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Lecturer(s)
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Bazaykin Yaroslav, doc. CSc., DSc.
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Course content
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1. Real numbers and their properties, suprema and infima, sequences. 2. Limits of sequences, their basic properties. 3. Calculus of limits of sequences. 4. Series of real numbers, their convergence, criteria of series of positive numbers. 5. Series of sign changing numbers, absolute and non-absolute convergence. 6. Continuity of functions and its properties. 7. Basic theorems on continuous functions. 8. Limits of functions. 9. Derivative of functions and its properties. 10. Mean value theorem and its consequences. 11. Derivatives versus monotonicity, convex functions. 12. Applications of derivatives, graphing functions. 13. Aproximation by polynomial functions, Taylor polynomials.
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Learning activities and teaching methods
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unspecified
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Learning outcomes
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Students will learn basic concepts of mathematical analysis, mainly precise definitions of continuity, limits and derivatives. They will also learn how to use those tools in other fields, as physics, economy, and in mathematics (graphing functions, approximation by polynomial functions).
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Prerequisites
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unspecified
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Assessment methods and criteria
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unspecified
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Recommended literature
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