Mathematics Analyze
Code  Completion  Credits  Range 

BD6B01MAA  Z,ZK  5  14KP+6KC 
 Lecturer:
 Natalie Žukovec
 Tutor:
 Natalie Žukovec
 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:
 http://math.feld.cvut.cz/0educ/pozad/bd6b01maa.htm
 No timetable has been prepared for this course
 The course is a part of the following study plans:

 Software Engineering and Technology (compulsory course in the program)