Course detail

Mathematics 1

FEKT-BKC-MA1Acad. year: 2024/2025

Vectors spaces, linear combination, linear dependence, basis and dimension of vector space. Matrices and systems of linear equations. Limit, continuity, derivative, l´Hospital's rule, Taylor polynomial, behavior of function. Antiderivative, indefinite integral. Definite integral and its applications. Improper integral. Number series, power series, Taylor series.

Language of instruction

Czech

Number of ECTS credits

7

Mode of study

Not applicable.

Guarantor

RNDr. Petr Fuchs, Ph.D.

Department

Department of Mathematics (UMAT)

Entry knowledge

Students should be able to work with expressions and elementary functions within the scope of standard secondary school requirements; in particular, they shoud be able to transform and simplify expressions, solve basic equations and inequalities, and find the domain and the range of a function.

Rules for evaluation and completion of the course

Maximum 20 points for individual assignments during the semester (at least 5 points for the course-unit credit); maximum 80 points for a written exam.

Aims

The goal of the course is to explain basic concepts and computational methods of linear algebra and differential and integral calculus.

Study aids

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

Not applicable.

Recommended literature

Not applicable.

Classification of course in study plans

  • Programme BKC-EKT Bachelor's 1 year of study, winter semester, compulsory
  • Programme BKC-MET Bachelor's 1 year of study, winter semester, compulsory
  • Programme BKC-TLI Bachelor's 1 year of study, winter semester, compulsory

Type of course unit

 

Lecture

52 hod., optionally

Teacher / Lecturer

RNDr. Petr Fuchs, Ph.D.

Syllabus

1. Základní matematické pojmy, funkce a posloupnosti.
2. Vektory, kombinace, závislost a nezávislost vektorů, báze a dimenze vektorového prostoru.
3. Matice a determinanty.
4. Soustavy lineárních rovnic a jejich řešení.
5. Diferenciální počet funkcí jedné proměnné, limita, spojitost, derivace.
6. Derivace vyšších řádů, Taylorův polynom.
7. L'Hospitalovo pravidlo, průběh funkce.
8. Integrální počet funkcí jedné proměnné, primitivní funkce, neurčitý integrál.
9. Integrace per partes, substituční metoda, integrace některých elementárních funkcí.
10. Určitý integrál a jeho aplikace.
11. Nevlastní integrál.
12. Číselné řady, kritéria konvergence.
13. Mocninné řady, Taylorovy řady.

Computer-assisted exercise

22 hod., compulsory

Teacher / Lecturer

RNDr. Petr Fuchs, Ph.D.

Project

4 hod., compulsory

Teacher / Lecturer

RNDr. Petr Fuchs, Ph.D.