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Lecturer(s)
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Švrček Jaroslav, RNDr. CSc.
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Riemel Tomáš, Mgr.
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Calábek Pavel, RNDr. Ph.D.
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Vítková Lenka, Mgr. Ph.D.
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Course content
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1. Number sets, supremum, infimum. 2. Number sequences, monotonicity, limits. 3. Functions and their characteristics, composite and inverse functions. 4. Limits of functions, continuity. 5. Differential calculus: Differentiation, the differential of a function, fundamental theorems, course of a function. 1. Primitive functions and the indefinite integral, selected techniques of integration. 2. The Riemann integral and its properties. 3. Application in geometry and physics. 4. Improper integrals. 5. Selected methods of solving ordinary differential equations. 6. Number series, criteria of convergence, operations with series.
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Learning activities and teaching methods
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Monologic Lecture(Interpretation, Training), Dialogic Lecture (Discussion, Dialog, Brainstorming)
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Learning outcomes
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Understand the mathematical tools of differential calculus of functions of a single variable. Understand the mathematical tools of integral calculus of functions of a single variable.
Comprehension Understand the mathematical tools of differential calculus of functions of a single variable. Understand the mathematical tools of integral calculus of functions of a single variable.
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Prerequisites
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unspecified
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Assessment methods and criteria
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Oral exam, Written exam
Credit: the student has to turn in all pieces of homework and obtain at least 40% of points in every short test during the semester and at least half of the possible points in the final (long) test. Exam:
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Recommended literature
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G. S. Simmons. (2005). Calculus With Analytic Geometry. McGraw-Hill.
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J. Brabec, B. Hrůza. (1989). Matematická analýza II. SNTL Praha.
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J. Brabec, F. Martan, Z. Rozenský. (1989). Matematická analýza I. Praha: SNTL.
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Jarník V. (1984). Diferenciální počet I. Akademia Praha.
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Jarník V. (1984). Integrální počet I. Academia Praha.
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Novák V. (1988). Diferenciální počet v R.. UJEP Brno.
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