The objective of the course is to acquire basic knowledge and master the basic methods of linear algebra, analytic geometry and mathematical analysis. Student should be able to apply the acquired knowledge from the above fields of mathematics in modeling of real problems from the field of technical sciences.

Upon completion of the course, the student has basic knowledge in algebra and mathematical analysis. The student understands the fundamental concepts and basic theorems from polynomials, linear equations, matrix calculus, free vectors, analytic geometry, real functions of real variables, definite and indefinite integrals and differential equations. He is able to solve tasks from the above fields and to follows courses in which algebra and mathematical analysis are applied. Acquired knowledge is used for solving mathematical models in professional courses.

Determinants, matrices and systems of linear equations. Analytic geometry in space. Real functions of real variables (limits, continuity, derivatives and their application). Definite and indefinite integrals (methods of integration, integration of rational and irrational functions and expressions with trigonometric, logarithmic and exponential functions, Newton-Leibniz formula, the application of definite integral). Differential equations of the first order (basic types, the initial problem). Differential equations of the higher order (lowering the order – the basic types, equations with constant coefficients).

Lectures, auditory practice, consultations with the course professor and assistant.