REAL NUMBERS AND RELATIVE TOPOLOGY, REAL FUNCTIONS OF A REAL VARIABLE, FUNCTIONAL LIMITS, DIFFERENTIABILITY, INTEGRAL, TAYLOR FORMULA, COMPLEX NUMBERS, NUMERICAL SERIES.

A. Laforgia, Calcolo differenziale e integrale, Ed. Accademica;
P. Marcellini e C. Sbordone, Esercizi di Matematica, Vol. 1, tomi 1--4, Ed. Liguori;

Number sets (N,Z,Q and R), axiomatic construction of R via supremum, Archimedean property, density of Q in R, construction of N and the inductive method, binomial formula and combinatorial calculus, real powers, Bernoulli inequality; topological concepts in R (accumulation and isolated points, open/closed sets and characterization, closure of a set) and Bolzano-Weierstrass theorem; complex numbers, polar representation and n-roots of unity; real functions with a real variable, domain, image and inverse functions; limits for functions and properties, limits of monotone functions; limits for sequences, special limits, the Napier number, the bridge theorem, limsup/liminf, sequences and topology, compact sets and characterization; continuous functions and their properties, continuity of the elementary functions, types of discontinuities and monotone functions, fundamental theorems on the continuous functions (zeroes, of intermediate values, Weierstrass); derivative of a function and properties, derivatives of elementary functions, fundamental theorems of the differential calculus (Fermat, Rolle, Cauchy, Lagrange, de l'Hopital, Taylor formula), monotonicity and sign of the derivative, degenerate local maxima/minima, convex/concave functions; graph of a function; Riemann integration and properties, integrability of continuous functions, primitives for elemntary functions, I and II fundamental theorems of the integral calculus, change of variables and integration by parts, rational functions, some special change of variables; series and convergence, geometric series, convergence criteria for positive series (comparison, asymptotic comparison, root, quotient, condensation) and for generic series (absolute convergence, Leibnitz); Taylor series, series of some elemtnary functions; improper integrals.

Analisi Matematica 1, C.D. Pagani, S. Salsa, editore Zanichelli
Analisi Matematica 1, E. Giusti, editore Bollati Boringhieri
Funzioni Algebriche e Trascendenti, B. Palumbo, M.C. Signorino, editore Accademica
Analisi Matematica, M. Bertsch, R. Dal Passo, L. Giacomelli, editore MCGraw-Hill

REAL NUMBERS AND RELATIVE TOPOLOGY, REAL FUNCTIONS OF A REAL VARIABLE, LIMITS OF FUNCTIONS, DIFFERENTIABILITY, INTEGRALS, TAYLOR FORMULA, COMPLEX NUMBERS, NUMERICAL SERIES.

A. Laforgia, Calcolo differenziale e integrale, Ed. Accademica;
P. Marcellini e C. Sbordone, Esercizi di Matematica, Vol. 1, tomi 1--4, Ed. Liguori;

1- Linear systems: matrix associated to a linear system; sum of matrices and multiplication by real numbers; reduced matrices; Gauss-Jordan algorithm.
2- Rows by columns product of matrices; invertible matrices; rank of a matrix; Rouche'-Capelli Theorem.
3- Geometrical vectors. Vector spaces. Subspaces. Generating vectors and linearly independent vectors.
4- Basis of a vector space: dimension of a vector space; Grassmann's formula.
5- Linear applications: Kernel and image of a inear application. Dimension of Kernel and Image of a linear application.
6- Matrix associated to a linear application. Diagonalization of linear operators.

S. Lang: "Linear Algebra" - Springer ed

Systems and linear systems of equations. Matrices with real elements. Properties and operations of matrices. Determinant of a square matrix and its properties. Invertible square matrices and their inverse matrix. Theorem of Laplace (only enunciated and applied). Rule of Sarrus (only enunciated and applied). Binet's Theorem (only enunciated and applied). Singular and non singular matrices. Linear dependence and linear independence of the columns (rows) of a matrix. The rank of a matrix. Cramer's theorem (only enunciated and applied). Kronecker's theorem (only enunciated and applied). Rouchè-Capelli's theorem (only enunciated and applied). How to solve linear systems.
Real vector spaces. Key examples. Linear combinations of vectors. Generators of a vector space. Linear dependence and linear independence of vectors. Basis and dimension of a vector space. Coordinates of a vector in a base. The theorem of completing to a base. Reduction in R^n. Change of basis and coordinate transformations. Orientation of R^n. Subspaces of R^n: bases, dimension, parametric equations, codimension, Cartesian equations. Intersection and sum of subspaces. Grassmann's formula (only enunciated and applied). Direct sums of subspaces. Standard scalar product in R^n and its properties. Norm of a vector. Cauchy-Schwarz inequality (only enunciated and applied). Angular measurements. Area of a parallelogram. Projection of a vector onto another. Orthogonal bases and orthonormal bases of space. Gram-Schmidt process (only enunciated and applied). Orthogonal complement of a subspace. Orthogonal projection of a vector onto a subspace. Changes of orthonormal bases. Orthogonal matrices. Definition and examples of linear transformation. Matrix of a linear transformation with respect to two fixed bases. Kernel and image of a linear transformation. Rank nullity theorem (only enunciated and applied). Linear injective, surjective, bijettive transformations. Isomorphisms and invertible matrices. Endomorphisms or operators of R^n. Operators and basic changes: similar matrices. Diagonalizable matrices and operators. Eigenvectors and eigenvalues of an operator. Eigenspaces. Spectrum of an operator. Characteristic polynomial and characteristic equation. How to compute eigenvalues and eigenvectors. Algebraic multiplicity and geometric multiplicity of an eigenvalue. The fundamental theorem on diagonalizability. Transpose of an operator. Symmetric and antisymmetric operators. The spectral theorem (only enunciated and applied). Orthogonal operators. Isometries and orthogonal matrices.

