Mathematics I.
| Code | Completion | Credits | Range | Language |
|---|---|---|---|---|
| 2011091 | Z,ZK | 7 | 4P+4C+0L | Czech |
- Course guarantor:
- Gejza Dohnal
- Lecturer:
- Luděk Beneš, Tomáš Bodnár, Marta Čertíková, Gejza Dohnal, Lukáš Hájek, Jan Halama, Marta Hlavová, Jiří Holman, Vladimír Hric, Jan Karel, Radka Keslerová, Milana Kittlerová, Matěj Klíma, Petr Louda, Olga Majlingová, Josef Musil, Tomáš Neustupa, Nikola Pajerová, Vladimír Prokop, Hynek Řezníček, David Trdlička, Jan Valášek
- Tutor:
- Luděk Beneš, Tomáš Bodnár, Marta Čertíková, Gejza Dohnal, Lukáš Hájek, Jan Halama, Martin Hanek, Marta Hlavová, Jiří Holman, Vladimír Hric, Jan Karel, Radka Keslerová, Milana Kittlerová, Matěj Klíma, Petr Louda, Olga Majlingová, Josef Musil, Tomáš Neustupa, Nikola Pajerová, Vladimír Prokop, Hynek Řezníček, Petr Sváček, David Trdlička, Jan Valášek
- 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 in 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 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 Tue Wed Thu Fri - Time-table for summer semester 2024/2025:
- Time-table is not available yet
- The course is a part of the following study plans: