Subject description - A8B01MC1

Summary of Study | Summary of Branches | All Subject Groups | All Subjects | List of Roles | Explanatory Notes               Instructions
A8B01MC1 Mathematics-Calculus1 Extent of teaching:4+2
Guarantors:Tkadlec J. Roles:P Language of
teaching:
CS
Teachers:Tkadlec J. Completion:Z,ZK
Responsible Department:13101 Credits:7 Semester:Z

Anotation:

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

Course outlines:

1. Elementary functions. Limit and continuity of functions.
2. Derivative of functions, its properties and applications.
3. Mean value theorem. L'Hospital's rule.
4. Limit of sequences. 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. Numerical evaluation of definite integral. Application to calculation of areas, volumes and lengths.
10. Improper integral.
11. Differential equations - formulation of the problem. Separation of variables.
12. First order linear differential equations (variation of parameter).
13. Applications. Numerical aspects.
14. Reserve.

Exercises outline:

1. Elementary functions. Limit and continuity of functions.
2. Derivative of functions, its properties and applications.
3. Mean value theorem. L'Hospital's rule.
4. Limit of sequences. 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. Numerical evaluation of definite integral. Application to calculation of areas, volumes and lengths.
10. Improper integral.
11. Differential equations - formulation of the problem. Separation of variables.
12. First order linear differential equations (variation of parameter).
13. Applications. Numerical aspects.
14. Reserve.

Literature:

1. M. Demlová, J. Hamhalter: Calculus I. ČVUT Praha, 1994
2. P. Pták: Calculus II. ČVUT Praha, 1997.

Requirements:

See http://math.feld.cvut.cz/0educ/pozad/b0b01ma1.htm

Webpage:

http://math.feld.cvut.cz/0educ/pozad/b0b01ma1.htm

Keywords:

limits, derivatives, integrals, series

Subject is included into these academic programs:

Program Branch Role Recommended semester
BPOES Common courses P 1


Page updated 13.5.2019 17:52:55, semester: Z,L/2020-1, L/2019-20, Z,L/2018-9, Z/2019-20, Send comments about the content to the Administrators of the Academic Programs Proposal and Realization: I. Halaška (K336), J. Novák (K336)