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Lecturer(s)
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Knobloch Roman, Mgr. Ph.D.
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Bittnerová Daniela, RNDr. CSc.
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Finěk Václav, doc. RNDr. Ph.D.
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Bittner Václav, Mgr. Ph.D.
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Břehovský Jiří, Mgr. Ph.D.
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Course content
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Lectures: 1. Infinite series, tests for convergence, absolute convergence. 2. Introduction to metric spaces, multivariable functions. 3. Continuity and limits of multivariable functions. 4. Partial derivatives, total differentials, the chain rule, directional derivatives. 5. Taylor's formula, implicit functions. 6. Repetition. 7. Relative extrema of multivariable functions. 8. Constrained and absolute extrema of multivariable functions. 9. First-order ordinary differential equations, existence and uniqueness of solutions. 10. Second-order ordinary differential equations with constant coefficients. 11. Introduction to numerical solution methods for first-order ordinary differential equations. 12. Introduction to multiple integrals, Fubini's theorem. 13. Substitutions in multiple integrals. 14. Repetition. Practice: 1. Repetition of integration. 2. Infinite series, tests for convergence, absolute convergence. 3. Infinite series, metric spaces, multivariable functions. 4. Continuity and limits of multivariable functions. 5. Partial derivatives, total differentials, the chain rule, directional derivatives. 6. Taylor's formula, implicit functions. 7. Repetition. 8. Relative extrema of multivariable functions. 9. Constrained and absolute extrema of multivariable functions. 10. Solution methods for first-order ordinary differential equations. 11. Solution methods for second-order ordinary differential equations. 12. Introduction to multiple integrals, Fubini's theorem. 13. Substitutions in multiple integrals. 14. Repetition.
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Learning activities and teaching methods
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Monological explanation (lecture, presentation,briefing)
- Class attendance
- 70 hours per semester
- Preparation for credit
- 28 hours per semester
- Preparation for exam
- 42 hours per semester
- Home preparation for classes
- 40 hours per semester
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Learning outcomes
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The subject represents an introduction to differential calculus of function of more (especially two) real variables, infinite series, double integrals, and an essential course of differential equations.
Infinite series, differential calculus of multivariable functions, ordinary differential equations, foundations of computational mathematics, and multiple integrals.
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Prerequisites
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Knowledge of subject Mathematics 1 (MA1-M).
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Assessment methods and criteria
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Combined examination
Credit: Active participation on seminars + tests. Exam: writtten.
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Recommended literature
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Brabec, J. - Hrůza, B.:. Matematická analýza II. Praha, 1986.
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Brabec, J.:. Matematická analýza II. Praha, 1979.
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Budinský, B. - Charvát, J.:. Matematika II. Praha, 1999.
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Ivan, J.:. Matematika 1; 2. Bratislava/Praha, 1989.
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Mezník, I. , Karásek, J., Miklíček, J.:. Matematika I pro strojní fakulty. SNTL, Praha, 1992.
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Nagy, J.:. Elementární metody řešení obyčejných diferenciálních rovnic. Praha, 1978.
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Nekvinda, M.:. Matematika II.. Liberec, 2000. ISBN 80-7083-374-2.
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Nekvinda, M.- Říhová, H. - Vild, J.:. Matematické oříšky II. TU Liberec, 2002.
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Rektorys, K. a další:. Přehled užité matematiky.. Praha, Prometheus, 2000. ISBN 80-85849-92-5.
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