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Lecturer(s)
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Lášek António, prof. RNDr. Ph.D.
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Siahkamari Josef, Mgr. Ph.D.
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Krausová Michaela, RNDr.
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Course content
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Week 1: Point-wise and uniform convergence of function sequences; Week 2: Function series; Week 3: Power series and their convergence; Fourier series; Week 4: Vector functions of one real variable and their properties; curves in Rn; Week 5: Subsets of Rn and their topological properties; Week 6: Functions of n variables, their limits and continuity; Week 7: Directional derivative, total differential, tangent manifolds; chain rule; Week 8: Solvability of functional equations and differentiation of implicit functions; Week 9: Fundamental notions of min/max theory in Rn; Week 10: Mapping from Rn to Rm, its continuity and differentiability; regular mappings and transformations of coordinate systems; Week 11: Double and triple integral, Fubini theorem, basic techniques; Week 12: Application of double and triple integrals in geometry and physics; Week 13: Integrals depending on parameters and their differentiation.
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Learning activities and teaching methods
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Multimedia supported teaching, Lecture, Practicum
- Preparation for an examination (30-60)
- 56 hours per semester
- Contact hours
- 78 hours per semester
- Preparation for comprehensive test (10-40)
- 24 hours per semester
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| prerequisite |
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| Knowledge |
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| popsat derivaci a integrál funkce jedné reálné proměnné |
| rozpoznat logické symboly, výroky a kvantifikátory |
| popsat posloupnost a řadu reálných čísel |
| formulovat Taylorovu větu |
| popsat spojitou a inverzní funkci |
| understand basic principles of differentiation of functions of one variable, |
| understand basic principles of integration of functions of one variable |
| understand basic principles from linear algebra |
| understand basic principles of sequences and series |
| Skills |
|---|
| derivovat a integrovat funkce jedné reálné proměnné |
| spočítat maximum, minimum, supremum a infimum číselné množiny |
| nakreslit graf inverzní funkce; algebraické, goniometrické, exponenciální a hyperbolické |
| rozhodnout o konvergenci a divergenci posloupnosti, řady a nevlastního integrálu |
| řešit optimalizační úlohy pro funkce jedné reálné proměnné |
| differentiate and integrate functions of one varibale |
| manage algebraic operations with vectors and matrices |
| compute eigenvalues and eigenvectors of matrices |
| determine convergence or divergence of sequences |
| determine convergence or divergence of series |
| find extremes of functions of one variable |
| Competences |
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| N/A |
| N/A |
| learning outcomes |
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| Knowledge |
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| popsat dvojné, trojné integrály a Fubiniovu větu |
| popsat mocninnou a Fourierovu řadu |
| popsat křivky a vlastnosti reálných funkcí vice proměnných |
| zavést derivace ve směru, parciální derivace, diferenciál a gradient |
| popsat funkční posloupnosti a řady |
| formulovat základní úlohy na maximum, resp. minimum |
| have knowledge of basic definitions and statements related to function sequences, function series, vector functions of one variable na real functions of one variable |
| understand basic principles of differentiation of functions of more variables |
| understand basic principles of integration of functions of more variables |
| understand basic principles of vector functions theory |
| understand basic principles of function sequences and function series |
| Skills |
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| počítat dvojné, trojné integrály a integrály s parametrem |
| spočítat derivace ve směru, parciální derivace, gradient a diferenciál funkcí více proměnných |
| vyřešit úlohy na hledání extrému funkcí více proměnných |
| rozpoznat vlastnosti reálných funkcí vice proměnných (spojitost, hladkost apod.) |
| rozvinout danou funkci v mocninnou nebo Fourierovu řadu |
| rozhodnout o konvergenci funkční posloupnosti a řady |
| perform operations with function sequences and function series |
| expand a function in power series or Fourier series |
| describe curves in Rn and perform simple operations with them |
| analyze basic properties of functions of more variables |
| determine directional and partial derivatives of functions of more variables |
| formulate basic extremal problems and solve them |
| compute double and triple integrals |
| work with integrals with parameters |
| Competences |
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| N/A |
| N/A |
| teaching methods |
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| Knowledge |
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| Lecture |
| Practicum |
| Multimedia supported teaching |
| Skills |
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| Multimedia supported teaching |
| Practicum |
| Lecture |
| Competences |
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| Lecture |
| Practicum |
| Multimedia supported teaching |
| assessment methods |
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| Knowledge |
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| Continuous assessment |
| Combined exam |
| Test |
| Skills |
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| Combined exam |
| Continuous assessment |
| Test |
| Competences |
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| Continuous assessment |
| Combined exam |
| Test |
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Recommended literature
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Brabec, Jiří; Hrůza, Bohuslav. Matematická analýza II. Praha : SNTL, 1986.
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Drábek, Pavel; Míka, Stanislav. Matematická analýza II. 3. nezm. vyd. Plzeň : ZČU, 1999. ISBN 80-7082-528-6.
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Thomson, Bruckner, Bruckner. Elementary real analysis. 2008. ISBN 978-1434843.
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