| Course title | Calculus II |
|---|---|
| Course code | UMB/565 |
| Organizational form of instruction | Lecture + Lesson |
| Level of course | Bachelor |
| Year of study | not specified |
| Frequency of the course | In each academic year, in the summer semester. |
| Semester | Summer |
| Number of ECTS credits | 8 |
| Language of instruction | Czech |
| Status of course | Compulsory |
| Form of instruction | unspecified |
| Work placements | unspecified |
| Recommended optional programme components | None |
| Lecturer(s) |
|---|
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| Course content |
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Content of lectures: 1. Sequences: definition, examples, basic concepts, convergence, absolute and relative convergence, theorems on sequences, definition of limsup and liminf of sequences, arithmetic and geometric sequences 2. Infinite series: sum of a series, Bolzano-Cauchy condition on series convergence, properties of series, criteria for convergence of series, absolute convergence 3. Functional sequences and series: point and uniform convergence, example of functional sequence with point convergence but not with uniform convergence, Weierstrass criterion of uniform convergence, properties of uniformly convergent sequences and series 4. Power series: range of convergence of power series and its determination, basic properties of power series, Taylor series 5. Indefinite integral: definition, basic properties, substitution method, integration by parts, methods of integration of rational, trignometric and irrational functions 6. Riemann (definite) integral: definition, basic concepts, existence, substitution method and integration by parts for Riemann integral, relationship between indefinite and Riemann integral (Newton formula) 7. Improper integral: definition, convergence, integral criterion for convergence of infinite series 8. Geometric application of Riemann integral: mean value of function, derivation of formulae for area between two curves, surfaces and volumes of solids of revolution, and length of curves Content of practicals: Practicing theoretical concepts on specific examples.
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| Learning activities and teaching methods |
Monologic (reading, lecture, briefing), Dialogic (discussion, interview, brainstorming), Demonstration, Projection
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| Learning outcomes |
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Introduction to series and single variable integration.
Student should be able to explain what are sequences of numbers and infinite series and also why a sum of infinite amount of numbers can be a finite number. Student should also know how to calculate limits of sequences and whether a given infinite series converges or not. Last but not least, student should understand meaning of integration of functions, why is it needed and which practical applications integration has. (S)he should also know how to define Riemann integral and how to work with it. |
| Prerequisites |
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Students are assumed to have knowledge of calculus covered by the courses Matematická analýza I (UMB564).
UMB/CV010 ----- or ----- UMB/CV551 ----- or ----- UMB/CV564 ----- or ----- UMB/010 ----- or ----- UMB/551 ----- or ----- UMB/564 |
| Assessment methods and criteria |
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Combined exam, Test, Interim evaluation
100% attendance of practicals (excused absence permitted), performance of all written tests on practicals and at least 50% success in these tests |
| Recommended literature |
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| Study plans that include the course |
| Faculty | Study plan (Version) | Category of Branch/Specialization | Recommended semester | |
|---|---|---|---|---|
| Faculty: Faculty of Science | Study plan (Version): Chemistry (1) | Category: Chemistry courses | 1 | Recommended year of study:1, Recommended semester: Summer |
| Faculty: Faculty of Science | Study plan (Version): Biophysics (1) | Category: Physics courses | 1 | Recommended year of study:1, Recommended semester: Summer |
| Faculty: Faculty of Science | Study plan (Version): Applied Mathematics (2010) | Category: Mathematics courses | 1 | Recommended year of study:1, Recommended semester: Summer |
| Faculty: Faculty of Science | Study plan (Version): Physics (1) | Category: Physics courses | 1 | Recommended year of study:1, Recommended semester: Summer |
| Faculty: Faculty of Science | Study plan (Version): Biophysics (1) | Category: Physics courses | - | Recommended year of study:-, Recommended semester: Summer |
| Faculty: Faculty of Science | Study plan (Version): Mathematics for future teachers (1) | Category: Mathematics courses | 1 | Recommended year of study:1, Recommended semester: Summer |
| Faculty: Faculty of Science | Study plan (Version): Mathematics for future teachers (1) | Category: Mathematics courses | 1 | Recommended year of study:1, Recommended semester: Summer |
| Faculty: Faculty of Science | Study plan (Version): Physics for future teachers (1) | Category: Physics courses | 1 | Recommended year of study:1, Recommended semester: Summer |