− M. Bordoni, Algebra Lineare, Progetto Leonardo, Bologna
− P. Maroscia, Introduzione alla Geometria e all’Algebra Lineare, Zanichelli

The course "Fondamenti di Informatica" introduces basic concepts of computer science. The course discusses approaches and methodologies for the design of algorithms to solve math problems. Further, the course shows methodologies for the design of programs and the implementation of algorithms. The main topics covered by the course are the following.

- Algorithms, input and output, flow charts, properties of the algorithms, algorithm's execution, conditional operators, control statements and loops, top-down design of algorithms, iterative problems and design of iterative algorithms.

- Introduction to programming, variables, expressions, types, conditional operators, control statements, and loops in Java, errors and exceptions, programming style, programming paradigms, object-oriented programming, objects and classes, runtime model, methods, parameter binding, strings, arrays, implementation of algorithms on strings and arrays, binary representation of data.

Luca Cabibbo. Fondamenti di informatica - Oggetti e Java - McGraw-Hill.

PARTE 1: Forme bilineari e forme bilineari simmetriche. Matrice associata ad una forma bilineare in una data base e forma bilineare associata ad una matrice in una data base. Formula del cambiamento di base. Matrici congruenti.
Il rango di una forma bilineare. Forma quadratica associata ad una forma bilineare simmetrica. Il teorema di diagonalizzazione delle forme quadratiche su un campo arbitrario. Il teorema di diagonalizzazione di forme quadratiche sul campo dei numeri complessi. Il teorema di diagonalizzazione delle forme quadratiche sul campo dei numeri reali (teorema di Sylvester): la segnatura. Classificazione delle forme quadratiche reali: (semi-)definite positive o negative, indefinite. Prodotto scalare su uno spazio vettoriale reale. Esempi: il prodotto scalare standard su R^n. Disuguaglianza di Schwarz. Norma indotta da un prodotto scalare e sue proprietà'.
Basi ortogonali e ortonormali. La matrice di cambiamento base tra due basi ortonormali e' ortogonale. Come trovare basi ortogonali: il processo di ortogonalizzazione di Gram-Schmidt. Esercizi su Gram-Schmidt. Criterio di Sylvester (senza dimostrazione): una matrice reale simmetrica e' definita positiva se e solo se i suoi minori principali angolo sono positivi. Somma ortogonale di sottospazi di uno spazio vettoriale euclideo. Operatori unitari. Operatori unitari e matrici ortogonali. Il gruppo degli operatori unitari e delle matrici unitarie. Il duale di uno spazio vettoriale. Esempi. La base duale. Una forma bilineare su uno spazio vettoriale definisce due operatori lineari da uno spazio vettoriale nel suo duale che coincidono se e solo se la forma e' simmetrica e sono isomorfismi se e solo se la forma bilineare e' non degenere. Richiami sugli spazi vettoriali: due spazi vettoriali sono isomorfi se e solo se hanno la stessa dimensione, fissare una base di uno spazio vettoriale corrisponde a fissare un isomorfismo dello spazio vettoriale nello spazio vettoriale numerico. Il duale di un'applicazione lineare tra spazi vettoriali e la sua matrice associata. L'operatore aggiunto (o trasposto) di un operatore in uno spazio vettoriale euclideo e la sua matrice associata. Operatori simmetrici. Il teorema spettrale per operatori simmetrici. Esercizi. Gli autospazi di un operatore simmetrico sono ortogonali. Il teorema spettrale per matrici. Il teorema spettrale per forme quadratiche. Esercizi. Gli spazi affini. Esempi: lo spazio affine canonico associato ad uno spazio vettoriale, lo spazio affine numerico. Sistemi di coordinate affini. Sottospazi affini. Il sottospazio affine generato da un insieme finito di punti. Punti affinemente indipendenti. Un sottospazio affine e' univocamente determinato dalla sua giacitura e da un suo qualsiasi punto. Un sottospazio affine e' uno spazio affine sulla sua giacitura. Equazioni parametriche e cartesiane di sottospazi affini si uno spazio affine numerico. Risoluzione di sistemi lineari non omogenei. Formula di Grassman per due sottospazi affini. Posizione relativa di due sottospazi affini: paralleli, incidenti o sghembi. Spazi proiettivi e spazi proiettivi numerici. Sistema di coordinate omogenee (o riferimento proiettivo). Sottospazi proiettivi. Equazioni cartesiane e parametriche di sottospazi proiettivi. Intersezione e Somma di sottospazi proiettivi: formula di Grassman. Gli spazi proiettivi come "completamenti" di spazi affini. Isomorfismi di spazi proiettivi. Un isomorfismo e' completamente determinato dall'immagine dei punti fondamentali e dal punto unita' rispetto ad un sistema di coordinate proiettive. Il gruppo delle proiettivita' di uno spazio proiettivo.Il gruppo delle proiettivita' dello spazio proiettivo numerico e' il gruppo lineare proiettivo, cioe' il gruppo delle matrici invertibili modulo non-zero automorfismi. Spazi affini euclidei e loro isometrie. I tre tipi di geometrie e i loro gruppi di trasformazione: la geometria proeittiva (reale o complessa) e le proiettivita', la geometria affine (reale o complessa) e le affinita', la geometria affine euclidea e le isometrie. Curve algebriche piane (nelle tre geometrie) e il problema della loro classificazione. Il problema della classificazione delle coniche. Classificazione delle coniche proiettive reali o complesse. Esercizi. Classificazione delle coniche affini reali o complesse. Esercizi. Classificazione delle coniche euclidee. Esercizi.

