| Course title | Mathematical Analysis 1 |
|---|---|
| Course code | KMA/MAF1 |
| Organizational form of instruction | Lecture + Exercise |
| Level of course | Bachelor |
| Year of study | 1 |
| Semester | Winter |
| Number of ECTS credits | 7 |
| Language of instruction | Czech |
| Status of course | Compulsory |
| 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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1. Introduction: On the structure of mathematics, sets, basic logic. 2. Sequences: The notion of limits, theorems on limits, boundedness and convergence. 3. Functions: The notion of functions, continuity, properties of continuous functions, limits, limits of composite functions, elementary functions. 4. Differentiation: Relation to limits and continuity, the differential of a function, mean value theorems, Taylor's polynomials, L'Hospital's rule. 5. Integration: Motivation, Newton's formula and the relation to differentiation, primitive functions, integration by parts, integration by substitution, integration of rational functions, more on integration techniques, the Riemann integral and the proof of Newton's formula. 6. Applications: Length, surface, volume, center of gravity, moment of inertia, numerical methods.
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| Learning activities and teaching methods |
Lecture, Dialogic Lecture (Discussion, Dialog, Brainstorming)
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| Learning outcomes |
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Understand differential calculus of functions of a single real variable
Comprehension Understand the mathematical tools of differential and integral calculus of functions of a single variable. |
| Prerequisites |
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Grammar school mathematics
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| Assessment methods and criteria |
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Oral exam, Written exam
Credit: active participation, the student has to pass two written tests (i.e. to obtain at least half of the possible points in each test). |
| 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 Science | Study plan (Version): Optics and Optoelectronics (2019) | Category: Physics courses | 1 | Recommended year of study:1, Recommended semester: Winter |
| Faculty: Faculty of Science | Study plan (Version): Biophysics - Specialization in General Biophysics (2024) | Category: Physics courses | 1 | Recommended year of study:1, Recommended semester: Winter |
| Faculty: Faculty of Science | Study plan (Version): Biophysics - Specialization in Molecular Biophysics (2024) | Category: Physics courses | 1 | Recommended year of study:1, Recommended semester: Winter |
| Faculty: Faculty of Science | Study plan (Version): Instrument and Computer Physics (2019) | Category: Physics courses | 1 | Recommended year of study:1, Recommended semester: Winter |
| Faculty: Faculty of Science | Study plan (Version): Applied Physics (2019) | Category: Physics courses | 1 | Recommended year of study:1, Recommended semester: Winter |
| Faculty: Faculty of Science | Study plan (Version): Digital and Instrument Optics (2019) | Category: Physics courses | 1 | Recommended year of study:1, Recommended semester: Winter |
| Faculty: Faculty of Science | Study plan (Version): General Physics and Mathematical Physics (2019) | Category: Physics courses | 1 | Recommended year of study:1, Recommended semester: Winter |
| Faculty: Faculty of Science | Study plan (Version): Nanotechnology (2019) | Category: Special and interdisciplinary fields | 1 | Recommended year of study:1, Recommended semester: Winter |