Matematika I a II @ FS ČVUT - mathematics

mathematics_i

anonymous@undisclosed.example.com (Anonymous) — 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

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.

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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mathematics_ii

anonymous@undisclosed.example.com (Anonymous) — Tue, 14 Apr 2026 11:47:54 +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

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

Examples:

The Collection of examples from Mathematics II written in Czech by authors E. Brožíková, M. Kittlerová and F. Mráz (2016) contains both examples and their solutions. Here you find several parts translated in English. The examples in English have the same numbering but they are without solutions (corresponding solution you can find in the Czech version, which is in the brackets). English translations will be added gradually. By the star (*) are denoted the examples, which go beyond the requirements of the exam this year.

Surface integral [Skalární] [Vektorový]
Divergence theorem [Gaussova-Ostrogradského věta]

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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