# Mathematics I

**ECTS credits:** 5

**Lectures:** 2

**Exercises:** 2

### Course objective:

Acquiring mathematical reasoning, consolidating important elements of high school mathematics, acquiring fundamentals of differential and integral calculus, and fundamentals of vector and matrix calculus.

### Course contents:

MATHEMATICAL LANGUAGE. Arithmetic expressions. Algebraic expressions. Equations. Qualitative, analytical and numerical solving of equations. The concept of function – function rule, function graph, domain, set of values. Continuity. Signs of functions. Increase, decrease and extrema. Concavity and inflection points. Limiting behaviour and the concept of limit. ELEMENTARY FUNCTIONS. Linear function. Square function. Polynomials and rational functions. Roots and powers. Exponential and logarithmic functions. Trigonometric and arcus functions. DIFFERENTATION. The concept of differentiation. Differential calculus. Mechanical applications of differentiation. INTEGRAL. The concept of an indefinite integral and basic calculating rules. Mechanical applications of an indefinite integral. The concept of a definite integral and basic calculating rules. Mechanical applications of a definite integral. Basic calculating rules. DIFFERENTIAL EQUATIONS. Basic concepts. A separation method. VECTORS. The concept of vectors. Vector operations, their geometric interpretations and calculus. MATRICES. Linear equation systems. Matrix algebra. Geometry of matrices.

### Competences:

Understanding and using mathematical language, understanding and using mathematical software, understanding and using the concept of a function, knowledge of elementary functions and the application of their properties in a given context, understanding and applying differential and integral calculus to the analysis of unequal processes, understanding and applying differential equations to the modelling of continuous deterministic processes, applying vectors in geometry and physics, understanding and applying matrices to the solving of linear equation systems and to the representation of affine transformations.

### Learning outcomes:

Having passed the exam, students will be able to: 1. Formulate the problem in mathematical language in the form of an expression, equation, differentiation, integral, differential equation, system of linear equations, vector and matrix expression (study outcome). 2. Use a quality, analytical and numerical approach when solving a problem (study outcome). 3. Identify the properties of a function from its graph. 4. Identify elementary functions in a problem and apply their properties. 5. Solve an equation or a system of equations, either individually or on the computer. 6. Solve a differentiation and an integral, either individually or on the computer. 7. Solve a differential equation, either individually or on the computer. 8. Solve a vector expression, either individually or on the computer. 9. Solve a matrix expression, either individually or on the computer. 10. Use abstraction in the problem analysis. These learning outcomes contribute to the following outcomes of the study programme of motor vehicle maintenance: - Present a motor vehicle status analysis. - Use teamwork skills in motor vehicle servicing. - Use computer technology in the resolution of motor vehicle issues. These learning outcomes contribute to the following outcomes of the study programme of aircraft maintenance: -Apply the concept of a quality system in an airline company or an aircraft maintenance organisation. -Make a diagram of change of the centre of gravity in compliance with the aircraft design performances, and with the operational limitations for aircraft flying and maintenance. -Solve problems and tasks in the field of mechanics, thermodynamics, electrical engineering, aerodynamics and fluid mechanics, relating to aircraft operations. -Analyse errors in operational flying from the reliability programme in aircraft maintenance. -Use information technology and electronic methods for instructing and self-study. The aforementioned learning outcomes contribute to the following learning outcomes of the professional study program of Computer System Maintenance: - Apply the theoretical fundamentals of mathematics, physics, and electrical engineering in computer science