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CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2018/2019

Calculus 1

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Code Completion Credits Range Language
01MAN Z 4 4+4 Czech
Lecturer:
Severin Pošta (guarantor)
Tutor:
Severin Pošta (guarantor), Pavel Eichler, Petr Gális, Jakub Kořenek, Edita Pelantová, Hanka Řada, Tomáš Smejkal, Zuzana Szabová, Lukáš Ulrych, Jana Vacková, Aleš Wodecki
Supervisor:
Department of Mathematics
Synopsis:

Basic calculus (real analysis, functions of one real variable, differential calculus).

Requirements:

No prerequisities.

Syllabus of lectures:

1. Basics of mathematical logic, equations and inequalities, goniometric functions, exponential and logarithmic functions, sums and products, induction.

2. Sets and mappings.

3. Real and complex sequence - limit, basic properties, limits of special sequences, number „e“ and exponential function, some elementary functions.

4. Limit and continuity of functions of one real variable - basic properties.

5. Derivative of functions - basic properties.

6. Basic theorems of differential calculus. 7. Constructing graphs of functions.

Syllabus of tutorials:

1. Basic properties of functions and mappings.

2. Supremum, Infimum.

3. Limits of sequences.

4. Acculumation points.

5. Limits of real functions.

6. Continuity.

7. Derivative, graphs of real functions.

Study Objective:

The goal of this course is to manage basic techniques of computing limits of sequences, limits of real functions of one real variable and of differential calculus.

Study materials:

Recommended references:

[1] Apostol: Mathematical Analysis, Addison Wesley, 1974.

[2] W. Rudin: Principles of Mathematical Analysis. McGraw-Hill, Mexico, 1980.

Note:
Time-table for winter semester 2018/2019:
Time-table is not available yet
Time-table for summer semester 2018/2019:
Time-table is not available yet
The course is a part of the following study plans:
Data valid to 2019-08-23
For updated information see http://bilakniha.cvut.cz/en/predmet4087206.html