# Subject description - A8B01MC1

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A8B01MC1 Mathematics-Calculus1
Roles:P Extent of teaching:4P+2S
Department:13101 Language of teaching:CS

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:

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