Selected Chapters from Mathematics (FSI-0KM)

Academic year 2025/2026
Supervisor: doc. Mgr. Petr Vašík, Ph.D.  
Supervising institute: ÚM all courses guaranted by this institute
Teaching language: Czech
Aims of the course unit:

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.
Learning outcomes and competences:
 
Prerequisites:
 
Course contents:

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
Teaching methods and criteria:
 
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.
Controlled participation in lessons:
 
Type of course unit:
    Lecture  13 × 2 hrs. compulsory                  
Course curriculum:
    Lecture 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.
Literature - fundamental:
1. Rektorys K. a spol.: Přehled užité matematiky I,II (SNTL, 1988)
2. Eliáš J., Horváth J., Kajan J. : Zbierka úloh z vyššej matematiky I, II, III, IV (Alfa Bratislava, 1985)
Literature - recommended:
1. Kříž, J., Křížová, H.: Matematika- vybrané statě k zahájení studia na strojní fakultě (skriptum VUT)
1. Děmidovič B. P.: Sbírka úloh a cvičení z matematické analýzy
2. Eliáš J., Horváth J., Kajan J. : Zbierka úloh z vyššej matematiky I, II, III, IV (Alfa Bratislava, 1985)
The study programmes with the given course:
Programme Study form Branch Spec. Final classification   Course-unit credits     Obligation     Level     Year     Semester  
B-FIN-P full-time study --- no specialisation -- Cr 2 Elective 1 1 W
B-MAI-P full-time study --- no specialisation -- Cr 2 Elective 1 1 W
B-MET-P full-time study --- no specialisation -- Cr 2 Elective 1 1 W
B-PDS-P full-time study --- no specialisation -- Cr 2 Elective 1 1 W
B-PRP-P full-time study --- no specialisation -- Cr 2 Elective 1 1 W
B-ZSI-P full-time study STI Fundamentals of Mechanical Engineering -- Cr 2 Elective 1 1 W
B-ZSI-P full-time study MTI Materials Engineering -- Cr 2 Elective 1 1 W
B-ENE-P full-time study --- no specialisation -- Cr 2 Elective 1 1 W
B-KSI-P full-time study --- no specialisation -- Cr 2 Elective 1 1 W
B-VKP-P full-time study --- no specialisation -- Cr 2 Elective 1 1 W
B-VTE-P full-time study --- no specialisation -- Cr 2 Elective 1 1 W
B-STR-P full-time study AIŘ Applied Computer Science and Control -- Cr 2 Elective 1 1 W
B-STR-P full-time study KSB Quality, Reliability and Safety -- Cr 2 Elective 1 1 W
B-STR-P full-time study SSZ Machine and Equipment Construction -- Cr 2 Elective 1 1 W
B-STR-P full-time study STG Manufacturing Technology -- Cr 2 Elective 1 1 W