PARTE 2: Equazioni differenziali di ordine uno: teorema di esistenza e unicita' Cauchy (senza dimostrazione) e risoluzione di equazioni differenziali al prim'ordine con variabili separate. Equazioni differenziali lineari di ordine n: lo spazio delle soluzioni come spazio affine di dimensione n (senza dimostrazione). Equazioni differenziali lineari di ordine uno: metodo risoluzione. Equazioni differenziali lineari di ordine n a coefficienti costanti: metodo di risoluzione ed esempio. Funzioni vettoriali ad una variabile (o archi di curve). Limiti e continuita'. Derivata e archi di curve regolari. Il vettore velocita', la velocita' scalare, il versore tangente di una curva regolare. Integrali di funzioni a valori vettoriali. Lunghezza di un arco di curva. Cambiamenti di parametrizzazione e parametrizzazione in forma d'arco. Integrali di linea e sue appplicazioni geometriche e fisiche. Il versore normale e la curvatura. La scomposizione dell'accelerazione. Digressione: il prodotto vettoriale nello spazio euclideo tridimensionale. Il versore binormale di una curva spaziale. Le formule di Frenet-Serret per le derivate del sistema di riferimento intrinseco di una curva. Le formule per la curvatura e la torsione. Esempi. Topologia di R^n: punti interni, di bordo (o frontiera) ed esterni di un sottoinsieme. L'interno e la chiusura di un sottoinsieme. Sottoinsiemi aperti o chiusi e loro proprieta'. Caratterizzazione dei chiusi in termini di convergenza di successioni. Sottoinsiemi limitati e compatti. Sottoinsiemi connessi. Funzioni reali di piu' variabili: limiti e continuita'. Criteri di esistenza del limite tramite maggiorazioni radiali e criteri di non esistenza del limite tramite restrizioni a curve. Proprieta' topologiche delle funzioni continue: l'immagine inversa di un aperto o di un chiuso e' aperta o chiusa (applicazione: il teorema della permanenza del segno), l'immagine di un compatto e' compatta (applicazone: teorema di Weiestrass sui massimi e minimi), l'immagine di un conneso e' connesso (applicazione: il teorema degli zeri). Funzioni derivabili, differenziabili e di classe C^1. L'iperpiano tangente al grafico di una funzione. Derivate direzionali e formula del gradiente. Calcolo delle derivate: gradiente di somma, prodotti o quozienti di funzioni derivabili, la formula di derivazione delle funzioni composte. Derivate parziali di ordine superiore. Funzioni di classe C^k e teorema di Schwartz sullo scambio dell'ordine di derivazione. La matrice Hessiana e il differenziale secondo. La formula di Taylor al secondo ordine con il resto di Lagrange e con il resto di Peano. Punti di massimo e minimo, globali e locali, forti e deboli. I punti di massimo e minimo locali sono punti critici. Lo studio dei punti critici tramite lo studio del segno della matrice Hessiana. Funzioni vettoriali di piu' variabili reali: continuita', derivabilita', differenziabilita', classe C^k. La matrice Jacobiana. La regola di derivazione di una composizione di funzioni. Le superfici parametrizzate in R^3: superfici regolare, piano tangente, versore normale. Esempi. Gli integrali doppi su un rettangolo: le funzioni continue sono integrabili, il calcolo dell'integrale con la doppia integrazione. Funzioni vettoriali di piu' variabili reali: continuita', derivabilita', differenziabilita', classe C^k. La matrice Jacobiana. La regola di derivazione della composizione di funzioni. Le superfici parametrizzate in R^3: superfici regolare, piano tangente, versore normale. Esempi. Gli integrali doppi su un rettangolo: le funzioni continue sono integrabili, calcolo dell'integrale doppio mediante doppia integrazione. Gli integrali doppi su domini x-semplici, y-semplici o regolari. Proprieta' dell'integrale doppio: linearita' nella funzione integranda, positivita' e monotonia, additivita' dell'integrale rispetto al dominio di integrazione, proprieta' di annullamento, teorema della media. Calcolo dell'integrale doppio su insiemi x-semplici o y-semplici mediante doppia integrazione. Diffeomorfismi locali e globali. Il teorema della funzione inversa. Esempi: coordinate polari, cilindriche, sferiche. Formula del cambiamento di variabili per il caloolo negli integrali doppi. Esercizi.

