Mathematical Seminar for Engineers (FSI-0MF)

Academic year 2025/2026
Supervisor: doc. Ing. Jiří Šremr, Ph.D.  
Supervising institute: ÚM all courses guaranted by this institute
Teaching language: Czech
Aims of the course unit:
 
Learning outcomes and competences:
 
Prerequisites:
 
Course contents:

The course is designed for students of the 1st year of study, it supplements courses Mathematics I, II, BM. Within the seminar, slightly different problems than typical "algorithmic" tasks will be solved; the problems will be formulated in such a way that students are forced to find the necessary mathematical apparatus on their own. However, there will be no difficult or tricky problems from mathematical competitions, the problems will be inspired by those solved in physics, mechanics and other technical disciplines, in which many unknowns or parameters usually occur and that can be solved in different ways.
Teaching methods and criteria:
 
Assesment methods and criteria linked to learning outcomes:
 
Controlled participation in lessons:
 
Type of course unit:
    Exercise  13 × 2 hrs. compulsory                  
Course curriculum:
    Exercise

The course is taught in the form of seminars with an emphasis on mutual cooperation and discussion.


Some of the discussed topics:


A possible use of complex numbers in geometry.
Vectors in solid mechanics.
Vector functions in dynamics of motion.
Positive /negative definiteness of matrices, criteria for local extremes of functions of several variables.
Method of Lagrange multipliers.
Optimization problems in mechanics.
Determinants in stability of equlibria of dynamical systems.
Linearization in models of population dynamics.
Mathematical modelling in evaluation of geometric characteristics in mechanics.
Applications of line and surface integrals.
Literature - fundamental:
1.

STEWART, James, Daniel CLEGG a Saleem WATSON. Calculus: early transcendentals. 9th Edition. Australia: Cengage, 2021, xxx, 1214 stran, A158 : ilustrace, grafy. ISBN 978-0-357-11351-6.
Literature - recommended:
1.

MUSILOVÁ, Jana a Pavla MUSILOVÁ. Matematika I: pro porozumění i praxi. 2., dopl. vyd. Brno: VUTIUM, 2009, xi, 339 s. : barev. il. ; 26 cm. ISBN 978-80-214-3631-2.
2.

MUSILOVÁ, Jana a Pavla MUSILOVÁ. Matematika pro porozumění i praxi: netradiční výklad tradičních témat vysokoškolské matematiky. II/1-2. Brno: VUTIUM, 2012, xiv, 341 s. : barev. il. ISBN 978-80-214-4071-5.
The study programmes with the given course:
Programme Study form Branch Spec. Final classification   Course-unit credits     Obligation     Level     Year     Semester  
B-OBN-P visiting student --- no specialisation -- Cr 2 Elective 1 1 S