| Course title | Mathematical Analysis 3 |
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| Course code | KMA/KAN3 |
| Organizational form of instruction | Seminary |
| Level of course | Bachelor |
| Year of study | not specified |
| Semester | Winter |
| Number of ECTS credits | 5 |
| Language of instruction | Czech |
| Status of course | Compulsory |
| Form of instruction | Face-to-face |
| Work placements | Course does not contain work placement |
| Recommended optional programme components | None |
| Course availability | The course is available to visiting students |
| Lecturer(s) |
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| Course content |
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Course program (syllabus): 1. Gaussian plane C, mapping of complex numbers in the Gaussian plane, convergence in C. Series of complex numbers, Bolzano-Cauchy criterion of convergence, absolute and relative convergence. Criteria of convergence for series. 2. Power series in C. Radius and circle of convergence. Properties of power series. 3. Term-by-term differentiating and integration of power series. 4. Taylor series. Definitions of trigonometric and exponential functions by power series. 5. Metric spaces: metric, norm, examples of metric spaces. 6. Metric spaces: other terms (distance of sets, open and closed sets, neighbourhoods of points, interior of a set, boundary etc.). 7. Metric spaces - convergence, continuity, limit. Complete and compact space. 8. Functions of more real variables. Definition, basic terms, contour lines, domains. 9. Differential and derivative (gradient) of functions of more real variables. Applications. 10. Directional derivatives, partial derivatives. Curves, surfaces, tangent, normal, tangent plane. 11. Partial derivatives of composite functions. Implicit functions. Solving equations. 12. Extremes of functions of more real variables. 13. Constrained and global extremes. 14. Reserve.
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| Learning activities and teaching methods |
Monological explanation (lecture, presentation,briefing)
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| Learning outcomes |
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Elementary concepts of metric spaces, compact and complete spaces. Differential calculus of a real fuction of several real variables.
Functions of several real variables. |
| Prerequisites |
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Analytic thinking. AN2E.
KMA/KAN2 ----- or ----- KMA/PAN2 |
| Assessment methods and criteria |
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Oral exam, Written exam
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| 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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