Course detail

Seminar on Applied Mathematics

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

The course is designed for students of the 2nd year od study, it follows topics in Mathematics I, II, III, BM and will introduce the students to the possibilities of using the basic mathematical apparatus in mathematical modelling in physics, mechanics and other technical disciplines. In seminars, some problems  will be selected that students have previously encountered, and these will be discussed in more detail from a mathematics point of view. Furthermore, mathematical modelling using differential equations as well as methods of analysis of the equations obtained will be shown.

Supervisor

doc. Ing. Jiří Šremr, Ph.D.

Department

Institute of Mathematics

Learning outcomes of the course unit

Prerequisites

Planned learning activities and teaching methods

Assesment methods and criteria linked to learning outcomes

Language of instruction

Czech

Aims

Specification of controlled education, way of implementation and compensation for absences

Type of course unit

 

Exercise

26 hours, compulsory

Syllabus

After agreement with the students, some of the following topics will be selected:



  • First-order partial differential equations, transport equation.

  • Sturm-Liouville problem for second-order ordinary differential equations.

  • Heat equation, Diffusion equation.

  • Wave equation in the plane, characteristics, initial value problem.

  • Bessel equation, Bessel functions.

  • Vibrations of a string and a membrane.

  • Equation of catenary.

  • First-order implicit differential equations, envelope of a family of curves.

  • Euler differential equation in stress-analysis of thick-walled cylindrical vessels and analysis of deformation of shells.

  • Green functions of two-point boundary value problem in analysis of bending of beams.

  • Fredholm property for periodic problems and stability of compressed bars.

  • Planar autonomous systems of ODEs: Stability and classification of equlilibria, phase portrait.

  • Linear oscillators with one degree of freedom, different kinds of damping.

  • Duffing equation, Jacobi elliptic functions.

  • Non-linear oscillators with one degree of freedom.

  • Linear oscillations with two degree of freedom.

  • Mathematical modelling of a population dynamic.

  • Mathematical modelling of motions of dislocations in crystals.