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

Language of instruction

Czech

Number of ECTS credits

2

Supervisor

doc. Mgr. Petr Vašík, Ph.D.

Department

Institute of Mathematics

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.

The study programmes with the given course

Programme B-KSI-P: Mechanical Engineering Design, Bachelor's, elective

Programme B-PDS-P: Industrial Design, Bachelor's, elective

Programme B-MAI-P: Mathematical Engineering, Bachelor's, elective

Programme B-PRP-P: Professional Pilot, Bachelor's, elective

Programme B-MET-P: Mechatronics, Bachelor's, elective

Programme B-VKP-P: Visual Communication in the Creative Industries, Bachelor's, elective

Programme B-ENE-P: Energy, Bachelor's, elective

Programme B-FIN-P: Physical Engineering and Nanotechnology, Bachelor's, elective

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

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

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

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

Programme B-STR-P: Engineering, Bachelor's
specialization STG: Manufacturing Technology, elective

Programme B-ZSI-P: Fundamentals of Mechanical Engineering, Bachelor's
specialization STI: Fundamentals of Mechanical Engineering, 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.