Course: Calculus III for Combined Studies

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Course title Calculus III for Combined Studies
Course code UMB/566K
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 winter semester.
Semester Winter
Number of ECTS credits 8
Language of instruction Czech
Status of course unspecified
Form of instruction Face-to-face
Work placements This is not an internship
Recommended optional programme components None
  • Eisner Jan, Mgr. Dr.
Course content
Content of lectures: 1. Infinite Series, convergence/divergence, absolute convergence of series. 2. Criteria for convergence of series - ratio test, root test. 3. Sequences and series functions - fundamental notions. 4. Criteria for convergence of series, uniform convergence. 5. Power series (Power series and functions, Maclaurin and Taylor series, Applications of series, Binomial series) 6. Fourier series. 7. Vector functions of multiple variables (continuity, limits, derivatives, gradient, total differential, Jacobian matrix) 8. Vector functions (parametric equations of curves, calculus with vector functions, arc length, tangent and normal vectors, velocity and acceleration, curvature) 9. Multiple integrals (double and triple integrals, Fubini's theorem, integrals in polar, cylindrical and spherical coordinates, change of variables, area and volume). 10. Curve integrals of 1st and 2nd type (in a scalar and in a vector fields).

Learning activities and teaching methods
Monologic (reading, lecture, briefing), Individual preparation for exam
  • Class attendance - 16 hours per semester
  • Preparation for classes - 32 hours per semester
  • Preparation for exam - 32 hours per semester
  • Preparation for credit - 16 hours per semester
Learning outcomes
To develop differential and integral calculus of functions of several variables.
We will work with sequences and series of numbers and functions. We learn how to decide about their convergence. We will expand functions into Taylor and Fourier series and show their connection to the original functions frow which the series were derived. We show how to calculate double and curve integrals.
We assume knowledge of differentail calculus of one and more variables and of integral calculus of one real variable (e.g. UMB/010K a UMB/565K).
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Assessment methods and criteria
Written examination

Simple written homeworks. Written exam. To pass the exam it is necessary to reach at least 50% points.
Recommended literature
  • A.Kufner, J.Kadlec. Fourierovy řady. Academia Praha, 1969.
  • J.Holenda. Řady. SNTL Praha, 1990.
  • M. Giaquinta, G. Modica. Mathematical Analysis. Function of One Variable.. Birkhäuser, Boston., 2003.
  • M. Giaquinta, G. Modica. Mathematical Analysis. An Introduction to Function of Several Variables.. Birkhauser, 2009.
  • S.I. Grossman. Calculus. John Wiley & Sons, Inc., 2005.
  • V. Jarník. Diferenciální počet II, Integrální počet II. Academia Praha, 1984.

Study plans that include the course
Faculty Study plan (Version) Category of Branch/Specialization Recommended year of study Recommended semester