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Basics of integral calculus, differential equations, infinite series and sequences, and series of functions.
Last update: Mošna František, RNDr., Ph.D. (30.01.2023)
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The primary goal of the course is to make students acquainted with the basics of integral calculus, with methods of solving and applications of differential equations, as well as with basic concepts, knowledge and contexts related to series and functional sequences and series. A secondary goal is to review, review and consolidate knowledge from previous courses in mathematical analysis. Last update: Mošna František, RNDr., Ph.D. (30.01.2023)
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lecture 2 hours per week, 24 hours in total seminars 1 hour per week, 12 hours in total preparation for seminars 1 hour per week, 12 hours in total reading mathematical literature 24 h homework - 8 h expected total time load of students - 80 h Last update: Mošna František, RNDr., Ph.D. (31.01.2023)
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basic: Veselý, Jiří: Matematická analýza pro učitele I, II. Matfyzpress, Praha 1997 Mošna, František: Obyčejné diferenciální rovnice, PedFUK Praha 2019 Došlá, Zuzana, Novák, Vítězslav: Nekonečné řady, MU Brno 2002 others: Jarník, V.: Integrální počet I, II. Academia, Praha 1984 Děmidovič, B. P.: Sbírka úloh a cvičení z matematické analýzy. Fragment, Praha 2004 Kalas, Josef, Ráb, Miloš: Obyčejné diferenciální rovnice, MU Brno 2001 Kalas, Josef, Pospíšil, Zdeněk: Spojité modely v biologii, MU Brno 2001 Ráb, Miloš: Metody řešení obyčejných diferenciálních rovnic, MU Brno 2012 Plch, Roman: Příklady z matematické analýzy, Diferenciální rovnice, MU Brno 2002 Barták, Jaroslav: Diferenciální rovnice, Praha 1984 Pelikán, Štěpán, Zdráhal, Tomáš: Matematická analýza, Číselné řady, posloupnosti a řady funkcí, UJEP Ústí n. L. 1994 Last update: Mošna František, RNDr., Ph.D. (30.01.2023)
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The exam consists of written and oral parts. The written part will focus on students' numerical knowledge and will include examples for calculating integrals, solving differential equations, deciding on convergence, uniform convergence and using the theory to calculate sums of series and limits. It will be possible for students to complete the written part already during the semester in the form of tests. The oral part of the exam is aimed at understanding the discussed concepts, relationships and contexts and usually consists of three questions (the first question examines a concept, definition, statement, context, introduction..., in the second question the student has to decide on the validity of the presented statement and his justify or support a decision with a counterexample, the third question refers to some kind of inference, proof, problem solving, etc.).
Last update: Mošna František, RNDr., Ph.D. (13.02.2023)
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Integral calculus - antiderivative, indefinite integral, calculation methods, Newton's and Riemann's definite integral, basic theorem of integral calculus Newton - Leibniz formula. Differential equation - existence, unicity of solution of differential equations, methods of solving (separation of variables, linear differential equations, variation of a constant), use of differetial equations. Series - convergence criteria (comparative, integral, quotient, square root, Leibniz), absolute convergence, sums of series. Sequences and series of functions - uniform convergence of sequences and series, Weierstrass criterion, power series, expansion of basic functions in power series, using for calculating limits. Last update: Mošna František, RNDr., Ph.D. (30.01.2023)
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https://dl1.cuni.cz/course/view.php?id=8039 Last update: Jančařík Antonín, doc. RNDr., Ph.D. (28.09.2019)
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