## MIN201 Mathematics II

Faculty of Science
Spring 2020
Extent and Intensity
4/2/0. 9 credit(s). Type of Completion: zk (examination).
Teacher(s)
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
Timetable
Mon 8:00–9:50 M5,01013, Tue 14:00–15:50 M6,01011
• Timetable of Seminar Groups:
MIN201/01: Wed 10:00–11:50 M6,01011, J. Slovák
Prerequisites
High school mathematics.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
there are 18 fields of study the course is directly associated with, display
Course objectives
The second part of the block of four courses in Mathematics. The entire course covers the fundamentals of general algebra and number theory, linear algebra, mathematical analysis, numerical methods, and combinatorics. This semester is concerned with the basic concepts of Calculus including numerical and applied aspects. The students will be able to work both practically and theoretically with the derivative and integral (indefinite and definite intergral) and use them for solving various applied problems and for the analysis of behavior of functions of one real variable. Students will understand the theory and use of infinite number series and functional series, they will also learn about applications of some integral transforms.
Learning outcomes
At the end of the course students will be able to:
work both practically and theoretically with the derivative and (indefinite and definite) integral ;
use calculus for solving various applied problems;
analyse the behavior of functions of one real variable;
understand the theory and use of infinite number series and power series;
use some integral transforms and Fourier series.
Syllabus
• 1. Creating the ZOO (4 weeks) – interpolation of data by polynomials and splines; axiomatics of real numbers; topology of real and complex numbers; scalar sequences, limits of sequenses and functions; continuity and derivatives; introduction of elementary functions via continuity; power series and goniometric functions;
• 2. Differential and integral Calculus (5 weeks) – higher order derivatives and Taylor expansion; extremes of functions; Riemann and Newton integration (area, volumes, etc.); uniform convergence and their consequences; Laurant series in complex variable; numerical derivatives and integration; stronger integration concepts
• 3. Continuous models (2 weeks) – aproximation of functions via orthogonal systems; Fourier series (including the numerical aspects); convolution (including numerical aspects), integral transforms, continuous and discrete Fourier transform
• 4. Metric spaces (2 weeks) - basic topological concepts, complete spaces, Banach fix point theorem, further comments
Literature
recommended literature
• SLOVÁK, Jan, Martin PANÁK and Michal BULANT. Matematika drsně a svižně (Brisk Guide to Mathematics). 1. vyd. Brno: Masarykova univerzita, 2013. 773 pp. ISBN 978-80-210-6307-5. doi:10.5817/CZ.MUNI.O210-6308-2013. Základní učebnice matematiky pro vysokoškolské studium info
• RILEY, K.F., M.P. HOBSON and S.J. BENCE. Mathematical Methods for Physics and Engineering. second edition. Cambridge: Cambridge University Press, 2004. 1232 pp. ISBN 0 521 89067 5. info
• Matematická analýza pro fyziky. Edited by Pavel Čihák. Vyd. 1. Praha: Matfyzpress, 2001. v, 320 s. ISBN 80-85863-65-0. info
Teaching methods
The lectures combining theory with problem solving will be based on material for individual learning, which should precede the lectures. Seminar groups devoted to solving computatinal/practical problems.
Assessment methods
Four hours of lectures, two hours of tutorial. Final written test followed by oral examination. Results of tutorials/homeworks are partially reflected in the assessment.
Language of instruction
Czech
Follow-Up Courses