(1) E. Sernesi: Geometria 1. Bollati Boringhieri.
(2) M. Bramanti, C.D. Pagani, S. Salsa: Analisi Matematica 2. Zanichelli.
(3) S. Salsa, A. Squellati: : Esercizi di Analisi Matematica 2. Zanichelli.

Symmetric bilinear forms and scalar products. Skewsymmetric bilinear forms. Degenerate and non-degenerate symmetric bilinear forms. The ordinary scalar product in R^n. The matrix of a symmetric bilinear form with respect to a basis. Examples of matrices of the same bilinear form with respect to different basis. Positive definite real symmetric matrices. Characterizations of symmetric matrices by the leading principal minors. Euclidean vector spaces and proper Euclidean vector spaces. Orthogonality between two vectors. Orthogonal systems of vectors and their linear independence. Fourier's coefficient. Gram-Schmidt's orthogonal algorithm. Scalar product matrices and change of basis. Norm of a vector. Versors. Orthonormal basis. Scalar product matrix with respect to orthonormal basis. Orthogonal matrices. Congruent matrices. Schwartz's inequality. Triangular inequality. Convex angle between two vectors. Quadratic forms. Polar symmetric bilinear form of a quadratic form. Orthogonal space to a vector. Orthogonal space to a vector subspace. Kernel of a symmetric bilinear form. The vector projection of a vector on a nonzero vector. Orthogonal operators and orthogonal matrices. Rank and signature of a symmetric bilinear form. Sylvester's law for symmetric bilinear forms. Hermitian forms and Hermitian spaces. Self-adjoint operators and unitary operators. Eigenvalues of hermitian matrices. Eigenvalues of symmetric matrices. Eigenvectors of different eigenvalues of a self-adjoint operator are orthogonal. The Spectral theorem. Symmetric operators and orthogonal operators. Diagonalizability of a quadratic form (canonical form). Diagonalizability of a symmetric bilinear form.
Affine and Euclidean plane geometry and Cartesian coordinate system in the plane: the midpoint of a segment; Cartesian and parametric equations of a straight line; intersecting and parallel lines; sheaves of straight lines; direction cosines of an oriented line; slope; angle between two lines; perpendicularity between lines; distance between two points, between a point and a line, between two parallel lines; area of a triangle; circumferences; change of coordinates. Affine geometry of the space and Cartesian coordinate systems in the Space: Cartesian and parametric equations of a plane; chenge from parametric equations to cartesian equations and viceversa; intersection and parallelism between planes; sheaves of planes; Cartesian and parametric equations of a straight line; direction vectors; parallelism between lines; coplanar and skew straight lines; intersecting lines; intersection and parallelism between a line and a plane; sheaves of straight lines; direction cosines of an oriented line; angle between two lines; perpendicularity between lines; vectors perpendicular to a plane; angle between two planes; orthogonal projection of a straight line onto a plane; angle between a line and a plane; perpendicularity between a line and a plane; distance between two points; distance between a point and a line or a plane; distance between two parallel lines or two parallel planes; distance between a line parallel to a plane; minimum distance between two skew lines; straight line perpendicular to two skew lines. Spheres and circles in the space. Vector product. Area of a parallelogram. Mixed product. Volume of the parallelepiped and of the tetrahedron. Ellipse, hyperbola and parabola as loci and their canonical equations. Foci, directrix, vertices, axes, center and eccentricity of a conic. Intersection of a straight line with a conic. General and degenerate conics. Reduction to canonical form of the equation of a conic section. Metric classification of conics. Method of invariants.
Ordinary differential equations. Order of a differential equation. Normal differential equations. Cauchy's problems. Some particular examples of first and second order differential equations and their solutions. Linear differential equation: general properties; homogeneous and non homogeneous linear differential equations; existence and uniqueness of the solution of a Cauchy problem for linear differential equations (without proof); linearly dependent and linearly independent real functions; wronskian of real functions: its definition and properties; general integral of a linear homogeneous differential equation (without proof); general integral of a linear non homogeneous differential equation (without proof); some particular examples of linear differential equations; Lagrange's method; homogeneous linear differential equations with constant coefficients and their general integral.
Regular curves (definition and properties), equivalent curves, oriented curves, the lenght of a curve, theorem of rectificability of C^1 curves (without proof), curvature of a plane curve, Frenet's formulas for plane curves. The derivative of a scalar product and of a vector product in R^n. Biregular curves; curves in R^3: curvature, torsion, Frenet's frame, Frenet formulas for curves in the space; existence and uniqueness of a curve in R^3, curvature and torsion given (without proof).

