Course: Mathematics 2

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Course title Mathematics 2
Course code KMA/YMAT2
Organizational form of instruction Lecture
Level of course Bachelor
Year of study not specified
Semester Winter
Number of ECTS credits 9
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
Lecturer(s)
  • Andres Jan, prof. RNDr. dr hab. DSc.
  • Závodný Miloslav, RNDr.
Course content
<ol> <li> Functions of a single real variable ? bounded, monotone, one-to-one functions. Composite functions, inverse functions. Overview of elementary functions. <li> Sequences of real numbers ? bounded, monotone sequences. Limit of a sequence, convergent and divergent sequences; limes superior, limes inferior . <li> Limit of a function ? definition, geometrical interpretation, computing rules. One-sided limits, infinite limits and limits at infinity. <li> Continuity of functions ? in a point, on an interval; points of discontinuity. Continuity of composite and inverse functions. <li> Differentiation ? definition, geometrical meaning, computing rules. Differentiation of composite and inverse functions. Differentiation of elementary functions. <li> Differential of a function, basic theorems of differential calculus. Graph sketching ? extreme values, convex and concave functions, asymptotes. <li> Primitive function, table of basic primitive functions. Computing rules ? per partes, substitutions, integration of rational functions. <li> Riemann integral ? definition, the fundamental theorem of integral calculus. Integration by parts, substitution methods for computing definite integral. <li> Geometrical applications of the definite integral ? computing areas, length of curves, volumes of bodies. <\lo>

Learning activities and teaching methods
Lecture
  • Attendace - 10 hours per semester
  • Preparation for the Exam - 120 hours per semester
  • Homework for Teaching - 100 hours per semester
  • Preparation for the Course Credit - 40 hours per semester
Learning outcomes
The course is an introduction to mathematical analysis of functions of a single variable. It is targeted at Computer Science Teaching students.
Knowledge
Prerequisites
Basic skills.

Assessment methods and criteria
Mark

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. Akademia Praha.
  • Jarník V. (1984). Integrální počet I. Academia Praha.
  • KOPÁČEK J. (2016). Matematická analýza nejen pro fyziky (I). Matfyzpress, Praha.
  • MÁDROVÁ V., MAREK J. (2013). Sborník úloh z diferenciálního počtu v R: (364 řešených příkladů a 1111 cvičení). Olomouc: Univerzita Palackého v Olomouci.
  • Míka S., Drábek P. (2003). Matematická analýza II. Západočeská univerzita Plzeň.
  • MÍKA S.,DRÁBEK P. (2003). Matematická analýza II.. Západočeská univerzita 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) Category of Branch/Specialization Recommended year of study Recommended semester