# Subject description - B6B01MAA

Summary of Study | Summary of Branches | All Subject Groups | All Subjects | List of Roles | Explanatory Notes               Instructions
B6B01MAA Mathematics Analyze
Roles:P Extent of teaching:2P+2S+2D
Department:13101 Language of teaching:
Guarantors:Habala P., Žukovec N. Completion:Z,ZK
Lecturers:Žukovec N. Credits:5
Tutors:Žukovec N. 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.

Course outlines:

 1 Introduction to calculus. 2 Real numbers, basic mathematical terminology. 3 Functions, elementary functions. 4 Limit of a function, continuity. 5 Derivative, properties and interpretations. 6 L'Hospital's rule, the Taylor polynomial. 7 Extrema of functions. Graph sketching. 8 Indefinite integral (antiderivative), basic methods. 9 Integrating rational functions using partial fractions. 10 Definite integral, properties and evaluation. 11 Improper integral, applications of integral. 12 Sequences. 13 Series.

Exercises outline:

Practical classes follow lectures thematically. While on lectures, the focus is on understanding of notions and on justifications of validity of claims, in exercises students learn to solve routine problems.
 1 Introduction to calculus. 2 Real numbers, basic mathematical terminology. 3 Functions, elementary functions. 4 Limit of a function, continuity. 5 Derivative, properties and interpretations. 6 L'Hospital's rule, the Taylor polynomial. 7 Extrema of functions. Graph sketching. 8 Indefinite integral (antiderivative), basic methods. 9 Integrating rational functions using partial fractions. 10 Definite integral, properties and evaluation. 11 Improper integral, applications of integral. 12 Sequences. 13 Series.

Literature:

 1 M. Demlová, J. Hamhalter: Calculus I. ČVUT Praha, 1994 2 P. Pták: Calculus II. ČVUT Praha, 1997. 3 Math Tutor http://math.feld.cvut.cz/mt

Requirements:

High-school mathematics.

Webpage: