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Claculus III - OCRM17UM24

Title:	Matematická analýza III
Guaranteed by:	Katedra matematiky a didaktiky matematiky (41-KMDM)
Faculty:	Faculty of Education
Actual:	from 2017 to 2017
Semester:	summer
E-Credits:	0
Examination process:	summer s.:
Hours per week, examination:	summer s.:8/8, Ex [HT]
Extent per academic year:	8 [hours]
Capacity:	unknown / unknown (unknown)
Min. number of students:	unlimited
4EU+:	no
Virtual mobility / capacity:	no
State of the course:	taught
Language:	Czech
Teaching methods:	combined

Guarantor:	doc. RNDr. František Mošna, Ph.D.

Opinion survey results Examination dates SS schedule Noticeboard

Annotation -

Differential equations, methods of solution, linear differential equations of 1st and 2nd order, series and its convergence, sequences and series of functions, uniform convergence, power series.

Last update: Mošna František, doc. RNDr., Ph.D. (24.05.2018)

Aim of the course -

Primary purpose of the course is to make students acquainted with basic mathods of differemtial equations solutions and applications and with basic ideas, knowledges and correlations concerning series and function sequences and series. Secondary aim is to prove, repetite and fix knowledges of previous mathematical analysis courses.

Last update: Mošna František, doc. RNDr., Ph.D. (13.09.2017)

Literature -

Knopp, Konrad: Theory and Application of Infinite Series, Blackie London 1957
Hyslop, James M.: Infinite Series, Oliver and Boyd Edinburgh 1965
Singal, M. K., Singal, A. R.: A first cours in Real Analysis, R.Chand New Delhi 1999
Ross, K.A.:Elementary Analysis: The Tudory of Calculus. Undergraduate texts in Mathematics, Springer New York-Heidelberg-Berlin 1980
Fischer, E.: Intermediate Real Analisis. Undergraduate Texts in Mathematics, Springer NewYork-Heidelberg-Berlin 1983

Last update: Mošna František, doc. RNDr., Ph.D. (24.05.2018)

Teaching methods -

Lecture and seminar.

Last update: Mošna František, doc. RNDr., Ph.D. (13.09.2017)

Requirements to the exam -

credit requirements: active participation at seminars, two control tests (the first on differential equations, the second on series, sequences and series of fiunctions), control tests consists from examples presented at materials on Moodle, (for both tests there will be two terms during the examination period for possible correction)
exam requirements: writing exam - examples, oral exam - understanding of given concepts, relationships in three questions (the first question examines certain concept, its definition, theorem, connections, introduction..., the second question asks the student to decide on validity of submitted state and justify his decision or support it by a counterexample, the third question relates to some process, proof, problem solving etc, )

Last update: Mošna František, doc. RNDr., Ph.D. (13.09.2017)

Syllabus -

Differential equations - existence and uniquity, methods of solutions of first order differential equations (separation of variables method and variation of constant method for linear ones) and second order equations (undetermined coefficients method), thair applications.
Series - tests for convergence (comparison, ratio, root, Leibniz, Abel, Dirichlet tests), absolut convergence, sums of series.
Sequences and series of functions - uniform convergence of sequences and series, tests (Weierstrass, Abel, Dirichlet tests), power series, power series expansion of basic functions, application for calculation of limits.

Last update: Mošna František, doc. RNDr., Ph.D. (24.05.2018)