Course detail

Mathematics 2

FSI-Z2M Acad. year: 2025/2026 Summer semester

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

Conditions for awarding the course-unit credit (0-100 points, minimum 50 points):

  • two written tests (each maximum 50 points); students who fail to score 50 points in total will be allowed to resit the test during the first week of the examination period.

Conditions for passing the exam (0-100 points, minimum 50 points):

  • written test (maximum 85 points),
  • discussion about the test and the oral part of the exam (maximum 15 points),
  • maximum 100 points, the overall classification is given by ECTS grade scale.

Lecture: Attendance at lectures is obligatory and checked, only one unexpected absence is allowed, absence may be compensated for based on an agreement with the teacher.

Seminar: Attendance in seminars is obligatory and checked, only one unexpected absence is allowed, absence may be compensated for based on an agreement with the teacher.

Language of instruction

Czech

Aims

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

The study programmes with the given course

Programme B-KSI-P: Mechanical Engineering Design, Bachelor's
branch ---: no specialisation, 5 credits, compulsory

Type of course unit

 

Lecture

26 hours, compulsory

Syllabus


  • Improper Riemann integral.

  • First-order ordinary differential equations (basic notions, direction field, initial value problem, solving of some first-order non-linear differential equations).

  • Higher-order ordinary differential equations (basic notions, linear differential equations, solving of higher-order non-homogeneous linear equations with constant coefficients, initial and boundary value problems).

  • Systems of first-order linear differential equations (solving of homogeneous systems of first-order linear equations with constant coefficients).

  • Functions of more real variables (basic notions, graph, level curves, vector function, vector field).

  • Differential calculus of functions of more variables (partial derivatives, directional derivative, gradient, continuity, differential, tangent plane, linear and quadratic approximations, potential vector field, potential, differential operators).

  • Double integrals (double integral, Fubini theorem, change to polar coordinates, applications).

  • Real sequences, introduction to series (series of reals, convergence, sum, geometric serie, convergence tests, reminder).

Exercise

39 hours, compulsory

Syllabus


  • Improper Riemann integral.

  • Solving of selected types of first-order non-linear differential equations, examples of a possible use in geometry and physics.

  • Solving of higher-order non-homogeneous linear equations with constant coefficients, examples of a possible use in dynamics and problems of strength analysis.

  • Solving of homogeneous systems of first-order linear equations with constant coefficients, illustration of solutions in the phase space.

  • Basic properties of functions of more real variables, vector field, examples of a possible use in geometry and evaluation of line integrals.

  • Evaluation of partial derivatives, linear and quadratic approximations, potential vector field, potential function, local extremes, examples of a possible use in physics.

  • Evaluation of double integrals, change of variables, examples of a possible use in geometry and physics.

  • Limit of a sequence, convergence tests for series of reals.