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Lecturer(s)
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Pitrová Veronika, RNDr. PhD., Ph.D.
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Opic Bohumír, doc. RNDr. DrSc.
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Course content
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1. Indefinite integral, integration by parts 2. Substitution in integrals, rational functions and partial fractions 3. Conversion to rational functions 4. Newton and Riemann integral, their calculation 5. Approximating definite integrals 6. Application of integrals: areas, volumes 7. Application of integrals: length of curve, area of surfaces 8. Application of integrals: centers of mass, work, force, Guldin theorems 9. Ordinary differential equations of 1st order (separable, linear) 10. Ordinary differential equations of 2nd order (linear) 11. Real-valued functions of more variables (limits, continuity) 12. Partial derivatives 13. Extremes of vector functions,(free and constrained) 14. Integration of vector functions. 15. Summary
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Learning activities and teaching methods
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unspecified
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Learning outcomes
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Basics of calculus, mainly integration (Newton and Riemann integral, its applications in geometry and physics), differential equations (simple ordinary diff.equations of first and second order), functions of more variables (partial derivative, extremes, integration).
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Prerequisites
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Teaching in English is meant only for erasmus and foreign students. In the case of a small number of students is teaching in a form of individual consultations.
KMA/K301
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Assessment methods and criteria
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unspecified
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Recommended literature
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ČERNÝ, I. Matematická analýza 2. část, Liberec, 1995.
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ČERNÝ, I. Matematická analýza 3. část, Liberec, 1996.
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JARNÍK, V. Integrální počet I, Praha, ACADEMIA, 1984.
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VESELÝ, J. Matematická analýza pro učitele I, II, Matfyz press, 1994.
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