Course detail

# Mathematics 1

FP-ma1PAcad. year: 2024/2025

The subject is part of the theoretical basis of the field. Learning outcomes of the course unit The aim of the course is to unify and supplement the students' knowledge in the areas of further teaching of basic mathematical concepts and to teach students the comprehension of using the linear algebra system to solve the linear equations and the differential functions of one variable (including basic applications in economic disciplines).

Language of instruction

Number of ECTS credits

Mode of study

Guarantor

Department

Entry knowledge

Rules for evaluation and completion of the course

Credit requirements:

Passing control tests and achieving at least 55% points or passing a comprehensive written work and achieving at least 55% points.

Awarding credit is a necessary condition for taking the exam.

Exam requirements:

The exam has a written and an oral part, with the focus of the exam being the oral part.

For all tasks in the written part, the calculation must be written down, or the procedure must be described, or the result must be justified verbally. The examples are divided into thematic groups. If the student does not achieve at least 50% of the total number of achievable points in each thematic group of examples, the written part and the entire exam are graded "F" (unsatisfactory) and the student does not proceed to the oral part.

If the student does not achieve at least 55% of the total number of achievable points in the written work, the written part and the entire exam are graded "F" (unsatisfactory) and the student does not proceed to the oral part.

The oral part, focused on knowledge of the theory, follows the written part, and also serves to resolve any ambiguities in the written part.

Completion of the subject for students with individual study:

Passing the comprehensive control test and achieving at least 55% points.

Awarding credit is a necessary condition for taking the exam.

The exam has a written and an oral part, with the focus of the exam being the oral part.

For all tasks in the written part, the calculation must be written down, or the procedure must be described, or the result must be justified verbally. The examples are divided into thematic groups. If the student does not achieve at least 50% of the total number of achievable points in each thematic group of examples, the written part and the entire exam are graded "F" (unsatisfactory) and the student does not proceed to the oral part.

If the student does not achieve at least 55% of the total number of achievable points in the written work, the written part and the entire exam are graded "F" (unsatisfactory) and the student does not proceed to the oral part.

The oral part, focused on knowledge of the theory, follows the written part, and also serves to resolve any ambiguities in the written part.

Participation in exercises is controlled.

Aims

The acquired knowledge and practical mathematical skills will in particular serve as a basis for acquiring knowledge and disseminating skills in economically oriented fields and for the correct use of mathematical software, and will be an important starting point for learning new knowledge in math mathematical subjects.

Study aids

Viz. literature

Prerequisites and corequisites

Basic literature

Marošová,M. - Mezník,I.: Cvičení z matematiky I. 2. vydání, FP VUT v Brně, Brno 2008 (CS)

Recommended reading

Elearning

**eLearning:**currently opened course

Classification of course in study plans

#### Type of course unit

Lecture

Teacher / Lecturer

Syllabus

1. Matrices (properties, matrix operations, rank calculation and inverse matrices)

2. Determinants (properties, rules and calculation of determinants)

3. Systems of linear equations (solvability, GEM and Cramer's rule)

4. Functions of one variable (basic characteristics of functions, properties, rational operations with functions, composite, simple, inverse functions, properties)

5. Elementary functions, constructions and displacements of graphs

6. Polynomials (roots of a polynomial and their determination, Horner's scheme)

7. Summary (linear algebra, basic properties of functions)

8. Sequences (bounded and monotonic sequences of real numbers, sequence limit)

9. Limit and continuity of a function (eigen and non-eigen limits at an eigen and non-eigen point, basic properties and rules for calculation, continuity at a point and on an interval, properties and rules for calculating with continuous functions)

10. Derivation of the 1st order (meaning, basic properties and rules, derivation of elementary functions)

11. Summary (properties of functions, polynomials, limits and continuity of functions)

12. Differential (differential and its use)

13. Derivatives of higher orders (derivatives of higher orders, l'Hospital's rule)

Exercise

Teacher / Lecturer

Syllabus

1. Basic mathematical concepts

2. Matrices (properties, matrix operations, rank calculation and inverse matrices)

3. Determinants (properties, rules and calculation of determinants)

4. Systems of linear equations (solvability, GEM and Cramer's rule)

5. Functions of one variable (basic characteristics of functions, properties, rational operations with functions, composite, simple, inverse functions)

6. Elementary functions, constructions and displacements of graphs

7. Repetition (linear algebra, basic properties of functions)

8. Polynomials (roots of a polynomial and their determination, Horner's scheme)

9. Sequences (bounded and monotonic sequences of real numbers, sequence limit)

10. Limit and continuity of a function (limit at a proper point, basic properties and rules for calculation, continuity at a point and on an interval)

11. Limit at a non-proprietary point (basic properties and rules for calculation)

12. Derivation of the 1st order (meaning, basic properties and rules, derivation of elementary functions)

13. Differential (differential and its use)

Elearning

**eLearning:**currently opened course