## MIN301 Mathematics III

Faculty of Science
Autumn 2020
Extent and Intensity
4/2/0. 9 credit(s). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Jan Slovák, DrSc. (lecturer)
doc. Mgr. Josef Šilhan, Ph.D. (seminar tutor)
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
Wed 8:00–9:50 M1,01017, Fri 13:00–14:50 M1,01017
• Timetable of Seminar Groups:
MIN301/01: Tue 12:00–13:50 M6,01011, J. Šilhan
Prerequisites
Recommended: knowledge of elementary functions, polynomials, rational functions. Further the elements of matrix calculus, as well as knowledge of vector spaces and linear mappings and basic tools of Calculus in one real variable. (MIN101 a MIN201)
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 19 fields of study the course is directly associated with, display
Course objectives
This is the third part of a four semester block of 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 Calculus in more variables and (ordinary) differential equations and, in the second half, graph theory including selected applications.
Learning outcomes
At the end of this course, students should be able to:
use methods of calculus in the case of functions in more variables, including integration over curves and surfaces; solve basic optimization problems; exploit differential equations in continuous modeling;
understand basic concepts of the graph theory and apply basic graph algorithms; manage simple usage of generating functions in combinatorial computations
Syllabus
• Calculus in more variables (5 weeks)- partial derivatives, differential, integral calculus in more variables, selected applications of Calculus
• Ordinary differential equations (3 weeks) - scalar and vector differential equations, numerical solutions.
• Graph theory (5 weeks) - elementary concepts; selected graph algorithms; generating functions
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 : a comprehensive guide. 2nd ed. Cambridge: Cambridge University Press, 2002. xxiii, 123. ISBN 0-521-81372-7. info
not specified
• MATOUŠEK, Jiří and Jaroslav NEŠETŘIL. Kapitoly z diskrétní matematiky. Čtvrté, upravené a dopln. Praha: Karolinum, 2009. 442 stran. ISBN 9788024617404. info
• PLCH, Roman, Zuzana DOŠLÁ and Petr SOJKA. Matematická analýza s programem Maple. Díl 1, Diferenciální počet funkcí více proměnných. (The Multivariable Calculus with program Maple. Part 1, Differencial calculus). prvni. Brno: Masarykova Universita, 1999. 80 pp. ISBN 80-210-2203-5. URL 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