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;

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

1- Linear systems: coefficient matrix; sum of matrices and product for scalars; reduced matricess: Gauss-Jordan algorithm.
2- Product rows for columns of matrices; invertible matrices; rank of a matrix: the Rouche'-Capelli Theorem.
3- Geometric vectors. Vector spaces. Subspaces. Generator vectors and linearly independent vectors.
4- Base of a vector space; dimension; the Grassmann formula.
5- Linear applications: kernel and image of a linear application. The Theorem of nullity plus rank.
6- Matrix associated with a linear application. Diagonalization of linear operators.

Geometria 1, E. Sernesi

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.

Scalar products and symmetrical bilinear forms. The standard scalar product on R^n. Examples. The matrix associated with a symmetrical bilinear form. Positive definite matrices and the criterion of the main minors. Examples.
Euclidean vector spaces. Length and versor of a vector. Orthogonality between vectors and orthogonal space to a vector. Orthonormal bases. Gram-Schmidt procedure.
Formula of transition from one base to another for the matrix of a scalar product. Schwarz's inequality. Triangular inequality.
Convex angle between two vectors. Orthogonal space to a vector or a subspace. Projection of a vector in the direction of a non-zero vector. The notion of quadratic form. The polar symmetrical bilinear form of a quadratic form. Orthogonal operators and orthogonal matrices.
Self-oadjoint operators and properties. Quadratic form associated with a self-adjoint operator. Eigenvalues ​​of a symmetric matrix. Spectral theorem of self-adjoint operators.
Spectral theorem of self-adjoint operators: procedure for diagonalizing a symmetric matrix. Exercises. Canonical forms of quadratic forms.
Sylvester's theorem. Affine geometry: coordinate systems in the plane. Lines in the Cartesian plane: Cartesian equation and parametric equation.
Affine geometry in the plane: Intersection of straight lines, parallelism and orthogonality, straight point distance, convex angle between two straight lines, sheaves of proper and improper lines.
Geometry in Cartesian space. Vector product and mixed product. Parametric and Cartesian equations of planes and lines.
Switch from parametric to Cartesian equations of planes and lines in the Cartesian space. Plane through 3 non aligned points. Intersections plane / plane, plane / line and line / line in space. Sheaves of proper planes.
Sheaves of improper planes, Affinity and isometry in a similar space. Examples. Conics in the Cartesian plane. Examples. Affine and metrical classification of conics. Fundamental theorem of affine-like classification of conics in the plane.
Similar properties and metrics of conics. General and degenerate conics, center conics and parables. Ellipses, parables and hyperbole: examples. Affine and metric classification of conics.
Reduction to the canonical and metric forms of conics. Examples.
Symmetries in the plane with respect to a point and a line. Center of symmetry of a conic in the center. Projective spaces: definition and examples.
Real projective plan. Lines and conics in the projective plane. Polarity with respect to a conic of the projective plane.
Generalities on differential equations. Differential equations of the first order. Differential equations with separable variables.
Linear differential equations of the first order. Linear differential equations with constant coefficients of order n.
Linear differential equations with constant coefficients of the second order. Method of constants variation. Vector functions: generalities and examples. Continuous curve arch.
Derivative of a regular function and arcs of regular curves. Curves in polar coordinates and reparametrizations. Length of a regular curve arc.
Arc parameter. Line integrals and applications for the calculation of surface areas, mass, center of gravity and moment of inertia relative to an axis of a material line. Elements of differential geometry: tangent, normal, curvature, and osculating circle. Binormal and the Frenet-Serret formulas.
Osculator plane to a curve, decomposition of acceleration and proof of Frenet-Serret formulas. Plane curves and their torsion. Functions in several variables: examples of graphical representation, limits and continuity. Examples.
Elements of topology of R ^ n: internal, external, border points, open, closed and connected sets. Open and closed sets defined by continuous functions, Theorem of Wierstarss and Theorem of the zeros. Partial derivatives, derivability and gradient. Examples.
Tangent plan and differentiability. Directional derivatives. Derivatives of a higher order and Schwarz's theorem. Free optimization: critical points and the criterion of the Hessian matrix. Double integrals: integration on rectangular domains, x-simple and y-simple sets. Conditions of integration on regular domains. Examples. Change of variables in the integral and integration in polar coordinates. Calculation of the volume of the sphere.
Vector fields and line integrals of second species. Gradient, rotor and divergence. Work of a vector field along a curve and circuits. Conservative and potential fields.
Conservative and potential fields: examples. Conservative and irrotational fields. Simply connected, convex and star like sets.

F. Flamini, A. Verra: Matrici e vettori. Corso di base di geometria e algebra lineare. Carocci.
M. Bramanti, C.D. Pagani, S. Salsa: Analisi Matematica 2. Zanichelli.

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

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

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

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; 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.

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.