1) Manlio Bordoni, Introduzione all'algebra lineare ed alla geometria analitica, Esculapio, 2013.
2) Francisco James Leon Trujillo-P. Mercuri, Elementi di algebra lineare, Efesto, 2016.
3) Francisco James Leon Trujillo-P. Mercuri, Geometria affine ed euclidea, Efesto, 2016.
4) M. Fusco-P. Marcellini-C. Sbordone, Analisi Matematica due, Liguori, 2001.
5) Lecture notes of the teacher

1. Electrostatic force and field in vacuum
- Electric charge and matter electronic structure.
- Coulomb's law and Newton's law of universal gravitation.
- Superposition principle.
- Concept of field; scalar and vector fields; flux lines.
- Electrostatic field.
- Motion of a charged particle in a electrostatic field.
- Electrostatic field flux and Gauss's law.
- Gauss's law applications to charged distributions having planar, cylindrical and spherical symmetry.

2. Electric work and electrostatic potential
- Electrostatic field circulation integral; conservative property of the electrostatic field.
- Electric potential computation.
- Electric potential energy.
- Relationship between electrostatic field and potential: gradient and equipotential surfaces.

3. Conductors and dielectrics
- Electric properties of conductors.
- Electrostatic induction; Faraday cage.
- Capacitance; capacitor.
- Capacitors in series and parallel; capacitor energy.
- Dielectrics, electric polarization and dielectric permittivity.
- D field and corresponding Gauss's law.

4. Electric current
- Electric current. Current density field J.
- Stationary conditions. Solenoidal property of the field J.
- local form of the Ohm's law.
- Ohm's law and Joule effect.
- Resistors in series and parallel.
- Electromotive field and electromotive force.
- Charging and discharging of a capacitor.
- Kirchhoff's circuit laws.

5. Magnetic field
- Magnetic interactions.
- Magnetic induction field B; Lorentz force.
- Biot-Savart law.
- Magnetic force on a current carrying conductor.
- Torque on a current carrying rectangular coil in a magnetic field.
- Charged particle motion in a magnetic field.
- Mass spectrometer and velocity selector.
- Solenoidal property of the field B; Gauss's law for the magnetic field.

6. Magnetic field sources
- Magnetic field of a current.
- Ampère-Laplace law applications: straight wire, circular coil.
- Forces between current carrying wires.
- Ampère's circuital law (in integral form) and applications.
- Magnetic properties of matter: diamagnetic, paramagnetic and ferromagnetic materials.
- H field and its circulation integral.

7. Electromagnetic induction
- Faraday's law. Lenz's law.
- Induced and motional Electromotive force.
- Inductance. Charging and discharging of an inductor.
- Magnetic energy.
- Mutual inductance.
- Ampere-Maxwell's law. Displacement current.
- Maxwell equations in integral form.

P. Mazzoldi, M. Nigro, C. Voci, "Elementi di Fisica. Vol. II: Elettromagnetismo - Onde", seconda edizione, Edises, Napoli

1. Electrostatic force and field in vacuum
- Electric charge and matter electronic structure.
- Coulomb's law and Newton's law of universal gravitation.
- Superposition principle.
- Concept of field; scalar and vector fields; flux lines.
- Electrostatic field.
- Motion of a charged particle in a electrostatic field.
- Electrostatic field flux and Gauss's law.
- Gauss's law applications to charged distributions having planar, cylindrical and spherical symmetry.

2. Electric work and electrostatic potential
- Electrostatic field circulation integral; conservative property of the electrostatic field.
- Electric potential computation.
- Electric potential energy.
- Relationship between electrostatic field and potential: gradient and equipotential surfaces.

3. Conductors and dielectrics
- Electric properties of conductors.
- Electrostatic induction; Faraday cage.
- Capacitance; capacitor.
- Capacitors in series and parallel; capacitor energy.
- Dielectrics, electric polarization and dielectric permittivity.
- D field and corresponding Gauss's law.

4. Electric current
- Electric current. Current density field J.
- Stationary conditions. Solenoidal property of the field J.
- local form of the Ohm's law.
- Ohm's law and Joule effect.
- Resistors in series and parallel.
- Electromotive field and electromotive force.
- Charging and discharging of a capacitor.
- Kirchhoff's circuit laws.

