# Subject description - A7B01MAA

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 A7B01MAA Mathematics Analyze Extent of teaching: 4+2 Guarantors: Roles: P Language ofteaching: CS Teachers: Completion: Z,ZK Responsible Department: 13101 Credits: 8 Semester: Z

Anotation:

This course is an introduction to differential and integral calculus. It covers basic properties of functions, limits of functions, derivative and its applications (graphing, Taylor polynomial) and definite/indefinite integral with its applications, sequences and series. At the end we also introduce calculus of more variables.

Course outlines:

 1 Functions, elementary functions. 2 Limit of functions, continuity. 3 Derivative, its interpretations and applications. 4 L'Hospital's rule, Taylor polynomial. 5 Extrema of functions. Graphing functions. 6 Antiderivative, basic methods of evaluation. 7 Integrating rational functions using partial fractions. 8 Definite integral, properties and evaluation. 9 Improper integral, applications of integrals. 10 Sequences. 11 Series. 12 Introduction to functions of more variables. 13 Functions of more variables, applications of calculus. 14 Back-up class.

Exercises outline:

 1 Functions. 2 Limit (elementary methods). 3 Limits, continuity. 4 Derivative. 5 Limits using l'Hospital's rule, Taylor polynomial. 6 Graphing functions, extrema. 7 Indefinite integral. 8 Indefinite integral - partial fractions. 9 Definite integral. 10 Improper integral. 11 Applications of derivative and integral. 12 Sequences, series. 13 Functions of more variables. 14 Back-up.

Literature:

 1 Math Tutor http://math.feld.cvut.cz/mt 2 J. Tkadlec: Diferenciální a integrální počet funkcí jedné proměnné. ČVUT Praha 2004. 3 Web page of P. Habala
http://math.feld.cvut.cz/habala/

Requirements: