| Course title | Mathematical Analysis 2 |
|---|---|
| Course code | KMA/MAF2 |
| Organizational form of instruction | Lecture + Exercise |
| Level of course | Bachelor |
| Year of study | not specified |
| Semester | Summer |
| 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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A. Differential Equations. 1. An invitation to differential equations: Decay of radioactive material, population models. 2. A detour: Spaces of infinite dimension, Hilbert and Banach spaces, fixed point theorems. 3. Existence and uniqueness of the solution to an ordinary differential equation. 4. Separable equations and other solution techniques. 5. A revision of linear algebra, linear differential equations. 6. Linear differential equations of higher order, solution techniques. 7. Application: Damped and forced oscillations. B: Functions of several variables. 1. The notion of functions of several variables, continuity and limits. 2. A second visit to spaces of higher dimension. 3. Differentiation. 4. Taylor polynomial. 5. Potential, vector fields, gradient, divergence, curl and application. 6. Implicit functions. 7. Minima and maxima of functions of several variables: Lagrange multipliers. C: Bonus. How differential equations relate to extrema of functions of several variables. An introduction to the calculus of variations. D: Series. 1. Series of non-negative numbers. 2. Absolute and non-absolute convergence. 3. Function series: Fourier analysis.
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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 equations and differential calculus of functions of several variables
Comprehension Understand basic ODEs and differential calculus of functions of several variables. |
| Prerequisites |
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Differential calculus of functions of a single variable.
KMA/MAF1 |
| Assessment methods and criteria |
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Oral exam, Written exam
Credit: 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): Instrument and Computer Physics (2019) | Category: Physics courses | 1 | Recommended year of study:1, Recommended semester: Summer |
| Faculty: Faculty of Science | Study plan (Version): Optics and Optoelectronics (2019) | Category: Physics courses | 1 | Recommended year of study:1, Recommended semester: Summer |
| Faculty: Faculty of Science | Study plan (Version): Biophysics - Specialization in Molecular Biophysics (2024) | Category: Physics courses | 1 | Recommended year of study:1, Recommended semester: Summer |
| Faculty: Faculty of Science | Study plan (Version): Digital and Instrument Optics (2019) | Category: Physics courses | 1 | Recommended year of study:1, Recommended semester: Summer |
| Faculty: Faculty of Science | Study plan (Version): Nanotechnology (2019) | Category: Special and interdisciplinary fields | 1 | Recommended year of study:1, Recommended semester: Summer |
| Faculty: Faculty of Science | Study plan (Version): General Physics and Mathematical Physics (2019) | Category: Physics courses | 1 | Recommended year of study:1, Recommended semester: Summer |
| Faculty: Faculty of Science | Study plan (Version): Applied Physics (2019) | Category: Physics courses | 1 | Recommended year of study:1, Recommended semester: Summer |
| Faculty: Faculty of Science | Study plan (Version): Biophysics - Specialization in General Biophysics (2024) | Category: Physics courses | 1 | Recommended year of study:1, Recommended semester: Summer |