Course title | Calculus II |
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Course code | UMB/565I |
Organizational form of instruction | Lecture + Lesson |
Level of course | Bachelor |
Year of study | 1 |
Frequency of the course | In each academic year, in the summer semester. |
Semester | Summer |
Number of ECTS credits | 6 |
Language of instruction | English |
Status of course | Compulsory |
Form of instruction | Face-to-face |
Work placements | This is not an internship |
Recommended optional programme components | None |
Lecturer(s) |
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Course content |
Content of lectures: Sequences and series of numbers and functions, criteria for convergence. Power and Taylor series. Indefinite integral, substitution method, integration by parts Riemann (definite) integral (Riemann sums, existence of Riemann integral), relationship between indefinite and Riemann integrals Application of definite integral (area between two curves, volumes of solids of revolution, lengths of curves, centers of mass, mean value, etc.) Transcendental functions (exponential, logarithmic, general power), inverse functions to trigonometric functions and hyperbolic functions Methods of integration (integration by parts, substitution method, integration of trigonometric functions, method of partial fractions, integration of rational functions) Improper integrals Methods of numerical integration (using programs Mathematica/Maple/Matlab) Functions of multiple variables (continuity, limits, partial derivatives, gradient, directional derivatives, total differential) Applications (local maxima and minima, constrained maxima and minima, global extremes) Content of practicals: Practicing theoretical concepts on specific examples.
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Learning activities and teaching methods |
Monologic (reading, lecture, briefing)
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Learning outcomes |
Mastering integration of functions of one variable and differential calculus of vector variables. To learn how to operate with sequences and series of numbers and functions.
Student will get skills in sequences and series of numbers and functions including power and Taylor series and learn criteria for convergence of series. We introduce antiderivative and Riemann and Newton integral, and see applications of intergral calculus of one real variable. We learn as well a differential calculus of functions of several variables including to find local and global extremal points of scalar functions in R2. |
Prerequisites |
differentail calculus of one real variable
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Assessment methods and criteria |
Written examination, Student performance assessment, Test
Active attendance of practicals (excused absence permitted). To pass the excercisses it is necessary to reach at least 50% points from 3-4 written tests. To pass the exam it is necessary to reach at least 50% points from the final exam written test. |
Recommended literature |
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Study plans that include the course |
Faculty | Study plan (Version) | Category of Branch/Specialization | Recommended semester | |
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Faculty: Faculty of Science | Study plan (Version): Bioinformatics (1) | Category: Informatics courses | 1 | Recommended year of study:1, Recommended semester: Summer |