5. Magnetic field
- Magnetic interactions.
- Magnetic induction field B; Lorentz force.
- Biot-Savart law.
- Magnetic force on a current carrying conductor.
- Torque on a current carrying rectangular coil in a magnetic field.
- Charged particle motion in a magnetic field.
- Mass spectrometer and velocity selector.
- Solenoidal property of the field B; Gauss's law for the magnetic field.

6. Magnetic field sources
- Magnetic field of a current.
- Ampère-Laplace law applications: straight wire, circular coil.
- Forces between current carrying wires.
- Ampère's circuital law (in integral form) and applications.
- Magnetic properties of matter: diamagnetic, paramagnetic and ferromagnetic materials.
- H field and its circulation integral.

7. Electromagnetic induction
- Faraday's law. Lenz's law.
- Induced and motional Electromotive force.
- Inductance. Charging and discharging of an inductor.
- Magnetic energy.
- Mutual inductance.
- Ampere-Maxwell's law. Displacement current.
- Maxwell equations in integral form.

P. Mazzoldi, M. Nigro, C. Voci, "Elementi di Fisica. Vol. II: Elettromagnetismo - Onde", seconda edizione, Edises, Napoli

Physical quantities and measurements.
Motion in one and more dimensions.
Newton’s laws.
Work and energy.
Conservative forces and potential energy.
The harmonic oscillator.
Motion and dynamics of particle systems.
The rigid body.

- P. Mazzoldi, M. Nigro, C. Voci, "Elementi di Fisica. Vol. I: Meccanica - Termodinamica", seconda edizione, Edises, Napoli
- R. Borghi, "Lezioni di Meccanica", amazon.com

Physical quantities and measurements.
Motion in one and more dimensions.
Newton’s laws.
Work and energy.
Conservative forces and potential energy.
The harmonic oscillator.
Motion and dynamics of particle systems.
The rigid body.

- P. Mazzoldi, M. Nigro, C. Voci, "Elementi di Fisica. Vol. I: Meccanica - Termodinamica", seconda edizione, Edises, Napoli
- R. Borghi, "Lezioni di Meccanica", amazon.com

Physical quantities and measurements.
Motion in one and more dimensions.
Newton’s laws.
Work and energy.
Conservative forces and potential energy.
The harmonic oscillator.
Motion and dynamics of particle systems.
The rigid body.

- P. Mazzoldi, M. Nigro, C. Voci, "Elementi di Fisica. Vol. I: Meccanica - Termodinamica", seconda edizione, Edises, Napoli
- R. Borghi, "Lezioni di Meccanica", amazon.com

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

Lecture notes
o Depaoli - Chimica Generale ed Inorganica - Ed. Ambrosiana
o Silvestroni, Rallo - Problemi di Chimica Generale - Ed. Masson
o Palmisano, Schiavello – Fondamenti di Chimica - EDISES

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

Lecture notes
o Depaoli - Chimica Generale ed Inorganica - Ed. Ambrosiana
o Silvestroni, Rallo - Problemi di Chimica Generale - Ed. Masson
o Palmisano, Schiavello – Fondamenti di Chimica - EDISES

Atom Structure: orbitals, poly-electron atoms, periodic table; bonds in chemistry (Lewis theory and VSEPR, Valence bond theory and hybridization); delocalized bond.

Mass relationship in chemical reactions; redox and oxidation number.

Solids: metallic, ionic, covalent and molecular crystals (weak bonds: van der Waals and hydrogen bond)

Gases: the ideal gas law, gas mixture, Dalton law, partial pressures.

Thermodynamics: nature and type of energy, the zero law of T.D., heat capacity, the first law of TD and Enthalphy. Calorimetry and thermochemistry. Born-Haber cycle; Carnot cycle. The second law of TD, Kelvin and Clausius statements, entropy and free energy, equilibrium conditions.

Liquids: saturation vapor pressure, Clapeyron law (thermodynamic demonstration), phase change, phase diagrams. Variance.

Chemical equilibrium: the equilibrium constant and the equilibrium law, heterogeneous equilibrium, thermal dissociation and dissociation degree.

Properties of liquid solutions: concentration units, the Raoult law and distillation, colligatives properties and freezing diagram, electrolytes. Arrhenius, Brönsted and Lewis acids and bases; pH; determination of pH for acidic and basic solutions, salt solutions, buffers.

Electrochemistry: electrical conductors (primary and secondary), Nernst’s equation, electrode potentials. Electrochemical cells: electrolytic cells, galvanic cells (primary and secondary), electrolysis, corrosion.

