Course detail

Selected Chapters from Mathematics

FSI-0KMAcad. year: 2025/2026

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

Language of instruction

Czech

Number of ECTS credits

2

Mode of study

Not applicable.

Guarantor

doc. Mgr. Petr Vašík, Ph.D.

Department

Institute of Mathematics (ÚM)

Entry knowledge

Students are expected to have basic knowledge of secondary school mathematics.

Rules for evaluation and completion of the course

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.

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.

Study aids

On the Eearning platform, practice exercises are provided for each topic.

The literature is the same as that for the 1M Mathematics I course.

Prerequisites and corequisites

Not applicable.

Basic literature

Eliáš J., Horváth J., Kajan J. : Zbierka úloh z vyššej matematiky I, II, III, IV (Alfa Bratislava, 1985)
Rektorys K. a spol.: Přehled užité matematiky I,II (SNTL, 1988)

Recommended reading

Děmidovič B. P.: Sbírka úloh a cvičení z matematické analýzy
Eliáš J., Horváth J., Kajan J. : Zbierka úloh z vyššej matematiky I, II, III, IV (Alfa Bratislava, 1985)
Kříž, J., Křížová, H.: Matematika- vybrané statě k zahájení studia na strojní fakultě (skriptum VUT)

Classification of course in study plans

  • Programme B-FIN-P Bachelor's 1 year of study, winter semester, elective
  • Programme B-MAI-P Bachelor's 1 year of study, winter semester, elective
  • Programme B-MET-P Bachelor's 1 year of study, winter semester, elective
  • Programme B-PDS-P Bachelor's 1 year of study, winter semester, elective
  • Programme B-PRP-P Bachelor's 1 year of study, winter semester, elective

  • Programme B-ZSI-P Bachelor's

    specialization STI , 1 year of study, winter semester, elective
    specialization MTI , 1 year of study, winter semester, elective

  • Programme B-ENE-P Bachelor's 1 year of study, winter semester, elective
  • Programme B-KSI-P Bachelor's 1 year of study, winter semester, elective
  • Programme B-VKP-P Bachelor's 1 year of study, winter semester, elective
  • Programme B-VTE-P Bachelor's 1 year of study, winter semester, elective

  • Programme B-STR-P Bachelor's

    specialization AIŘ , 1 year of study, winter semester, elective
    specialization KSB , 1 year of study, winter semester, elective
    specialization SSZ , 1 year of study, winter semester, elective
    specialization STG , 1 year of study, winter semester, elective

Type of course unit

 

Lecture

26 hod., compulsory

Teacher / Lecturer

doc. Mgr. Petr Vašík, Ph.D.

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.