Calculus 1
| Code | Completion | Credits (ECTS) | Range | Language |
|---|---|---|---|---|
| 01MAN | Z | 4 | 4+4 | Czech |
- Relations:
- It is not possible to register for the course 01MAN if the student is concurrently registered for or has already completed the course 01MAT1 (mutually exclusive courses).
- In order to register for the course 01MAN2, the student must have successfully completed or received credit for and not exhausted all examination dates for the course 01MAN.
- It is not possible to register for the course 01MAN if the student is concurrently registered for or has previously completed the course 01MAT1 (mutually exclusive courses).
- The course 01MANZ can be graded only after the course 01MAN has been successfully completed.
- Course guarantor:
- Pavel Strachota
- Lecturer:
- Pavel Strachota
- Tutor:
- Adam Blažek, Maksym Dreval, Jakub Kořenek, Mikuláš Kučera, Filip Moučka, Severin Pošta, Pavel Strachota, Jakub Waclawek, Filip Záhon Persidský
- Supervisor:
- Department of Mathematics
- Synopsis:
-
Basic calculus (real analysis, functions of one real variable, differential calculus).
- Requirements:
-
No prerequisites.
- 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. The set of real numbers, axiom of completeness, supremum and infimum.
4. Real and complex sequence - limit, basic properties, limits of special sequences, number „e“ and exponential function, some elementary functions.
5. Construction of real powers and logarithms.
6. Limit and continuity of functions of one real variable - basic properties.
7. Derivatives of functions - basic properties.
8. Fundamental theorems of differential calculus
9. Graph of a function and its construction - monotonicity, local extrema, convexity and concaveness, asymptotes.
- 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 2025/2026:
- Time-table is not available yet
- Time-table for summer semester 2025/2026:
- Time-table is not available yet
- The course is a part of the following study plans:
-
- Fyzikální inženýrství - Počítačová fyzika (PS)
- Aplikovaná algebra a analýza (compulsory course in the program)
- Aplikace informatiky v přírodních vědách (compulsory course in the program)
- Aplikované matematicko-stochastické metody (compulsory course in the program)
- Jaderné inženýrství - Aplikovaná fyzika ionizujícího záření (PS)
- Fyzikální inženýrství - Fyzikální inženýrství materiálů (PS)
- Fyzikální inženýrství - Fyzika plazmatu a termojaderné fúze (PS)
- Fyzikální inženýrství - Inženýrství pevných látek (PS)
- Jaderná a částicová fyzika (compulsory course in the program)
- Jaderné inženýrství - Jaderné reaktory (PS)
- Fyzikální inženýrství - Laserová technika a fotonika (PS)
- Matematické inženýrství - Matematická fyzika (PS)
- Matematické inženýrství - Matematická informatika (PS)
- Matematické inženýrství - Matematické modelování (PS)
- Kvantové technologie (compulsory course in the program)
- jaderné inženýrství - Radioaktivita v životním prostředí (PS)
- Vyřazování jaderných zařízení z provozu (compulsory course in the program)
- Physical Engineering - Physical Engineering od Materials (PS)