MDA102 Mathematics II

Faculty of Science
Autumn 2024
Extent and Intensity
0/0. 8 credit(s). Type of Completion: zk (examination).
Asynchronous teaching
Teacher(s)
doc. 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
no prerequisites
Course Enrolment Limitations
The course is offered to students of any study field.
Course objectives
The second basic introductory course of the Mathematics block of the programme. The five courses aim at the development of basic skills and knowledge in all four main approaches: algebraic, geometric, combinatorial, and infinitesimal, as well as the ability to enjoy computer-assisted solutions to problems. This course focuses on elementary infinitesimal concepts and tools.
Learning outcomes
understanding basic features of the real line and complex plane and convergence of values;
sound application of linear algebra concepts in infinitesimal analysis;
computer-assisted approach to simple continuous modelling, numerical methods, and approximations
Syllabus
  • polynomial interpolation (1 week);
    topology of the real line and the complex plane, convergence, spaces of elementary functions, and power series (3 weeks);
    elements of differential and integral calculus in 1D, including numerical aspects (5 weeks);
    Fourier series and Fourier transform in 1D (4 weeks)
Literature
  • Jan Slovák et al, Brisk Guide to Mathematics, www.math.muni.cz/~slovak/BG.pdf, Chapters 5-7
  • Ioannis Chrysikos et al, Script Project in Sage, available online, in preparation
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;
one short synchronously written assignments during the term;
one final synchronously written assignment, followed by colloquial discussions/exams in small groups
Language of instruction
English
Follow-Up Courses
Study support
https://is.muni.cz/auth/el/sci/podzim2024/MDA102/index.qwarp
Further comments (probably available only in Czech)
Study Materials
Teacher's information
https://is.muni.cz/auth/el/sci/podzim2024/MDA102/index.qwarp
The full information on study aid is collected in the interactive syllabi of the course, see https://is.muni.cz/auth/el/sci/podzim2024/MDA101/index.qwarp -- the study aid is dynamically completed during the semester, following the needs and feedback of the students, it is mainly based on texts, videos, home work assignements, code illustrative examples etc.
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