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CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2019/2020

Calculus

The course is not on the list Without time-table
Code Completion Credits Range Language
AE4B01MA2 Z,ZK 8 4+2
Prerequisite:
Linear Algebra (AE0B01LAG)
Lecturer:
Tutor:
Supervisor:
Department of Mathematics
Synopsis:

This is an introductory course to calculus. In the first part we study limits, continuity and derivative of real functions of one variable. Then we define the indefinite integral, discuss basic integration methods, the definite integral and its applications. We extend the discussion to real functions of more variables, partial derivatives and multiple integrals. We conclude with the study of real numerical series.

Requirements:

In order to obtain the certificate of attendance, students are required to actively participate in the laboratory class, hand in the assigned homework and obtain a sufficient score during lab tests. Only students who obtain attendance certificate („zapocet“) are allowed to take the exam.

Syllabus of lectures:

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. Newton-Leibniz formula.

9.Improper integral.Applications of integrals.

10.Sequences, introduction to series.

11.Functions of two or more variables. Partial derivatives.

12.Maximum and minimum for functions of two variables.

13.Duble integrals.

Syllabus of tutorials:

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. Newton-Leibniz formula.

9.Improper integral.Applications of integrals.

10.Sequences, introduction to series.

11.Functions of two or more variables. Partial derivatives.

12.Maximum and minimum for functions of two variables.

13.Duble integrals.

Study Objective:
Study materials:
Note:
Further information:
http://math.feld.cvut.cz/vivi/
No time-table has been prepared for this course
The course is a part of the following study plans:
Data valid to 2019-10-14
For updated information see http://bilakniha.cvut.cz/en/predmet12819004.html