MDA201 Mathematics III

Faculty of Science
Spring 2025
Extent and Intensity
0/0/0. 12 credit(s). Type of Completion: zk (examination).
Teacher(s)
Dr. Ioannis Chrysikos (lecturer)
prof. RNDr. Jan Slovák, DrSc. (lecturer)
Guaranteed by
prof. RNDr. Jan Slovák, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Prerequisites
the knowledge of MDA101 and MDA102 is expected
Course Enrolment Limitations
The course is offered to students of any study field.
Course objectives
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.
Learning outcomes
understanding how to employ topology of metric spaces; more advanced concepts in mathematical analysis; more advanced computer assisted continuous modelling
Syllabus
  • 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)
Literature
  • Jan Slovák et al, Brisk Guide to Mathematics, www.math.muni.cz/~slovak/BG.pdf, Chapters 7-9
Teaching methods
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
Assessment methods
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
Language of instruction
English
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