MATHEMATICS

Elements of Combinatorics:
Arrangements, permutations and simple combinations, binomial coefficients, definitions and properties.

Matrices and Determinants:
Definitions and properties of matrices, diagonal matrices, transposed, opposite and inverse matrices. Operations on matrices, determinants, Laplace's theorems, Sarrus' rule, general properties of determinants, minor and rank or characteristic of a matrix.

Systems of Linear Equations:
Generalities on systems of linear equations, Rouchè-Capelli theorem, Cramer's theorem, systems of m equations in n unknowns, homogeneous systems.

Real Variable Functions:
Trigonometric functions, compound functions, inverse functions, limits of a function, theorems on limits, the uniqueness of the limit, theorem of the permanence of the sign, theorem of comparison, limit of the sum, of the product, of the quotient, etc. .. of functions, notable limits.

Continuous Functions:
Definitions and first properties, continuity, Neper's number, maxima and minima, inverse function.

Derivatives:
Definition and geometric meaning of the derivative, operations on derivatives and derivation rules, derivation of trigonometric functions, derivation of compound and inverse functions, differentiability and continuity, differential, successive derivatives, relative maxima and minima, asymptotes, concavity and convexity, inflections, graphs of functions.
Theorems of Rolle, Cauchy, Lagrange, De L'Hopital, indeterminate forms.

Trascendent Functions:
Inverse trigonometric functions, logarithm function, exponential function, hyperbolic functions.

Imtegration:
Indefinite integral, definition and properties, relationship between integrability and derivability, immediate integrals, definite integral.

ELEMENTS OF PHYSICS

Description of reality: models, theories, laws and measures; The international system of measurement; Scalar quantities and vector quantities; sum and difference of vectors; decomposition of vectors along assigned directions; dot product, vector product, mixed product.

Kinematics:
Generality. Motion of the material point. Coordinate systems. Linear speed and acceleration. Uniform and varied circular motion; speed and angular acceleration.

Dynamics:
Newton's laws (I, II and III) and their applications. Dynamics of the material point. Friction forces. Work and kinetic energy. Conservative forces. Potential energy; conservation of energy. Power. dissipative forces. Momentum and its conservation; bumps and their classification. Motion of rigid systems and equilibrium conditions. Moment of inertia and angular momentum for rotations about a fixed axis; moment of forces; second cardinal law of system mechanics. Kinetic energy; rolling and the role of friction. Work and Power.

Fluids:
Fluid statics and applications. Fluid dynamics: flow, law of conservation of flow. Bernoulli's theorem and applications. Real fluids: surface tension and capillarity.

A. M. Bigatti, L. Robbiano. Matematica di base. Casa Editrice Ambrosiana (Milano).
D. Halliday, R. Resnick, J. Walker. Fondamenti di Fisica. (Volume I, Meccanica e Termologia). Casa Editrice Ambrosiana (Milano).