Course detail

# Mathematics in Electrical Engineering 1

Vectors spaces, linear combination, linear dependence. Matrices and systems of linear equations. Limit, continuity, derivative, behavior of function. Antiderivative, indefinite integral. Definite integral and its applications. Number 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;
- translate a mathematical text in the above fields (from English to Czech and vice versa).

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. The knowledge of English at intermediate level is required.

Co-requisites

Not applicable.

Recommended optional programme components

Not applicable.

Not applicable.

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 30 points for the total of 2 tests written during the semester (at least 10 points for the course-unit credit). The exam can be taken only if the score is 10 or better. Maximum 70 points for a written exam.

In case of coronavirus restrictions resulting in the impossibility to write a test in person at faculty premises, work during the semester will be awarded by:
- maximum 15 points in case of only 1 test
- 0 points in case of no test
The exam can be taken if the score will be 5 or better (in case of 1 test), or all students will be able to take the exam (in case of no tests). Maximum points for the exam will be such that the total of 100 points is reached.

Language of instruction

Czech, English

Work placements

Not applicable.

Course curriculum

1. Basic mathematical concepts.
2. Vectors, linear combination and dependence of vectors.
3. Matrices and determinants.
4. Systems of linear equations and their solutions.
5. Limit and continuity of function.
6. Derivatives.
7. Behaviour of function.
8. Antiderivative, indefinite integral.
9. Definite integral and its applications.
10. Number series, convergence tests.

Aims

The goal of the course is to explain basic concepts and computational methods of linear algebra and differential and integral calculus. The students will further learn to translate mathematical texts in the above fields (from English to Czech and vice versa).

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

Lectures are not compulsory, practice classes are compulsory.

Classification of course in study plans

• Programme AJEI-H Bachelor's

branch H-AEI , 1. year of study, winter semester, 5 credits, compulsory

#### Type of course unit

Lecture

26 hours, optionally

Teacher / Lecturer

Computer-assisted exercise

26 hours, compulsory

Teacher / Lecturer

eLearning

eLearning: opened course