Brown - LeMay CHEMISTRY, THE CENTRAL SCIENCE Pearson

Road transport, Railway transport and elements of transportation Economy

Cantarella G.E. Sistemi di trasporto: Tecnica ed Economia 2007 UTET

Vectors. Moment of a vector with respect to a point. Resultant force and resultant moment of a system of vectors. Equivalence of systems of vectors. Planar systems. Linear transformations on vector spaces. Second-order tensors. Differentiation of vector and tensor functions. Gradient and divergence. Divergence theorem. Stokes’ theorem.
Centroid of a material system. First moments and moments of inertia of a planar region. Moments of inertia of a planar region with respect to lines passing through a given point. Mohr’s circles. Polarity and involutions determined by the ellipse of inertia.
Equilibrium of a material point. Constraints. Infinitesimal rigid displacements. Euler’s theorem. Work in a rigid displacement. Equilibrium equations of rigid bodies. Beams and frames. Diagrams of the components of force and couple resultants. Forces exerted by the constraints. Principle of virtual work for rigid bodies. Statically determined structures. Graphic statics.
Deformation of a continuous body. Measures of deformation. Principal strains. Volume change. Compatibility conditions. Equilibrium equations of deformable bodies. Stress tensor. Principal stresses. Plane stress. Moor’s circles for stresses. Constitutive equations. Hyperelastic materials. Energy functional. Clapeyron’s theorem. Equilibrium problem. Betti’s theorem. Virtual work principle for deformable bodies. Von Mises and Tresca yield criteria.
Saint-Venant’s problem. Extension, bending, torsion, and shear of beams. Equilibrium differential equations for a beam. Limitations of the theory. Allowable stress. Euler’s critical load.
Effects of imperfect constraints and temperature variations. Mohr’s analogue. Hyperstatic beams. Continuous beams. Analysis of structures by means of virtual work principle, force and displacement methods.

Notes written by the teacher, published on the “moodle” page of the course. Reference texts are given in the bibliography of the notes.

- Some characteristics of fluids, Cauchy theorem and the stress tensor.
- Fluid kinematics: Lagrangian and Eulerian flow descriptions, the acceleration field, laminar and turbulent flows.
- Govening equations for fluid mechanics: continuity and momentum equations.
- Fluid statics: pressure field, manometry, hydrostatic force on a plane surface, hydrostatic force on a curved surface.
- Ideal flows: the Euler model, the Bernoulli theorem, dynamic force on a surface.
- Uniform viscous flow in pipes: Darcy-Weisbach formula, coefficient of friction, Moody diagram, single and multiple pipe systems.
- Permanent and unsteady flow in pipes: Continuity and momentum equations, water hammer.
- Uniform free surface flows: flow in channels, Chezy formula, discharge calculation, specific energy, Froude number.
- Non uniform free surface flows: gradually varied flows, equation of continuity, momentum equation, channels on mild and steep slope, forms of water surface, the hydraulic jump, rapidly varied flows (underflow gates, channel with variable bed floor, channel with variable width).
- Flow in porous media, Darcy equation.
- Physical models and similitude.

D. Citrini e G. Noseda, Idraulica, Casa Editrice Ambrosiana
M. Mossa e F. Petrillo, Idraulica, Casa Editrice Ambrosiana

- fluid continuum model
- body forces and surface forces
- Cauchy stress tensor
- kinematics - velocity and acceleration, pathlines and streamlines
- conservation laws: differential and integral form
- hydrostatics
- ideal fluid Bernoulli's theorem
- uniform flows: one dimensional dissipative model
- pipe flow

Theory:
Citrini, Noseda – Idraulica - Ed. Ambrosiana
Mossa, Petrillo – IDRAULICA. Ed. Casa Editrice Ambrosiana, Milano

Applications:
Alfonsi, Orsi – Problemi di idraulica e meccanica dei fluidi. Ed. Casa Editrice Ambrosiana, Milano

Part 1 – Hydrology
1.9) Rainfall: rainfall genesis, rainfall measurements, rainfall regimes, intense rainfall, rainfall amount at the catchment scale.
1.10) Evapotranspiration: phenomenology and measures.
1.11) Catchment and hydrogeological basin definitions: water balance.
1.12) Groundwater hydrology: unsaturated zone and aquifers.
1.13) Surface water storage: lakes, snow and glaciers.
1.14) Surface water flow: flow discharge measurements, river regimes, low and base flow, probabilistic models.
1.15) Hydrologic losses and runoff generation machismos.
1.16) Rainfall-runoff models: lumped linear models, kinematic and linear reservoir models.
Parte 2 – Water supply
2.7) Water use: domestic water, sustainable water use.
2.8) Water-intake hydraulic structures for surface water.
2.9) Artificial lakes.
2.10) Water transport, open channel flow.
2.11) Water transport, aqueducts, network configurations, pipelines, manufactures, pumping stations.
2.12) Urban reservoirs.

Calenda, G. (2016). Infrastrutture Idrauliche. Vol. 1 – Idrologia e Risorsa Idrica, Edizioni Efesto, Roma.

Methods for structural assessment of structures
The yield design theory
Yield design theory of masonry structures
Diagnosis techniques and experimental evaluation of mechanical properties
Structural assessment of arched and vaulted structures
Damages induces by crushing, soil settlement and earthquake action
Structural assessment od masonry structures in seismic area
Seismic analysis against local collapse mechanisms
Shear strength of masonry panels and seismic global analysis
Structural rehabilitation techniques: examples and design projects.

