Course detail

Mathematical Seminar for Engineers

FSI-0MF Acad. year: 2025/2026 Summer semester

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.

Language of instruction

Czech

Number of ECTS credits

2

Supervisor

doc. Ing. Jiří Šremr, Ph.D.

Department

Institute of Mathematics

Entry knowledge

Linear algebra, differential and integral calculus.

Rules for evaluation and completion of the course

Absence tolerated based on an agreement with the teacher.

Condition for awarding of the course-unit credit: Active participation in seminars.

Aims

Aim of the course: The main aim of the seminar is to get students to:

  • think when solving problems requiring the use of a basic mathematical apparatus,
  • adopt a creative approach to solving problems,
  • "not be afraid" to try different solutions if the first idea does not lead to the goal.

Another goal is to show the students that there is often a difference between the ability to solve basic problems in a common "mathematical" formulation and the ability to solve a problem in which a suitable mathematical apparatus needs to be found.

Acquired knowledge and skills: The students will try applying the mathematical apparatus discussed in courses Mathematics I, II and BM to various problems that are solved in mechanics and other technical disciplines. After completing the course:

  • the students learn to think through the assignment and select essential information from the known facts,
  • the students will be able to create a "strategy" for solving the problems and choose the appropriate mathematical apparatus.

The students will also understand that even very simple tasks can be quite laborious and vice versa, so they could be better prepared to solve the problems in the follow-up courses, where there are usually many unknowns or parameters and the necessary mathematical apparatus is not part of the formulation of the studied problem.

The study programmes with the given course

Programme B-OBN-P: Common Offer, Bachelor's, elective

Type of course unit

 

Exercise

26 hours, compulsory

Syllabus

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.