Course: Mathematical Analysis 3

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Course title Mathematical Analysis 3
Course code KMA/MA3M
Organizational form of instruction Lecture + Exercise
Level of course Bachelor
Year of study not specified
Semester Winter
Number of ECTS credits 8
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)
  • Tomeček Jan, doc. RNDr. Ph.D.
  • Rachůnková Irena, prof. RNDr. DrSc.
  • Pavlačková Martina, RNDr. Ph.D.
  • Andrášik Richard, Mgr.
  • Pastor Karel, doc. Mgr. Ph.D.
Course content
1. Pointwise convergence of functional sequences and series. 2. Criteria of the uniform convergence. 3. Power series and Taylor series. Fourier series. 4. Sequences in R^n. 5. Real functions of several real variables. Limit and continuity of functions. 6. Directional and partial derivatives. Differentials. 7. Taylor formula and local extrema of functions of more variables. 8. Derivatives of composite maps. Implicit functions theorems. 9. Relative local extrema and global extrema. Applications.

Learning activities and teaching methods
Lecture, Work with Text (with Book, Textbook)
  • Attendace - 78 hours per semester
  • Preparation for the Course Credit - 45 hours per semester
  • Preparation for the Exam - 95 hours per semester
  • Homework for Teaching - 25 hours per semester
Learning outcomes
Understand principles of the differential calculus of real functions of more real variables and the theory of function series.
Analysis Analyse a behaviour of function series and local and global properties of real functions of several real variables.
Prerequisites
Knowledge of the theory of Sequences and Series of Real Numbers and Differential Calculus of Real Functions of one Real Variable.
KMA/MA2M

Assessment methods and criteria
Oral exam, Written exam

Credit: to pass a written test. Exam: to know and to understand the subject and be able to apply it on standard examples.
Recommended literature
  • Brabec J., Hrůza B. (1989). Matematická analýza II. SNTL, Praha.
  • J. K. Hunter, B. Nachtergaele. (2001). Applied Analysis. World Scientific.
  • Kojecká J., Rachůnková I. (1989). Řešené příkklady z matematické analýzy III.. Olomouc.
  • R. Sikorski. (1976). Diferenciální a integrální počet. Academia, Praha.
  • Rachůnek, L., Rachůnková, I. (2004). Diferenciální počet funkcí více proměnných. VUP Olomouc.
  • 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 Mathematics and Applications (1) Mathematics courses 2 Winter