Mathematics Analysis
Code  Completion  Credits  Range 

B6B01MAA  Z,ZK  5  2P+2S+2D 
 The course cannot be taken simultaneously with:
 Mathematical Analysis 1 (B0B01MA1)
 Lecturer:
 Natalie Žukovec (guarantor)
 Tutor:
 Natalie Žukovec (guarantor)
 Supervisor:
 Department of Mathematics
 Synopsis:

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.
 Requirements:

Highschool mathematics.
 Syllabus of lectures:

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.
 Syllabus of tutorials:

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.
 Study Objective:
 Study materials:

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
 Note:
 Further information:
 https://moodle.fel.cvut.cz/courses/B6B01MAA
 Timetable for winter semester 2021/2022:

06:00–08:0008:00–10:0010:00–12:0012:00–14:0014:00–16:0016:00–18:0018:00–20:0020:00–22:0022:00–24:00
Mon Tue Wed Thu Fri  Timetable for summer semester 2021/2022:
 Timetable is not available yet
 The course is a part of the following study plans:

 Software Engineering and Technology (compulsory course in the program)
 Software Engineering and Technology (compulsory course in the program)
 Software Engineering and Technology (compulsory course in the program)
 Software Engineering and Technology (compulsory course in the program)
 Software Engineering and Technology (compulsory course in the program)
 Software Engineering and Technology (compulsory course in the program)