Matematika I a II @ FS ČVUT

mathematics_ii

bodnart@undisclosed.example.com (Tomáš Bodnár) — Tue, 12 May 2026 19:49:58 +0000

Mathematics II

This course is intended for foreign students studying at our faculty and domestic students who registered for this subject in their study plan. Conditions and requirements for this course are almost identical to the equivalent course being held in Czech language.

Content:

Functions of several variables - domain, limit, continuity, partial derivatives, extrema, implicit function. Multiple integrals - double and triple integral, Fubini's theorem, applications Line integral, surface integral, Gauss theorem, potential.

Schedule of Lectures in academic year 2025/2026
Schedule of Tutorials in academic year 2025/2026

Lecturers

doc. Mgr. Ing. Tomáš Bodnár, Ph.D., Office: KN:D-303

lectures: Monday 12:30-14:00 and Wednesday 14:15 - 15:45.
tutorials: Thursday 10:45 - 12:15 and Friday 10:45 - 12:15.
seminar: Wednesday 17:00-19:00 Room: KN:D-105

Ing. Anna Lancmanová, Office: KN:D-305a

tutorials: Thursday 9:00 - 10:30 and Friday 9:00 - 10:30.

In the case of any problem (especially with assessments from tutorials, or with exams) contact your teacher.

Tutorials, assessments

Tutorials are obligatory. Assessment from tutorials (written in the study record) confirms student's presence and activity at the tutorials and elaboration of homework and tests. During the semester only 4 absences are allowed (without additional homework), or 6 with additional homework. Higher number of absences in tutorials will automatically lead to the assessment not being awarded. Assessment is a necessary condition for the exam. (i.e. student can make the exam only with the assessment written in the study record.) The assessments are written in the last semestral week, not later than one week after. Exceptions are possible only with the explicit agreement of the chair of the institute.

Exams

The exams from Mathematics II will be organized in the same way as in Mathematics I. There are several necessary conditions to be fulfilled by students in order to be admitted to the exam:

Student must have a valid assessment from tutorials registered in the electronic system KOS. (students without valid assessment can't subscribe for the exam)
Student has to subscribe (register) in the KOS system for the chosen date and level of the exam. (students who will be not subscribed for the exam in the KOS system can't participate in the exam)
Student should come to the exam in time, i.e. he/she should be present in the examination room at least 10 minutes before the official start of the exam. (students who will come late, will be not allowed to participate in the exam)
Student has to bring his/her Student Identification Card. (students will be not allowed to participate in the exam without presenting this card)
The use of smartphones, smart-watch or any other kind of communication devices during the exam is strictly prohibited.
It is advised to bring a watch (non-smart, showing just the time) allowing to follow the time remaining for completing the written test.

These conditions will be followed strictly, without any exceptions.

Dates of exams: Monday 25.5., 1.6., 8.6., 15.6., 22.6., 2026, and Thursday 28.5., 4.6., 11.6., 18.6., 25.6. and 10.9. 2026

The detailed information is available in the Notice of exams from Mathematics II for the academic year 2025/26.

Sample exam tests: Exam 1, Exam 2, Exam 3

Literature:

Neustupa, J., Kračmar S.: Mathematics II, CTU Publishing House, Prague, 1996,
Textbook scan (English, old version), Textbook (Czech, new version)
NEW Textbook (English, experimental version)
NEW Exercises (English, experimental version)
Finney, R. L., Thomas, G.B.: Calculus, Addison-Wesley, New York, Ontario, Sydney, 1994

Web additional sources:

Keisler, H. J.: Elementary Calculus: An Infinitesimal Approach, 2nd edition, Prindle, Weber & Schmidt, 1986.
Calculus Volume I., Volume II., Volume III., provided by https://cnx.org/.

Timetable:

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ma2_en_exercises.pdf

bodnart@undisclosed.example.com (Tomáš Bodnár) — Tue, 12 May 2026 19:40:07 +0000

ma2_en_textbook.pdf

bodnart@undisclosed.example.com (Tomáš Bodnár) — Tue, 12 May 2026 19:39:50 +0000

mii_2026_vyhlaska2.pdf

bodnart@undisclosed.example.com (Tomáš Bodnár) — Wed, 22 Apr 2026 12:04:05 +0000

ma2_2026_schedule_tutorials.pdf

bodnart@undisclosed.example.com (Tomáš Bodnár) — Wed, 22 Apr 2026 09:49:51 +0000

infozk_matii

bodnart@undisclosed.example.com (Tomáš Bodnár) — Wed, 22 Apr 2026 09:42:10 +0000

Co je třeba znát z Matematiky II?

Vyhláška o zkouškách z Matematiky II v akademickém roce 2025/2026

Ukázka zkouškových testů Alfa(2019) Beta(2019) (23.3.2019)

Poznámka: Alfa a Beta vyjadřuje stupeň obtížnosti (Alfa = standardní, Beta = snížená). Od akademického roku 2023/2024 bylo toto členění zrušeno a používá se pouze standardní obtížnost.

