Mathematic and Physics

For the Mathematics and Statistics part (48 h):
· Numeric sets;
· Operations on sets;
· Direct and inverse proportionality;
· Percentages;
· Radicals;
· Logarithms;
· Exponentials;
· First degree integer and fractional equations;
· Whole and fractional second degree equations;
· Equations of degree higher than the second;
· Integer and fractional systems of first degree equations;
· Integer and fractional systems of second degree equations;
· Whole and fractional first degree inequalities;
· Whole and fractional second degree inequalities;
· Systems of first degree integer and fractional inequalities;
· Systems of integer and fractional second degree inequalities;
· Elements of trigonometry;
· Limits;
· Derivatives;
· Elements of mathematical logic;
· Elements of Descriptive Statistics;
For the Physics part (32h):
· Preliminary elements: physical quantities; unit of measure; scientific notation and orders of magnitude; significant figures; scalar and vector quantities; operations with vectors (addition, subtraction, scalar product and vector product, decomposition).
· Kinematics: speed and acceleration (average and instantaneous); uniform rectilinear motion; uniformly accelerated motion; uniform circular motion and harmonic motion; parabolic motion.
· Dynamics of the material point: the three principles of dynamics (with practical applications); examples of forces: weight force, elastic force, constraint force, friction force; momentum; moment of a force; levers.
· Work and energy: definition of work; mechanical energy; kinetic energy and kinetic energy theorem; conservative forces; gravitational and elastic potential energy; conservation of mechanical energy and its applications.
· States of aggregation of matter: outline of intermolecular forces; qualitative description of the gaseous, liquid and solid states.
· States and dynamics of liquids: pressure; Pascal's law; Stevino's law; Archimedes' principle; scope; Bernoulli's theorem and its applications
· Thermodynamics: heat and temperature; mode of heat transmission; changes of state; thermal capacity and specific heat; particular transformations of a gas (isobar, isochore, isothermal and cyclic); equation of state for ideal gases; work of compression and expansion of a gas; internal energy; first and second law of thermodynamics; thermodynamic cycles; efficiency of a thermal machine.
· Electricity: electric charge and Coulomb's law; electric field of a point charge; electric field flux and Gauss' theorem; electric potential and electric potential energy; direct electric current; Ohm's laws; Kirchhoff's laws; solving electrical circuits.
· Magnetism: fundamental magnetic phenomena (wire crossed by current, coil and solenoid).