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

Road transport, Railway transport and elements of transportation Economy

SISTEMI DI TRASPORTO: TECNICA ED ECONOMIA AUTORE G. E. CANTARELLA EDITORE UTET

Vector Theory. Vector quantities. 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.
Geometry of material systems. 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 rigid bodies. 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 exercised by the constraints. Principle of virtual work for rigid bodies. Statically determined structures. Graphic statics.
Equilibrium of deformable bodies. 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. Mohr’s circles. Constitutive equations. Hyperelastic materials. Clapeyron’s theorem. Equilibrium boundary-value problems. Betti’s theorem. Virtual work principle for deformable bodies. Von Mises and Tresca yield criteria.
Beam theory. 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.
Theory of structures. Effects of imperfect constraints and temperature variations. Mohr’s analogue. Hyperstatic beams. Continuous beams. Analysis of planar trusses and frames by means of virtual work principle, force and displacement methods.
Introduction to plastic analysis of structures. Plastic moment of a beam section. Plastic hinges. Collapse of a structure due to transformation into a mechanism. Load factor. Static and kinematic theorems.

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

Fluid continuum model - Body forces and surface forces. Cauchy stress tensor – Kinematics - Velocity and acceleration, pathlines and streamlines, discharge - The conservation laws: differential and integral form – Hydrostatic - Ideal fluids. Bernoulli’s theorem - Steady and uniform flows: one dimensional dissipative model. Pipe flows. Free surface flows in channels – Introduction to hydraulics groundwater. Darcy’s law. Artesian and phreatic aquifers.

AUTORI: M. MOSSA E A.F. PETRILLO
TITOLO: IDRAULICA
EDITO DA: CASA EDITRICE AMBROSIANA

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.

Handouts provided by the Professor (HTTP://ELEARNING.DIA.UNIROMA3.IT/MOODLE/)

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

G. TESORIERE 'STRADE FERROVIE E AEROPORTI' VOLL. I E II. UTET EDITORE.
Teaching material provided by the Professor

External actions
Methods for the design and dimensioning of structures;
The partial safety coefficients and the limit states format;
Characteristic values and design values;
Classification and model of external loads;
Exercise load, snow load, wind action.

Steel structures
Materials and products, mechanical characteristics;
Steel constructions: structural typologies, construction details of civil and industrial buildings;
Design of structural elements under traction compression and flexure;
Technologies of welded and bolted junctions;
Design of welded and bolted junctions;
Buckling phenomena and design of members subjected to buckling.

Reinforced concrete structures
Mechanical properties of steel and concrete;
RC members: beams, columns;
RC Beams: elastic and ultimate limit state design under bending and shear;
RC Columns: elastic and ultimate limit state design under compression and bending;
Design of steel bars, stirrups, anchorages and details;
RC structures: frames and slabs. Details and examples.

R. GIANNINI
TEORIA E TECNICA DELLE COSTRUZIONI CIVILI, EDIZIONI CITTÀSTUDI, 2011.

NATURE AND COMPOSITION OF SOIL – SOIL CLASSIFICATION – STRENGTH AND DEFORMATION OF SOIL GEOSTATIC STRESSES – FIEL TESTS – 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 – SHALLOW FOUNDATIONS – 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.
FRICKER, J.D. - FUNDAMENTALS OF TRANSPORTATION ENGINEERING

COURSE OBJECTIVES
The course introduces the student to problems of designing structures in no seismic zone. In particular, several aspects concerning reinforced concrete structures will be examined in depth. According to the teaching approach the student will develop a design of a small R.C. structure, applying the concepts acquired during the lessons.

SYLLABUS
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.

LEARING VERIFICATION METHOD AND EXAMINATIONS
The student will participate, during the course, to classroom exercises on the design of a reinforced concrete building.
The exam consists of an oral test on the topics covered during the lectures and a discussion on the exercises. To access the exam the student must have completed and provided the exercises to the teacher at the end of the course.

TEACHING METHOD
Face to face learning and classroom exercises.

• 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)

Description of the general characteristics of a water project
1. legislation;
2. preliminary and final design;
3. project organization:
3.1. report,
3.2. tables and figures,
3.3. appendices.
Hydraulic design of sewer
1 data base construction;
2 objectives;
3 definition of boundary conditions;
4 definition of project variables;
5 design of major hydraulic structures;
6 special hydraulic structures:
6.1 energy dissipation systems,
6.2 design of pumping stations,
6.3 first flush and overflow diverters;
7 examples of hydraulic numerical models.
The exercises will be devoted to the development of design of water projects: sewer system

Hydrology:
GUIDO CALENDA , INFRASTRUTTURE IDRAULICHE VOLUME 1: IDROLOGIA E RISORSE IDRICHE, LIBRERIA EFESTO, VIA CORRADO SEGRE, 11 – 00146 ROMA
Sewer sistem:
Lecture notes by teacher.
Link: http://moodle2.ing.uniroma3.it/moodle/