Calculus 1

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).

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:

Edita Pelantová, Pavel Strachota

Lecturer:

Miroslav Kolář, Edita Pelantová, Pavel Strachota

Tutor:

Maksym Dreval, Tomáš Hrdina, Miroslav Kolář, Filip Konopka, Jakub Kořenek, Filip Moučka, Edita Pelantová, Severin Pošta, Pavel Strachota

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 2024/2025:

	06:00–08:0008:00–10:0010:00–12:0012:00–14:0014:00–16:0016:00–18:0018:00–20:0020:00–22:0022:00–24:00
Mon	roomBR:103 Strachota P. 10:00–11:50 (lecture parallel1) Břehová 7 roomTR:209 Kořenek J. 12:00–13:50 (parallel nr.104) Trojanova 13 roomTR:208 Moučka F. 12:00–13:50 (parallel nr.107) Trojanova 13 roomTR:210 Pelantová E. 12:00–13:50 (parallel nr.108) Trojanova 13 roomTR:112 Kolář M. 12:00–13:50 (lecture parallel2) Trojanova 13
Tue	roomTR:208 08:00–09:50 (parallel nr.201) Trojanova 13 roomBR:115 Dreval M. 12:00–13:50 (parallel nr.103) Břehová 7 roomBR:10 Dreval M. 14:00–15:50 (parallel nr.106) Břehová 7
Wed	roomTR:212 Kořenek J. 10:00–11:50 (parallel nr.104) Trojanova 13 roomTR:209 Konopka F. 12:00–13:50 (parallel nr.101) Trojanova 13 roomTR:209 Dreval M. 14:00–15:50 (parallel nr.103) Trojanova 13 roomTR:207 Hrdina T. 12:00–13:50 (parallel nr.102) Trojanova 13 roomTR:201 Dreval M. 12:00–13:50 (parallel nr.105) Trojanova 13
Thu	roomBR:103 Strachota P. 12:00–13:50 (lecture parallel1) Břehová 7 roomTR:112 Kolář M. 14:00–15:50 (lecture parallel2) Trojanova 13
Fri	roomBR:11 Hrdina T. 08:00–09:50 (parallel nr.102) Břehová 7 roomTR:207 Konopka F. 10:00–11:50 (parallel nr.101) Trojanova 13 roomTR:209 Dreval M. 12:00–13:50 (parallel nr.105) Trojanova 13 roomTR:208 Dreval M. 10:00–11:50 (parallel nr.106) Trojanova 13 roomTR:208 12:00–13:50 (parallel nr.201) Trojanova 13 roomTR:204 Moučka F. 10:00–11:50 (parallel nr.107) Trojanova 13 roomTR:210 Pelantová E. 10:00–11:50 (parallel nr.108) Trojanova 13

Time-table for summer semester 2024/2025:

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 - Computational physics (PS)
• Quantum Technologies (compulsory course in the program)
• Nuclear and Particle Physics (compulsory course in the program)
• Physical Engineering - Physical Engineering od Materials (PS)
• Mathematical Engineering - Mathematical Physics (PS)
• Physical Engineering - Plasma Physics and Thermonuclear Fusion (PS)