Course detail

# Mathematics 1

FEKT-BKC-MA1Acad. year: 2020/2021

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.

Learning outcomes of the course unit

After completing the course, students should be able to:
- decide whether vectors are linearly independent and whether they form a basis of a vector space;
- add and multiply matrices, and compute the determinant and the inverse of a square matrix;
- solve a system of linear equations;
- differentiate and find the tangent to the graph of a function;
- sketch the graph of a function including extrema, points of inflection and asymptotes;
- integrate using basic formulas including integration by parts;
- evaluate a definite integral using the Fundamental Theorem of Calculus;
- compute the area of a region using the definite integral;
- discuss the convergence of a number series.

Prerequisites

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.

Co-requisites

Not applicable.

Recommended optional programme components

Not applicable.

Recommended or required reading

Krupková, Fuchs: Matematika 1 (CS)
Kolářová: Matematika 1 – Sbírka úloh (CS)

Planned learning activities and teaching methods

Teaching methods are specified in Article 7 of Study and Examination Regulations.

Assesment methods and criteria linked to learning outcomes

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.

Language of instruction

Czech

Work placements

Not applicable.

Course curriculum

1. Basic mathematical concepts, functions and sequences.
2. Vectors, combination, dependence and independence of vectors, basis and dimension of vector space.
3. Matrices and determinants.
4. Systems of linear equations and their solutions.
5. Differential calculus of one variable, limit, continuity, derivative.
6. Derivatives of higher orders, Taylor polynomial.
7. L'Hospital's rule, behaviour of function.
8. Integral calculus of one variable, antiderivative, indefinite integral.
9. Integration by parts, substitution method, integration of some elementary functions.
10. Definite integral and its applications.
11. Improper integral
12. Number series, convergence tests.
13. Power series, Taylor series.

Aims

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

Specification of controlled education, way of implementation and compensation for absences

Tutorials are not compulsory.

Classification of course in study plans

• Programme BKC-EKT Bachelor's, 1. year of study, winter semester, 7 credits, compulsory
• Programme BKC-MET Bachelor's, 1. year of study, winter semester, 7 credits, compulsory
• Programme BKC-TLI Bachelor's, 1. year of study, winter semester, 7 credits, compulsory

#### Type of course unit

Lecture

52 hours, optionally

Teacher / Lecturer

Computer-assisted exercise

22 hours, compulsory

Teacher / Lecturer

Project

4 hours, compulsory

Teacher / Lecturer