Course: Mathematical Analysis I

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Course title Mathematical Analysis I
Course code KMA/P336
Organizational form of instruction Lecture + Lesson
Level of course Bachelor
Year of study 2
Semester Winter
Number of ECTS credits 3
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)
  • Lacková Veronika, RNDr. Ph.D.
  • Eisenmann Petr, doc. PaedDr. CSc.
Course content
Real numbers and their properties, suprema and infima, sequences Limits of sequences, their basic properties Calculus of limits of sequences Series of real numbers, their convergence, criteria of series of positive numbers Series of sign changing numbers, absolute and non-absolute convergence Continuity of functione and its properties Basic theorems on continuous functions Limits of functions Derivative of functions and its properties Mean value theorem and its consequences Derivatives versus monotonicity, convex functions Applications of derivatives, graphing functions Aproximation by polynomial functions, Taylor polynoms

Learning activities and teaching methods
unspecified
Learning outcomes
Prerequisites
unspecified

Assessment methods and criteria
unspecified
Recommended literature
  • ČERNÝ, Ilja. Inteligentní kalkulus.
  • ČERNÝ, Ilja. Matematická analýza II. Liberec: Technická univerzita, 1996. ISBN 80-7083-188-X.
  • ČERNÝ, Ilja. Matematická analýza I. Liberec: Technická univerzita, 1995. ISBN 80-7083-188-X.
  • JARNÍK, Vojtěch. Integrální počet I. Praha: Academia, 1984.
  • KOPÁČEK, Jiří. Matematická analýza pro fyziky I. Praha: Matfyzpress, 1997. ISBN 80-85863-74-X.
  • VESELÝ, Jiří. Matematická analýza pro učitele. Praha: Matfyzpress, 1997. ISBN 80-85863-23-5.


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): Mathematics (double subject) (A14) Category: Mathematics courses 2 Recommended year of study:2, Recommended semester: Winter
Faculty: Faculty of Science Study plan (Version): Mathematics (double subject) (A14) Category: Mathematics courses 2 Recommended year of study:2, Recommended semester: Winter
Faculty: Faculty of Science Study plan (Version): Mathematics (double subject) (A14) Category: Mathematics courses 2 Recommended year of study:2, Recommended semester: Winter