Course: Mathematics 2

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Course title Mathematics 2
Course code KMA/MA2AA
Organizational form of instruction Lecture + Exercise
Level of course Bachelor
Year of study not specified
Semester Winter
Number of ECTS credits 5
Language of instruction Czech
Status of course Compulsory
Form of instruction Face-to-face
Work placements This is not an internship
Recommended optional programme components None
Lecturer(s)
  • Pastor Karel, doc. Mgr. Ph.D.
  • Netuka Horymír, RNDr. Ph.D.
  • Fišer Jiří, RNDr. Ph.D.
Course content
1. The function of one variable - bounded, monotone, simple, composite function, inverse function, survey of elementary functions. 2. Sequence, the limit of sequence - bounded sequence, monotone sequence, convergent sequence, divergent sequence, limes superior, limes inferior. 3. The limit of function - the geometric sense of the limit of function, finite limit, infinite limite, limit on the right, limit on the left. 4. The continuity of function - continuity of a function at a point, points of discontinuity, continuity on an interval, continuity in parts, continuity of a composite and an inverse function. 5. The derivative of function - the definition of the derivative of function, the geometric sense of the derivative of function, the rules of differentation, the derivative of composite function, the derivative of inverse function, the derivative of elementary functions. 6. The course of function - the differential of function, the basic theorems of differential calculus, the extrema of function, convex and concave curves, asymptotes. 7. Indefinite integral - primitive function, the survey of basis indefinite integrals, integration by parts, change of variable in an indefinite integral, primitives of rational functions. 8. The Riemann definite integral - introducing of a notion, the fundamenthal theorem of integral calculus, integration by parts and change in a definite integral. 9. The geometric interpretation of definite integral - the area of plane surface, arc length, the volume of solid.

Learning activities and teaching methods
Lecture, Dialogic Lecture (Discussion, Dialog, Brainstorming)
  • Attendace - 52 hours per semester
  • Homework for Teaching - 20 hours per semester
  • Preparation for the Course Credit - 20 hours per semester
  • Preparation for the Exam - 60 hours per semester
Learning outcomes
Understand calculus of functions of a single real variable
Comprehension Understand the mathematical tools of differential and integral calculus of functions of a single variable.
Prerequisites
Mathematics of secondary school.

Assessment methods and criteria
Oral exam, Written exam

the student has to understand the subject
Recommended literature
  • Adams R.A. (1991). Calculus: a complete course. Addison-Wesley New York.
  • Finney R.L., Thomas G.B. (1992). Calculus. Addison-Wesley New York.
  • Jarník, V. (1984). Diferenciální počet I. Academia, Praha.
  • Jarník V. Integrální počet I. libovolné vydání.
  • Míka S., Drábek P. (2003). Matematická analýza II. Západočeská univerzita Plzeň.
  • Míka S., Drábek P. (2003). Matematická analýza I. ZČU Plzeň.
  • Schwabik Š.,Šarmanová P. (2000). Malý průvodce historií integrálu. MU Brno.
  • Škrášek J., Tichý J. (1990). Aplikace matematiky I. a II.. SNTL Praha.


Study plans that include the course
Faculty Study plan (Version) Branch of study Category Recommended year of study Recommended semester
Faculty of Science Computer Science for Education (1) Informatics courses 2 Winter
Faculty of Science Applied Computer Science (1) Informatics courses 2 Winter