Course: Mathematical Analysis 3

« Back
Course title Mathematical Analysis 3
Course code KMA/MMAN3
Organizational form of instruction Lecture + Exercise
Level of course Bachelor
Year of study not specified
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)
  • Pastor Karel, doc. Mgr. Ph.D.
  • Vodák Rostislav, RNDr. Ph.D.
  • Ligurský Tomáš, RNDr. Ph.D.
  • Pavlačková Martina, RNDr. Ph.D.
Course content
1. Sequences and series of functions: Pointwise and uniform convergence, convergence criteria (esp. the Weierstrass criterion). Properties of the limit function - limit, continuity, derivative and integral. 2. Power series: Radius, interval and domain of convergence. Uniform convergence of power series. Taylor series, Taylor expansion of elementary functions. Approximate computing via series. 3. Metric spaces: Metric on a set, examples of metric spaces. Normed linear space. Classification of points according to a set. Open and closed sets and their properties. Convergent and Cauchy sequences of points. 4. Functions and mappings in Euclid spaces: Practical aplications. Limit and continuity of a mapping (function). Properties of continuous functions on compact sets.

Learning activities and teaching methods
Lecture, Dialogic Lecture (Discussion, Dialog, Brainstorming)
  • Attendace - 52 hours per semester
  • Preparation for the Course Credit - 10 hours per semester
  • Preparation for the Exam - 30 hours per semester
Learning outcomes
Understand basic notions concerning function series and metric spaces.
Comprehension Understand basic notions concerning function series and metric spaces.
Prerequisites
Differential calculus of functions of several variables, integration on the real axis.
KAG/MA2
----- or -----
KAG/MMA2
----- or -----
KMA/MA2M

Assessment methods and criteria
Oral exam

Credit: the student has to pass two written tests (i.e. to obtain at least half of the possible points in each test). Attendance at seminars: absence is tolerated at most three times. Exam: the student has to understand the subject and be able to prove the principal results.
Recommended literature
  • Brabec J., Hrůza B. (1989). Matematická analýza II. SNTL, Praha.
  • J. Kojecká, I Rachůnková. (1989). Řešené příklady z matematické anylýzy 3. UP Olomouc.
  • Novák V. (1985). Nekonečné řady. UJEP Brno.
  • V. Jarník. (1976). Diferenciální počet I a II. SPN, Praha.


Study plans that include the course
Faculty Study plan (Version) Branch of study Category Recommended year of study Recommended semester
Faculty of Science Discrete Mathematics (2016) Mathematics courses 2 Winter
Faculty of Science Mathematics (1) Mathematics courses 2 Winter