credits 5 Semesters Winter Completion Assessment + Examination Language of teaching undefined Extent of teaching 2P+2S+2D
Annotation
This course is an introduction to differential and integral calculus. It covers basic properties of functions, limits of functions, derivative and its applications (graphing, Taylor polynomial) and definite/indefinite integral with its applications, sequences and series.
Course outlines
1. Introduction to calculus.
2. Real numbers, basic mathematical terminology.
3. Functions, elementary functions.
4. Limit of a function, continuity.
5. Derivative, properties and interpretations.
6. L'Hospital's rule, the Taylor polynomial.
7. Extrema of functions. Graph sketching.
8. Indefinite integral (antiderivative), basic methods.
9. Integrating rational functions using partial fractions.
10. Definite integral, properties and evaluation.
11. Improper integral, applications of integral.
12. Sequences.
13. Series.
Exercises outlines
Practical classes follow lectures thematically. While on lectures, the focus is on understanding of notions and on justifications of validity of claims, in exercises students learn to solve routine problems.

1. Introduction to calculus.
2. Real numbers, basic mathematical terminology.
3. Functions, elementary functions.
4. Limit of a function, continuity.
5. Derivative, properties and interpretations.
6. L'Hospital's rule, the Taylor polynomial.
7. Extrema of functions. Graph sketching.
8. Indefinite integral (antiderivative), basic methods.
9. Integrating rational functions using partial fractions.
10. Definite integral, properties and evaluation.
11. Improper integral, applications of integral.
12. Sequences.
13. Series.
Literature
1. M. Demlová, J. Hamhalter: Calculus I. ČVUT Praha, 1994
2. P. Pták: Calculus II. ČVUT Praha, 1997.
3. Math Tutor http://math.feld.cvut.cz/mt
Requirements
High-school mathematics.