# Subject description - B0B01MA1

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B0B01MA1 Mathematical Analysis 1
Roles:P Extent of teaching:4P+2S
Department:13101 Language of teaching:CS
Tutors:Dvořák J., Křepela M., Pospíšil K., Sobotíková V., Tkadlec J. Semester:Z,L

Anotation:

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

Study targets:

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

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 Rows, criteria of convergence. 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 Rows, criteria of convergence. 12 Introduction to differential equations. 13 Other topics of mathematical analysis.

Literature:

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

Requirements:

Webpage: