ECTS credits: 4
Acquiring the knowledge of testing function flow and its application to the optimisation problems. Acquiring integration techniques and their application to the calculation of surface and volume. Solving second-order linear differential equations and the application to linear systems. Differentiation and integration of scalar functions with multiple arguments and vector functions of one or several arguments, with the application to the mathematical formulation of classical mechanics and classical electrodynamics.
TESTING FUNCTION FLOW. Limit calculus and limiting behaviour. Increase, decrease and extrema. Optimum problems. Concavity and inflection points. Drawing a qualitative graph analytically and with the help of a computer. INTEGRATION TECHNIQUES. Substitution. Partial integration. Integration methods. SECOND-ORDER LINEAR DIFFERENTIAL EQUATIONS. With constant coefficients and simpler free members. SINGLE ARGUMENT VECTOR FUNCTIONS: derivative and integrated. Application to motion and curves. MULTI-ARGUMENT SCALAR FUNCTIONS: partial derivatives. Tangential plane and differential. Directional differentiations and gradient. Double and triple integrals. INTEGRATION ON CURVES AND PLANES of scalar and vector fields. Conservative fields. BASIC THEOREMS OF VECTOR ANALYSIS. Theorems on gradient, divergence and rotation of the vector field and the application to basic laws of electromagnetism.
Analysis of function flow. Setting and solving optimisation problems. Solving complex integrals. Application to the calculation of surface and volume. Understanding and solving second-order linear differential equations, differentiation and integration on a part of the plane, a part of the space, on a curve and surface. Application to classical mechanics and electrodynamics. Use of the SageMath program package in solving these problems.
Having passed the exam, students will be able to: 1. Analyse function flow, analytically and using software. 2. Set and solve specific optimisation problems, analytically and using software. 3. Calculate more complex integrals, individually and using software. 4. Calculate figure surface areas and body volumes, individually and using software. 5. Solve second-order linear differential equations with constant coefficients, individually and using software. 6. Calculate various differentiations (partial, directional, gradient, divergence and rotation) of one or several argument scalar and vector functions. 7. Calculate various integrals (partial, directional, gradient, divergence and rotation) of one or several argument scalar and vector functions. 8. Identify the mathematical apparatus in basic equations of classical mechanics and electrodynamics. 9. Apply mathematical concepts to the analysis and modelling of multi-dimensional problems. 10. Use techniques of differentiation, integration and solving linear differential equations in obtaining the final solution of the problem. 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 outcomes of the professional study program of Computer System Maintenance: -Apply the theoretical fundamentals of mathematics, physics, and electrical engineering in computer science