Subject description - B0B01MA1A

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B0B01MA1A Mathematical Analysis 1 Extent of teaching:4+2
Guarantors:Sobotíková V. Roles:P Language of
teaching:
CS
Teachers:Sobotíková V. Completion:Z,ZK
Responsible Department:13101 Credits:6 Semester:Z,L

Anotation:

This is an introductory course to differential and integral calculus of functions of one real variable.

Study targets:

The aim of the course is to introduce students to basics of differential and integral calculus of functions of one variable.

Content:

Real numbers. Properties of functions. Elementary functions. Limit and continuity of functions. Derivative of functions, its properties and applications. Indefinite integral. Riemann integral. Improper integral. Application of integrals. Series and convergence tests. Introduction to linear differential equations.

Course outlines:

1. Real numbers. Elementary functions.
2. Limit and continuity of functions.
3. Derivative of functions, its properties and applications.
4. Mean value theorem. L'Hospital's rule, Taylor polynomial.
5. Local and global extrema and graphing functions.
6. Indefinite integral, basic integration methods.
7. Integration of rational and other types of functions.
8. Definite integral (using sums). Newton-Leibniz formula.
9. Improper integral. Application of integrals.
10. Sequences and their limits.
11. Series, convergence tests.
12. Introduction to differential equations.
13. Other topics of mathematical analysis.

Exercises outline:

1. Real numbers. Elementary functions.
2. Limit and continuity of functions.
3. Derivative of functions, its properties and applications.
4. Mean value theorem. L'Hospital's rule, Taylor polynomial.
5. Local and global extrema and graphing functions.
6. Indefinite integral, basic integration methods.
7. Integration of rational and other types of functions.
8. Definite integral (using sums). Newton-Leibniz formula.
9. Improper integral. Application of integrals.
10. Sequences and their limits.
11. Series, convergence tests.
12. Introduction to differential equations.
13. Other topics of mathematical analysis.

Literature:

[1] J. Stewart, Single variable calculus, Seventh Edition, Brooks/Cole, 2012, ISBN 0538497831.

Requirements:

For information, see http://math.feld.cvut.cz/0educ/pozad/b0b01ma1a.htm (in Czech).

Webpage:

http://math.feld.cvut.cz/veronika/vyuka/ma1A-ma1.htm

Keywords:

limit, continuity, derivative, primitive function, Riemann integral, improper integral, numerical series

Subject is included into these academic programs:

Program Branch Role Recommended semester
BPEK_2018 Common courses P 1
BPBIO_2018 Common courses P 1
BPEEM2_2018 Electrical Engineering and Management P 1
BPEEM1_2018 Applied Electrical Engineering P 1
BPEEM_BO_2018 Common courses P 1


Page updated 14.6.2019 17:52:56, semester: Z,L/2020-1, L/2018-9, 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)