| Course title | Calculus III for Combined Studies |
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| Course code | UMB/566K |
| Organizational form of instruction | Lecture + Lesson |
| Level of course | unspecified |
| Year of study | not specified |
| Frequency of the course | In each academic year, in the winter semester. |
| Semester | Winter |
| Number of ECTS credits | 8 |
| Language of instruction | Czech |
| Status of course | unspecified |
| 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 |
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Content of lectures: 1. Infinite Series, convergence/divergence, absolute convergence of series. 2. Criteria for convergence of series - ratio test, root test. 3. Sequences and series functions - fundamental notions. 4. Criteria for convergence of series, uniform convergence. 5. Power series (Power series and functions, Maclaurin and Taylor series, Applications of series, Binomial series) 6. Fourier series. 7. Vector functions of multiple variables (continuity, limits, derivatives, gradient, total differential, Jacobian matrix) 8. Vector functions (parametric equations of curves, calculus with vector functions, arc length, tangent and normal vectors, velocity and acceleration, curvature) 9. Multiple integrals (double and triple integrals, Fubini's theorem, integrals in polar, cylindrical and spherical coordinates, change of variables, area and volume). 10. Curve integrals of 1st and 2nd type (in a scalar and in a vector fields).
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| Learning activities and teaching methods |
Monologic (reading, lecture, briefing), Individual preparation for exam
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| Learning outcomes |
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To develop differential and integral calculus of functions of several variables.
We will work with sequences and series of numbers and functions. We learn how to decide about their convergence. We will expand functions into Taylor and Fourier series and show their connection to the original functions frow which the series were derived. We show how to calculate double and curve integrals. |
| Prerequisites |
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We assume knowledge of differentail calculus of one and more variables and of integral calculus of one real variable (e.g. UMB/010K a UMB/565K).
UMB/CV565 ----- or ----- UMB/565 ----- or ----- UMB/565K |
| Assessment methods and criteria |
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Written examination
Simple written homeworks. Written exam. To pass the exam it is necessary to reach at least 50% points. |
| Recommended literature |
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| Study plans that include the course |
| Faculty | Study plan (Version) | Category of Branch/Specialization | Recommended semester |
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