Course detail

Selected Chapters from Mathematics

FSI-0KM Acad. year: 2025/2026 Winter semester

The subject reflects the content of the basic mathematics course, specifically the course 1M Mathematics I, in the first semester.

  1. Quadratic equations and inequalities, Horner's scheme
  2. Vector product, matrices, determinant
  3. Inverse matrices, linear equations, systems of linear equations
  4. Exponential and logarithmic functions – formulas, graphs, equations
  5. Domain of a function
  6. Trigonometric functions, inverse trigonometric functions
  7. Analytical geometry – line, plane, circle, ellipse (center form, parametric equations)
  8. Derivative of a function
  9. Geometric interpretation of the derivative – slope of the tangent, local extrema, inflection points, asymptotes
  10. Parametric functions, Taylor polynomial, differential
  11. Indefinite integral – substitution, integration by parts
  12. Definite integral
  13. Applications of the definite integral

Supervisor

doc. Mgr. Petr Vašík, 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

The course is concluded with a credit. The credit can be obtained by achieving a score of 50 % or higher on the test. The test is available to course participants on the Elearning platform of the 0KM course and can be retaken.

The primary scheduling unit is a lecture, and attendance at lectures is recommended.

Language of instruction

Czech

Aims

The aim of the course is to review, supplement, and consolidate knowledge of those parts of high school mathematics that students find most challenging during their first year of studies at FME.

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

The study programmes with the given course

Programme B-ENE-P: Energy, Bachelor's
branch ---: no specialisation, 2 credits, elective

Programme B-KSI-P: Mechanical Engineering Design, Bachelor's
branch ---: no specialisation, 2 credits, elective

Programme B-PDS-P: Industrial Design, Bachelor's
branch ---: no specialisation, 2 credits, elective

Programme B-MAI-P: Mathematical Engineering, Bachelor's
branch ---: no specialisation, 2 credits, elective

Programme B-MET-P: Mechatronics, Bachelor's
branch ---: no specialisation, 2 credits, elective

Programme B-PRP-P: Professional Pilot, Bachelor's
branch ---: no specialisation, 2 credits, elective

Programme B-FIN-P: Physical Engineering and Nanotechnology, Bachelor's
branch ---: no specialisation, 2 credits, elective

Programme B-STR-P: Engineering, Bachelor's
branch AIŘ: Applied Computer Science and Control, 2 credits, elective

Programme B-STR-P: Engineering, Bachelor's
branch KSB: Quality, Reliability and Safety, 2 credits, elective

Programme B-ZSI-P: Fundamentals of Mechanical Engineering, Bachelor's
branch MTI: Materials Engineering, 2 credits, elective

Programme B-STR-P: Engineering, Bachelor's
branch SSZ: Machine and Equipment Construction, 2 credits, elective

Programme B-STR-P: Engineering, Bachelor's
branch STG: Manufacturing Technology, 2 credits, elective

Programme B-ZSI-P: Fundamentals of Mechanical Engineering, Bachelor's
branch STI: Fundamentals of Mechanical Engineering, 2 credits, elective

Type of course unit

 

Lecture

26 hours, compulsory

Syllabus

Week 1: Quadratic equations, solving inequalities.
Week 2: Equations and inequalities with the absolute value.
Week 3: Goniometry, goniometric equations.
Week 4: Powers, exponencial equations.
Week 5: Logarithms, logarithmic equations.
Week 6: Conical sections.
Week 7: Analytic geometry.
Week 8: Systems of linear equations.
Week 9: Irrational equations and inequalities.
Week 10: Elemantary functions and graphs.
Week 11: Derivative of a function.
Week 12: Limits.
Week 13: The shape of a graph.