CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2023/2024

# Calculus 1

Code Completion Credits Range Language
01MAN Z 4 4+4 Czech

The course 01MANA can be graded only after the course 01MAN has been successfully completed.

The course 01MANB can be graded only after the course 01MAN has been successfully completed.

In order to register for the course 01MANZ, the student must have successfully completed or received credit for and not exhausted all examination dates for the course 01MAN.

Garant předmětu:
Edita Pelantová, Pavel Strachota
Lecturer:
Miroslav Kolář, Edita Pelantová, Pavel Strachota
Tutor:
Monika Balázsová, Antonie Brožová, Maksym Dreval, Miroslav Kolář, Jakub Kořenek, Filip Moučka, Edita Pelantová, Severin Pošta, Pavel Strachota, Rudolf Šmolka
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 2023-12-09
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