BASIC NOTIONS OF MATHEMATICS
Functions: concept of function, independent and dependent variables, composite functions, inverse function.
Elementary functions: graphs, geometric and analytical properties.
Limits of a function: finite to finite limit, limit from the right, limit from the left, finite limit to infinity, infinite limit to infinity.
Some theorems about limits: existence theorem for monotonous functions, comparison theorem, limits of elementary functions.
Continuous functions: definition of continuity, discontinuity of a function, types of discontinuity, continuity of elementary functions.
Derivatives of a function. Slope of a non-linear function: incremental ratio, rate of change of the function, derivative of a function, derivable functions, relationship between derivability and continuity, second derivative.
Calculation of derivatives and their algebra: derivative of a constant, derivative of a power functions. Formulas for other fundamental derivatives.
Differential: differential of a function and its geometrical meaning.
Integral calculus. Indefinite integral: integral function, primitive function, indefinite integral, linearity of the integral.
Methods of integration: some fundamental primitives, calculation of immediate integrals, integration by parts, integration by substitution.
Defined integrals: geometrical meaning, corollary of the fundamental formula of integral calculus, calculation of defined integrals.
ELEMENTS OF MECHANICS
Introduction to physics: physical quantities, measurement errors, orders of magnitude and significant figures. Error propagation.
Introduction to kinematics: position vector, definition of average speed and instantaneous speed. Definition of uniformly accelerated motion and parabolic motion. Definition and properties of Uniform Circular Motion. Description, characteristics and main parameters of uniformly accelerated circular motion and harmonic motion.
Introduction to Dynamics: Description of the 3 principles of dynamics, momentum, gravitational force. Definition of Dynamic Friction and Static Friction. Introduction to Viscous Friction and applications to centrifugation and elastic forces. Equations and fundamental parameters of the Simple Pendulum. Rigid body: definition of barycenter, momentum of forces. Moment of inertia and equation of rotational motion. Statics: conditions of translational and rotational stability.
Momentum of a pair of forces. Concept of field, definition of work of a force. Definition of kinetic energy and potential energy and related theorems. Mechanical energy, principles of conservation of energy. Dissipative forces and power of a force.
Fluid mechanics: Pascal's principle, Stevino's law, Archimedes' principle. Pressure measurements, definition and equations describing surface tension and capillarity. Equation of continuity, Bernoulli's Theorem, Torricelli's Theorem. Laminar and turbulent motion.
ELEMENTS OF THERMODYNAMICS
Boyle's law, Gay-Lussac, Equation of State of Perfect Gases, Real Gases and Van der Waals law. Dalton's law and concept of work in thermodynamics
Zero principle, definition of heat and temperature.
First principle of thermodynamics, heat capacity. Specific heat at constant volume and pressure, molar specific heat.
Second principle of thermodynamics: formulation of Lord Kelvin and Clausius. Efficiency of a thermal machine. Definition of entropy, formulation of the second principle of thermodynamics using the state function entropy. Order and disorder in natural systems.
ELEMENTS OF ELECTROMAGNETISM
Concept of charge, electrical induction, Coulomb force.
Definition of Electric Field: calculation of electric field for generic charge distribution. Electric dipole. Definition of flux of a vector and Gauss' Law. Potential Energy and Electric Potential, definitions, calculation of electric field from potential and vice versa.
Definition of capacitance. Series and parallel connections of capacitors: equivalent capacitance.
Electric current: Ohm's law, resistor connections in series and parallel. Electrical energy and power, Kirchhoff's laws, Joule effect.
Magnetic field: general introduction and Laplace's and Biot's and Savart's laws
Lorentz force, Ampere's theorem differences and similarities with the electrostatic field. Electromagnetic induction and Faraday-Newmann law.