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Lecturer(s)
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Ludvík Pavel, RNDr. Ph.D.
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Rachůnková Irena, prof. RNDr. DrSc.
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Tomeček Jan, doc. RNDr. Ph.D.
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Course content
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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.
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Learning activities and teaching methods
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Lecture, Work with Text (with Book, Textbook)
- Attendace
- 78 hours per semester
- Preparation for the Exam
- 95 hours per semester
- Preparation for the Course Credit
- 45 hours per semester
- Homework for Teaching
- 25 hours per semester
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Learning outcomes
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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.
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Prerequisites
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Knowledge of the theory of Sequences and Series of Real Numbers and Differential Calculus of Real Functions of one Real Variable.
KMA/MMA2
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Assessment methods and criteria
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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.
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Recommended literature
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Brabec J., Hrůza B. (1989). Matematická analýza II. SNTL, Praha.
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Edwards, C. H. (2014). Advanced Calculus of Several Variables. Academic Press.
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J. K. Hunter, B. Nachtergaele. (2001). Applied Analysis. World Scientific.
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Kojecká J., Rachůnková I. (1989). Řešené příkklady z matematické analýzy III.. Olomouc.
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Rachůnek, L., Rachůnková, I. (2004). Diferenciální počet funkcí více proměnných. VUP Olomouc.
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V. Jarník. (1976). Diferenciální počet I a II. SPN, Praha.
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