Pisani, M.A., Consolidamento delle Strutture, Hoepli, Milano, 2012
Giuffré, A. Letture sulla meccanica delle murature storiche, Ed. Kappa, Roma.
Mastrodicasa, S., Dissesti statici delle strutture edilizie, Hoepli, Milano, 1993.

Definitions and principles of road design
Evaluation of the mobility and transport demand
Road cross section design
Principles of mechanics
Horizontal and vertical geometrical aligment
Principles of railways design
Road materisals
Pavement
Airports

A. Benedetto, STRADE FERROVIE AEROPORTI, UTET Università, Torino, 2016

- NATURE AND COMPOSITION OF SOIL – SOIL CLASSIFICATION
– STRENGTH AND DEFORMATION OF SOIL - LABORATORY TESTS
- GEOSTATIC STRESSES
– FIELD TESTING FOR STRENGTH AND DEFORMATION
– FLOW OF WATER THROUGH A SOIL MASS
– COMPRESSIBILITY OF SOILS AND OEDOMETER TEST
– SETTLEMENT AND CONSOLIDATION
– DRAINED AND UNDRAINED SHEAR STRENGTH
– LIMITING STRESS STATES IN A SOIL MASS
– EARTH RETAINING STRUCTURES
– FOUNDATION SYSTEMS
– SETTLEMENT ANALYSES OF SHALLOW FOUNDATIONS
- PILES FOUNDATIONS
– BEARING CAPACITY OF A SINGLE PILE
– STABILITY OF SLOPES

LAMBE T.W. & WHITMANN R.W., SOIL MECHANICS, J. WILEY & SONS, LONDON
LANCELLOTTA R., GEOTECNICA, ZANICHELLI, BOLOGNA.
COLLESELLI COLOMBO. ELEMENTI DI GEOTECNICA. ZANICHELLI. BOLOGNA
BERARDI R. – FONDAMENTI DI GEOTECNICA. EDIZIONI CITTA’ STUDI

In relation with the three project phases:
- analysis of the impact and constraints to select project alternatives;
- optimization of project choices in environmental key;
- determination of axis and section geometries of each project alternatives;
- general site plan with drainages, ditch, slope, sump, ..etc.
- engineering structures;
- technical contract rules, prices list, etc.

C. BENEDETTO, M.R. DE BLASIIS “ISTRUZIONI PER LA REDAZIONE DEI PROGETTI DI STRADE E DEGLI STUDI D'IMPATTO AMBIENTALE” - ARACNE EDITORE;
G. TESORIERE "STRADE FERROVIE E AEROPORTI", VOLL. I E II. - UTET EDITORE;
A. BENEDETTO “STRADE FERROVIE AEROPORTI” - UTET EDITORE;
HANDNOUTS AND SLIDES PROVIDED BY THE TEACHER.

Transport system supply, networks, graphs and volume-delay functions. Level of service (LOS). Transport demand models, origin-destination matrix, sample survey methods – traffic assignment model – benefits-costs analysis. The course is characterized by the adoption of a software for the macro simulation of the transport systems.

Handnouts and slides provided by the professor.

Methods for the assessment of the structural safety and for the design of the structures (allowable stresses, load and resistance factor design methods). The current design philosophy for reinforced concrete structures: serviceability limit states (cracking and deformation control) and ultimate limit states (shear and bending moment, axial load and bending moment, shear, lateral instability). The structural organism and preliminary design choices for reinforced concrete frame structures.
Modeling of the structures for the evaluation of forces and for the design of structural members: design of decks (typologies, dimensioning criteria, loads evaluation, design of reinforcement, verifications), design of beams and columns (typologies, dimensioning criteria, loads evaluation, design of reinforcement), design of foundations (plinths and ground beams). Validation of the structural analysis. Graphical representation of a structural design.

• Giannini R., Teoria e Tecnica delle Costruzioni Civili, 2011
• AICAP - Guida all’uso dell’Eurocodice 2 - Vol I°, II°
• Ghersi, Il Cemento Armato, Dario Flaccovio Ed.
• Cinuzzi, Gaudiano, Progetto di Strutture in c.a. – ESA ed.
• Dettagli costruttivi di strutture in calcestruzzo armato, Aitec 2011
• AICAP, Costruzioni in calcestruzzo, composte acciaio-calcestruzzo (commentario al DM 14/01/2008)

• General description of a hydraulic work:
o Legislation;
o preliminary, final and executive project;
o organization of the work;
o reporting;

• Design of sewage and urban flood protection systems:
o definition of input variables and boundary conditions;
o design of main structural components;
o special works: energy dissipation systems, pumping stations, shuttlecock basins.

• Examples of numerical hydraulic models.

• Design of hydraulic works.

• Lecture notes.
• Infrastrutture Idrauliche, Volume 1 - Idrologia e Risorse Idriche. Autor: Guido Calenda. Efesto - Libreria Efesto - Via Corrado Segre, 11 Roma (marzo 2015)