| Course title | - |
|---|---|
| Course code | USE/AKMAT |
| Organizational form of instruction | Lesson |
| Level of course | Bachelor |
| Year of study | 1 |
| Semester | Winter |
| Number of ECTS credits | 1 |
| Language of instruction | Czech |
| Status of course | Optional |
| Form of instruction | Face-to-face |
| Work placements | This is not an internship |
| Recommended optional programme components | None |
| Lecturer(s) |
|---|
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| Course content |
|
Numerical sequences and series Numerical sequence and its limit, the sum of numbers. Convergence and divergence of sequences and series. Real functions of one variable Elementary functions (polynomial, rational angle, power, exponential, logarithmic, trigonometric, inverse trigonometric, hyperbolic, hyperbolometrické). Limit and continuity. Heine's theorem. Properties of continuous functions. Differential calculus of real functions of one real variable Derivative of a function, its geometrical and physical interpretation. Basic rules for differentiation, derivatives and differentials of higher order. Theorem on the growth function and its applications. Local and global extremes. Function inflection points, asymptotes graph, graph of a function. Application tasks to extremes functions. Integral calculus of real functions of one real variable Primitive functions, the calculation of the basic types of indefinite integrals (method of integration by parts and substitution methods). Definite Riemann integral, integral mean value. Geometric and physical applications of the definite integral (length of curve, volume and surface of revolution, center of gravity, momentum and inertia). Functional sequences and series Functional sequence, Taylor polynomial. Power series, differentiation and integration of power series. Taylor series, the development of elementary functions into Taylor series.
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| Learning activities and teaching methods |
| unspecified |
| Learning outcomes |
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Competence in the fundamentals of mathematics, students will be able to solve tasks and problems differential and integral calculus of functions of one variable and finally realizes connections with physical and technological applications. |
| Prerequisites |
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Knowledge and skills from the Mathematics preparatory course.
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| Assessment methods and criteria |
|
unspecified
A necessary condition for obtaining credit is at least 70% attendance at seminars. In addition, credit will be given only if the student succeeds in at least 70% of tests and assignments. |
| Recommended literature |
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| Study plans that include the course |
| Faculty | Study plan (Version) | Category of Branch/Specialization | Recommended semester | |
|---|---|---|---|---|
| Faculty: Faculty of Mechanical Engineering | Study plan (Version): Materials (17) | Category: Special and interdisciplinary fields | 1 | Recommended year of study:1, Recommended semester: Winter |