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.
- Quadratic equations and inequalities, Horner's scheme
- Vector product, matrices, determinant
- Inverse matrices, linear equations, systems of linear equations
- Exponential and logarithmic functions – formulas, graphs, equations
- Domain of a function
- Trigonometric functions, inverse trigonometric functions
- Analytical geometry – line, plane, circle, ellipse (center form, parametric equations)
- Derivative of a function
- Geometric interpretation of the derivative – slope of the tangent, local extrema, inflection points, asymptotes
- Parametric functions, Taylor polynomial, differential
- Indefinite integral – substitution, integration by parts
- Definite integral
- Applications of the definite integral
Language of instruction
Number of ECTS credits
Mode of study
Guarantor
Department
Entry knowledge
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
Basic literature
Rektorys K. a spol.: Přehled užité matematiky I,II (SNTL, 1988)
Recommended reading
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
Teacher / Lecturer
Syllabus
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.