Matrices and vectors (calculations using matrices, determinants, invertible matrices; systems of linear equations, Cramer’s rule, Gaussian elimination; vectors in plane and space, scalar, vector and triple product; lines and planes in space). Linear transformations (presentation of linear transformations with a matrix, eigenvalues, eigenvectors). Tensors (definition, examples, operations between tensors, use). Curves and surfaces (curves in ... Read more
Introduction and historical overview: composition and operation of computers; peripheral hardware; software; programme languages and programming; fundamentals of operating systems; computer networks; computers and technological and measurement processes; Internet, protocols and services; user software.
Introduction: drawings and numbers in engineering. Monge projection: structural and metric tasks. Analytic geometry in space. Elevated projection (topographic maps).
Forces at the same point: assembly, dismantling, balance. Forces without a common point: assembly, pairs of forces – moment. Reduction of forces: system of forces in a point, the projection of moments onto any axis. Structural elements: classification, grading loads, supports, ties, degrees of freedom. Internal forces and load moments. Trusses. Contact friction. Stress vector ... Read more
Methods, definitions and basic concepts in chemistry. Atoms, molecules, ions and compounds. Basic chemical reactions and reactions in aqueous solutions. Thermochemistry. The electron composition of the atom, periodicity, chemical bonds and molecular structure. Gases, liquids and solids and intermolecular forces. Solutions. Basics of chemical kinetics. Chemical equilibrium. Acids and alkali. Spontaneity of chemical reactions. Electrochemistry. ... Read more
Introduction: scalar, vector quantities, units, measurements, measurement errors. Mechanics: forces and Newton’s laws (incl. adhesion and friction force, gravitation above and under the surface, between bodies), torque forces, examples from statics and dynamics; momentum (incl. jet force, opposing jet force, jet propulsion); angular momentum; work and energy (incl. elastic energy, rotational kinetic energy); elastic and ... Read more
Numbers (real numbers; complex numbers). Fundamentals of functions with one variable (basic concepts, calculations using functions, bijective function inversions, overview of elementary functions; continuous functions, limits). Derivatives (definition of a derivative and the derivatives of elementary functions, rules for derivations, the geometric meaning of a derivative, rising and falling functions, convexity/concavity, stationary points and their ... Read more