Summary of Study | Summary of Branches | All Subject Groups | All Subjects | List of Roles | Explanatory Notes               Instructions
 AD3B01MA1 Mathematics 1 Extent of teaching: 28+6 Guarantors: Roles: P,V Language ofteaching: CS Teachers: Completion: Z,ZK Responsible Department: 13101 Credits: 8 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-Leibnitz 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: