Subject description - B6B01MAA

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B6B01MAA Mathematics Analyze
Roles:P Extent of teaching:2P+2S+2D
Department:13101 Language of teaching:
Guarantors:Habala P., Žukovec N. Completion:Z,ZK
Lecturers:Žukovec N. Credits:5
Tutors:Žukovec N. Semester:Z

Anotation:

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 outline:

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.

Webpage:

http://math.feld.cvut.cz/0educ/pozad/b6b01maa.htm

Subject is included into these academic programs:

Program Branch Role Recommended semester
BPSIT Common courses P 3


Page updated 25.5.2020 05:52:04, semester: Z,L/2020-1, Z,L/2019-20, Send comments about the content to the Administrators of the Academic Programs Proposal and Realization: I. Halaška (K336), J. Novák (K336)