Numerical sets (N, Z, Q and R), axiomatic construction of R, construction of N and principle of induction, complex numbers; elements of topology in R and Bolzano-Weierstrass theorem; real functions of real variable, limits of functions and their properties, limits of sequences, notable limits, the Napier number; continuous functions and their properties; derivative of functions and their properties, the fundamental theorems of differential calculus (Fermat, Rolle, Cauchy, Lagrange, de l'Hopital, Taylor's formula), convex / concave functions; function graph; Riemann integration and properties, integrability of continuous functions, fundamental theorem of integral calculus, integration by substitution and by parts, integration rules; numerical series, simple and absolute convergence, convergence criteria for series with positive terms and for series with any terms; Taylor series; improper integrals.

Analisi matematica I Marcellini-Sbordone
Analisi matematica I Pagani-Salsa
Esercitazioni di Matematica Marcellini-Sbordone

Numerical sets (N, Z, Q and R), axiomatic construction of R, construction of N and principle of induction, complex numbers; elements of topology in R and Bolzano-Weierstrass theorem; real functions of real variable, limits of functions and their properties, limits of sequences, notable limits, the Napier number; continuous functions and their properties; derivative of functions and their properties, the fundamental theorems of differential calculus (Fermat, Rolle, Cauchy, Lagrange, de l'Hopital, Taylor's formula), convex / concave functions; function graph; Riemann integration and properties, integrability of continuous functions, fundamental theorem of integral calculus, integration by substitution and by parts, integration rules; numerical series, simple and absolute convergence, convergence criteria for series with positive terms and for series with any terms; Taylor series; improper integrals.

Analisi matematica I Marcellini-Sbordone
Analisi matematica I Pagani-Salsa
Esercitazioni di Matematica Marcellini-Sbordone

1. Linear systems: matrix associated to a linear system; the sum of matrices and multiplication by real numbers; reduced matrices; Gauss-Jordan algorithm.
2. Rows by columns product of matrices; invertible matrices; the rank of a matrix; Rouché-Capelli Theorem.
3. Geometrical vectors. Vector spaces. Subspaces. Generating vectors and linearly independent vectors.
4. Basis of a vector space: the dimension of a vector space; Grassmann's formula.
5. Linear applications: Kernel and image of a linear application. Dimension of Kernel and Image of a linear application.
6. Matrix associated to a linear application. Diagonalization of linear operators.
7. Symmetric bilinear forms. Lengths, angles, orthogonality. Orthogonal and orthonormal bases. Gram-Schmidt algorithm.
8. Quadratic forms. Spectral Theorem. Diagonalization and classification of quadratic forms in a Euclidean space. Sylvester bases and Sylvester canonical form. Vector product in a Euclidean space of dimension three.
Analytic geometry in the plane and in space. Cartesian and parametric equations of linear spaces. Proper and improper sheaves of lines and planes. Determination of reciprocal position of linear varieties from their equations. Conics and quadrics.

Flamini-Verra "Matrici e vettori" Carocci ed.

* Basic concepts *
Problems and algorithms
Computer architecture
Languages and Compilation
I / O, variables and constants

* Operations *
Types of data
Expressions
Boolean algebra

* Control structures *
Selection
Iteration
Functions

* Data structures *
Array
Strings
Matrices

* Advanced concepts *
Integrated development environments
Libraries
File

The course uses the C and Python programming languages.

A. Bellini, A. Guidi, "Linguaggio C. Una guida alla programmazione con elementi di Python", VI Edizione, McGraw-Hill.

* Basic concepts *

Problems and algorithms
Computer architecture
Languages and Compilation
I / O, variables and constants



* Operations *

Types of data
Expressions
Boolean algebra



* Control structures *

Selection
Iteration
Functions



* Data structures *

Array
Strings
Matrices



* Advanced concepts *

Integrated development environments
Libraries
File


The course uses the C and Python programming languages.

