CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2023/2024

# Mathematics I

Code Completion Credits Range Language
2011056 Z,ZK 8 4P+4C Czech
Garant předmětu:
Gejza Dohnal
Lecturer:
Luděk Beneš, Tomáš Bodnár, Marta Čertíková, Gejza Dohnal, Lukáš Hájek, Jan Halama, Marta Hlavová, Jiří Holman, Vladimír Hric, Radka Keslerová, Petr Louda, Tomáš Neustupa, Nikola Pajerová, Vladimír Prokop, Jan Valášek
Tutor:
Luděk Beneš, Tomáš Bodnár, Jan Halama, Martin Hanek, Jan Karel, Milana Kittlerová, Matěj Klíma, Stanislav Kračmar, Olga Majlingová, Josef Musil, Tomáš Neustupa, Vladimír Prokop, Hynek Řezníček, Petr Sváček, David Trdlička
Supervisor:
Department of Technical Mathematics
Synopsis:

In the course, greater emphasis is placed on the theoretical basis of the concepts discussed and on the derivation of basic relationships and connections between concepts. Students will also get to know the procedures for solving problems with parametric input. In addition, students will gain extended knowledge in some thematic areas: eigennumbers and eigenvectors of a matrix, Taylor polynomial, integral as a limit function, integration of some special functions.

Requirements:

Knowledge of high school mathematics in the range of a real gymnasium.

Syllabus of lectures:

1. Basics of linear algebra – vectors, vector spaces, linear independence of vectors, dimensions, bases.

2. Matrix, operation, rank. Determinant. Regular and singular matrices, inverse matrices.

3. Systems of linear equations, Frobenian theorem, Gaussian elimination method.

4. Eigennumbers and eigenvectors of a matrix.

5. Differential calculus of real functions of one variable. Sequence, monotony, limit.

6. Limit and continuity of a function. Derivation, geometric and physical meaning.

7. Monotonicity of a function, local and absolute extrema, convexity, inflection point. Asymptotes, graph of the function.

8. Taylor polynomial, remainder after n-th power. Approximate solution of the equation f(x)=0.

9. Integral calculus of real functions of one variable – indefinite integral, integration by parts, integration by substitution.

10. Definite integral, its calculation.

11. Application of a definite integral: surface area, volume of a rotating body, length of a curve, application in mechanics.

12. Numerical calculation of the integral.

13. Improper integral.

Syllabus of tutorials:

The same as lectures.

Study Objective:

Gain an understanding of basic mathematical concepts and methods and be able to apply them in other engineering subjects.

Study materials:

Neustupa, J.: Mathematics I, CTU Publishing House, Prague, 1996,

Finney, R. L., Thomas, G.B.: Calculus, Addison-Wesley, New York, Ontario, Sydney, 1994

Note:
Further information:
https://mat.nipax.cz/mati
Time-table for winter semester 2023/2024:
 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 roomT4:D1-266Halama J.14:15–15:45(lecture parallel1)DejvicePosluchárna 266 roomT4:D1-266Halama J.09:00–10:30(lecture parallel1)DejvicePosluchárna 266 roomT4:C2-436Majlingová O.09:00–10:30(lecture parallel1parallel nr.101)DejvicePosluchárna 436 roomT4:C2-438Prokop V.09:00–10:30(lecture parallel1parallel nr.102)DejvicePosluchárna 438 roomT4:C2-436Majlingová O.10:45–12:15(lecture parallel1parallel nr.101)DejvicePosluchárna 436 roomT4:C2-438Prokop V.10:45–12:15(lecture parallel1parallel nr.102)DejvicePosluchárna 438
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 2024-07-19
Aktualizace výše uvedených informací naleznete na adrese https://bilakniha.cvut.cz/en/predmet10592702.html