MDA201 Mathematics III

Přírodovědecká fakulta
jaro 2025
Rozsah
0/0/0. 12 kr. Ukončení: zk.
Vyučující
doc. Dr. Ioannis Chrysikos (přednášející)
prof. RNDr. Jan Slovák, DrSc. (přednášející)
Garance
prof. RNDr. Jan Slovák, DrSc.
Ústav matematiky a statistiky – Ústavy – Přírodovědecká fakulta
Dodavatelské pracoviště: Ústav matematiky a statistiky – Ústavy – Přírodovědecká fakulta
Předpoklady
the knowledge of MDA101 and MDA102 is expected
Omezení zápisu do předmětu
Předmět je otevřen studentům libovolného oboru.
Cíle předmětu
Continuation of the basic Mathematics block of the programme. The course aims at development of basic skills and knowledge in all four main approaches: algebraic, geometric, combinatorial, infinitesimal, as well as ability to enjoy the computer assisted solutions to problems. In particular, the course focuses on continuous mathematical modelling concepts and tools.
Výstupy z učení
understanding how to employ topology of metric spaces; more advanced concepts in mathematical analysis; more advanced computer assisted continuous modelling
Osnova
  • topology in context of metric spaces (2 weeks);
    calculus in more variables (constraint extrema, integration, general Stokes theorem - 4 weeks);
    ordinary differential equations (intro to qualitative approach, geometry of ODEs - 3 weeks);
    elements of partial differential equations (elementary classical methods, Cauchy-Kowalewska, etc. - 2 weeks);
    comments towards variational calculus and complex analysis (1 week);
    comments towards complex analysis (1 week)
Literatura
  • Jan Slovák et al, Brisk Guide to Mathematics, www.math.muni.cz/~slovak/BG.pdf, Chapters 7-9
Výukové metody
essentially asynchronous approach, based on introductory short presentations plus homework assignments, complete pdf materials, and Sage/Matlab supported tutorials;
complemented by synchronous communication with the tutor upon agreement
Metody hodnocení
weekly homework assignments during the semester, including peer to peer reviews;
active presentation of some homeworks to the lecturer/tutor;
two short synchronously written assignments during the term;
one final synchronously written assignment, followed by colloquial discussions/exams in small groups
Vyučovací jazyk
Angličtina
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