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tutorial_april_16-17.pdf - vytvořeno

bodnart@undisclosed.example.com (Tomáš Bodnár) — Sun, 19 Apr 2026 07:02:26 +0000

ma2_2026_exams.pdf - vytvořeno

bodnart@undisclosed.example.com (Tomáš Bodnár) — Tue, 14 Apr 2026 11:43:20 +0000

ma2_2026_schedule_lectures.pdf

bodnart@undisclosed.example.com (Tomáš Bodnár) — Tue, 31 Mar 2026 10:09:11 +0000

matii

bodnart@undisclosed.example.com (Tomáš Bodnár) — Fri, 13 Feb 2026 18:56:34 +0000

Matematika II

Základní informace k předmětu

Týdenní plány přednášek

Týdenní plány cvičení a seminářů

Doporučená literatura

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mathematics_i

bodnart@undisclosed.example.com (Tomáš Bodnár) — Fri, 13 Feb 2026 14:54:15 +0000

Mathematics I

This course is intended for foreign students studying at our faculty and domestic students who registered it.

Content of the course:

Introduction to linear algebra - vectors, vector spaces, matrices, determinants, systems of linear equations. Analytic geometry in E_3 - straight lines and planes. Calculus of functions of single variable - limit, continuity, derivative, extrema, behaviour of a function, indefinite integral, methods of integration, definite integral.

Plan of lectures in academic year 2025/26

Lecturers

doc. Mgr. Ing. Tomáš Bodnár, Ph.D., Office: KN:D-303

lectures: Monday, 12:30 - 14:00 and Wednesday, 14:15 - 15:45.

Mgr. Hynek Řezníček, Office: KN:D-205b

tutorials: Tuesday, 9:00 - 10:30 and Friday 12:30 - 14:00.

Ing. Anna Lancmanová, Office: KN:D-305a

tutorials: Tuesday, 10:45 - 12:15 and Friday 9:00 - 10:30.

In the case of any problem (especially with assessments from tutorials, or with exams) contact your teacher.

Tutorials, assessments

Preliminary plan of tutorials in academic year 2025/26
Hynek Řezníček - Tutorial information

Exams

There are several necessary conditions to be fulfilled by students in order to be admitted to the exam:

Student must have a valid assessment from tutorials registered in the electronic system KOS. (students without valid assessment can't subscribe for the exam)
Student has to subscribe (register) in the KOS system for the chosen date and level of the exam. (students who will be not subscribed for the exam in the KOS system can't participate in the exam)
Student should come to the exam in time, i.e. he/she should be present in the examination room at least 10 minutes before the official start of the exam. (students who will come late, will be not allowed to participate in the exam)
Student has to bring his/her Student Identification Card. (students will be not allowed to participate in the exam without presenting this card)
The use of smartphones, smart-watch or any other kind of communication devices during the exam is strictly prohibited.
It is advised to bring a watch (non-smart, showing just the time) allowing to follow the time remaining for completing the written test.

These conditions will be followed strictly, without any exceptions.

Dates of exams: January 5, 8, 12, 15, 19, 22, 26, 29 and February 2, 5, 9, 12, 2026.

NEW: Following the direct request of the Vice-Dean for Education doc. Ing. Jan Skočilas, Ph.D., an additional examination term from Mathematics I was open for Thursday, February 19, 2026 (13:00-15:00, room KN:D-104).

The detailed information is available in the Notice of exams from Mathematics I for the academic year 2025/26.

Sample exam tests: Exam 1, Exam 2, Exam 3, Exam 4, Exam 5

Some notes & Common mistakes: Notes & Mistakes

Literature:

Neustupa, J.: Mathematics I, CTU Publishing House, Prague, 1996
Neustupa, J.: Mathematics I, updated electronic version Part I, Part II, Part III-old version
Neustupa, J. and Kračmar, S.: Problems in Mathematics I, CTU Publishing House, Prague, 1999
Selected problems from the textbook Problems in Mathematics I
Selected problems from the exam tests in previous years
Recommended Czech materials Základní literatura:
Keisler, H. J.: Elementary Calculus: An Infinitesimal Approach, 2nd edition, Prindle, Weber & Schmidt, 1986.
Calculus Volume I., Volume II., Volume III., provided by https://cnx.org/.
College algebra, provided by https://cnx.org/

Timetable:

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literatura_m2

dohnal@undisclosed.example.com (Gejza Dohnal) — Mon, 12 Jan 2026 17:00:08 +0000

Základní literatura:

[1] J. Neustupa: Matematika II. Skriptum Strojní fakulty. Vydavatelství ČVUT, Praha 2015 (Základní skriptum k předmětu Matematika II) Elektronická verze v pdf je ke stažení zde.

[2] Sbírka příkladů z Matematiky II (v elektronické podobě)

[3] Ukázka zkouškových testů Alfa(2019) Beta(2019) (23.3.2019)

[4] J. Neustupa: Matematika I. Skriptum Strojní fakulty. Vydavatelství ČVUT, Praha 2015

Další doporučená literatura:

Číslovaný seznam

[5] E. Brožíková, M. Kittlerová: Sbírka příkladů z Matematiky II. Skriptum Strojní fakulty (vyprodáno). Vydavatelství ČVUT, Praha 2003, dotisk 2007. (Sbírka řešených i neřešených příkladů.) zde v elektronické podobě

[6] K. Rektorys a spol.: Přehled užité matematiky I, II.

[7] M. Čertíková: Řešené příkady a poznámky ke cvičením

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