CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2023/2024

# Calculus 1

Code Completion Credits Range Language
01MAN Z 4 4+4 Czech
Garant předmětu:
Severin Pošta
Lecturer:
Miroslav Kolář, Edita Pelantová, Severin Pošta
Tutor:
Monika Balázsová, Antonie Brožová, Petr Gális, Lukáš Heriban, Miroslav Kolář, Jakub Kořenek, Filip Moučka, Edita Pelantová, Severin Pošta, Radovan Zeman
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 2023/2024:
Time-table is not available yet
Time-table for summer semester 2023/2024:
Time-table is not available yet
The course is a part of the following study plans:
Data valid to 2023-08-30
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