A. Bellini, A. Guidi, "Linguaggio C. Una guida alla programmazione con elementi di Python", VI Edizione, McGraw-Hill.

Atom Structure: orbitals, poly-electron atoms, periodic table; covalent bond, delocalized bond.
Mass relationship in chemical reactions; redox and oxidation number.
Solids: metallic crystal, ionic crystal, molecular crystal, covalent crystal.
Gases: the ideal gas law, partial pressures.
Thermodynamics: nature and type of energy, the zero law of T.D., heat capacity, the first law of TD and Enthalphy, the second law of TD, entropy and free energy, equilibrium conditions.
Liquids: phase change, phase diagrams.
Chemical equilibrium: the equilibrium constant and the equilibrium law
Properties of liquid solutions: concentration units, the Raoult law and distillation, colligatives properties and freezing diagram, electrolytes.
Solutions of strong and weak electrolytes. Acids and bases, pH; Salt hydrolysis; buffer solutions.
Elettrochemistry

Tro, CHEMISTRY. A Molecular Approach, Pearson ED. or any general chemistry text, as long as it is of university level.

Introduction
- Physical quantities and units
- Fundamentals on vector algebra

Kinematics of a material point
- Kinematics quantities in the rectilinear motion
- Uniformly accelerated rectilinear motion
- Simple harmonic motion
- Kinematics in 2-D and 3-D
- Motion trajectory
- Tangential and normal components of acceleration
- Parabolic motion
- Circular motion
- Relative motion

Dynamics of a material point
- Principles of Dynamics and Newton's laws
- Momentum and Impulse
- Equilibrium and constraint reaction forces
- Gravitational force
- Weight and motion under gravity
- Forces and motion
- Forces of dry friction
- Inclined plane
- Elastic force and mass-spring system
- Tension force in ropes
- Applications to circular motion
- Viscous force
- Electrical charge and Coulomb force
- Simple pendulum
- Inertial and non-inertial reference frames
- Inertial forces

Work and Energy
- Work and power
- Work of weight, elastic and dry friction forces
- Work-energy theorem. Applications
- Conservative forces. Potential energy
- Central forces
- Gravitational and electrostatic potential energies
- Conservation of mechanical energy. Applications
- Stability conditions for static equilibrium

Dynamics of systems of material points
- systems of material points. Internal and external forces
- First cardinal equation for systems dynamics
- Center of mass and its motion
- Conservation of momentum
- Collisions (brief notes)
- Moment of a force and angular momentum
- Second cardinal equation for systems dynamics
- Conservation of angular momentum
- Koenig theorems

Rigid body dynamics
- Definition of rigid body and its properties
- Continuous bodies. Density and center of mass
- Rigid body kinematics. Angular velocity
- Rigid body dynamics. Rotations around a fixed axis
- Moment of inertia
- Huygens-Steiner theorem
- Compound pendulum
- Rolling motion
- Equilibrium for a rigid body

Thermodynamics
- Kinetic theory of ideal gases (brief notes)
- Temperature and pressure
- Thermodynamic systems and states
- Thermodynamic equilibrium
- Mechanical work and heat
- First law of thermodynamics
- Thermodynamic processes (adiabatic, reversible, irreversible)
- Heat capacity and specific heat
- Ideal gas law
- Specific heat of ideal gases
- Cyclic processes and the Carnot cycle
- Second law of thermodynamics
- Carnot's theorem
- Clausius theorem
- Entropy (brief notes)

P. Mazzoldi, M. Nigro, C. Voci, "Elementi di Fisica - Meccanica e Termodinamica, ed. Edises
C. Mencuccini, V. Silvestrini, "Fisica - Meccanica e Termodinamica", Ed. Ambrosiana

Economia aziendale: organizations and firms. The business context. Business strategy and value creation. Corporate governance and its institutional pillars. Business organizations and business combination. Internal control systems. General purpose annual reports objective and financial reporting assumptions and principles.

Avallone et al. (2022). Lessons of Business Administration and Accounting. Giappichelli, Turin.