Course: Calculus II

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Course title Calculus II
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)
  • Eisner Jan, Mgr. Dr.
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.

Learning activities and teaching methods
Monologic (reading, lecture, briefing)
  • Class attendance - 56 hours per semester
  • Preparation for classes - 28 hours per semester
  • Preparation for credit - 28 hours per semester
  • Preparation for exam - 56 hours per semester
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

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
  • S.I. Grossman: Calculus. John Wiley & Sons Inc., 2005.
  • H. Anton, I. Bivens, S. Davis. Calculus. 2012. ISBN 978-0-470-64.


Study plans that include the course
Faculty Study plan (Version) Category of Branch/Specialization Recommended year of study Recommended semester
Faculty: Faculty of Science Study plan (Version): Bioinformatics (1) Category: Informatics courses 1 Recommended year of study:1, Recommended semester: Summer