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

The course "Fondamenti di Informatica" introduces basic concepts of computer science. The course discusses approaches and methodologies for the design of algorithms to automatically 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, compiling and executing programs, binary representation of the information, variables, expressions, types, conditional operators, control statements, and loops in C, errors and exceptions, programming style, functions, parameter binding and return values, strings, arrays, implementation of algorithms on strings, arrays, and file.

Author: Bellini, Guidi
Title: Linguaggio C - Guida alla programmazione con elementi di Python
Edition: 6-th edition
Editor: McGraw-hill
Year: 2021

1- Symmetric bilinear forms. Lengths, angles, orthogonality. Orthogonal and orthonormal bases. Gram-Schmidt algorithm.
2- Quadratic forms. Spectral Theorem. Diagonalization and classification of quadratic forms in a Euclidean space. Sylvester bases and Sylvester canonical form. Vectorial product in a euclidean space of dimension three.
3- 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 recyprocal position of linear varieties from their equations.
4- Parametrised curves. Regular curves. Rectifiability and length. Curvilinear parameter. Orthonormal mobile basis. Curvatere, torsion, curvature ray and obsculating plane. Frenet formulas.
5- Functions of several real variables and their graphs. Elements of the topology of R^n. Continuity, partial derivatives, differentiability. Gradient and directional derivatives.
6- Higher order derivatives and Schwarz Theorem, Hessian matrix and its interpretation.
7-Vector valued functions of several real variables..
8-Differential equations.

F. Flamini; A. Verra: "Matrici e vettori -Corso di base di geometria e algebra lineare" Carocci ed.
Notes from the lectures

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)

R. Borghi, “Lezioni di Meccanica”, Amazon.it

R. Borghi, “Esercizi e Problemi di Fisica. I. Meccanica”, Amazon.it

R. P. Feynman, “La Fisica di Feynman,” (Voll. I e II), Zanichelli, Bologna
“The Feynman Lectures on Physics,” http://www.feynmanlectures.caltech.edu/ (versione online)

E. Fermi, "Termodinamica", Bollati Boringhieri, Torino.

Definition of substance, chemical elements and their symbols, atomic number, mass number, isotopes, periodic table, compounds, molecules and chemical formula.
Atomic mass unit, atomic weight, formula weight, mole, Avogadro's number; calculation of mass percent composition of a compound, calculation of the empirical formula of a compound. Chemical reactions (stoichiometry): symbolism, stoichiometric coefficients, balancing simple reactions, reaction yield, limiting reagent, indirect analysis. Electronegativity, definition of oxidation number and rules for its determination; oxidation-reduction reactions and their balancing.
Classification and nomenclature of inorganic compounds: elements, monoatomic ions, basic oxides, acid oxides, hydroxides, hydracides, oxoacids, salts and reactions producing them.
Atomic structure: Bohr model and quantization, quantum numbers and energy levels; stationary wave, wave-particle dualism for the electron, Heisenberg uncertainty principle, wave functions, orbitals, probability; shape of orbitals and graphical representation; energy of orbitals, electronic configuration and aufbau, periodic properties, atomic size, ionization energy, electronic affinity, electronegativity.
Chemical bonding: definition of chemical bonding according to Lewis theory, ionic bonding, covalent bonding, bond energy, bond distance, bond order; rules for constructing molecular structure (octet rule), formal charge, resonance and resonance energy, exceptions to octet rule; spatial arrangement of molecules, VSEPR theory; valence bonding (VB) theory, σ-type and π-type bonding, hybrid orbitals.
Crystalline and amorphous solids; metallic solids, metal bonding, properties; ionic solids, properties; molecular solids, intermolecular forces, hydrogen bonding; covalent solids.
Definition of pressure, volume and temperature and their units, perfect gas model and equation, molar volume, absolute and relative density; gas mixtures, Dalton's law, partial pressures.
Definition of thermodynamic system: type and state; thermodynamic variables; reversible and irreversible transformations; graphical representation; thermal equilibrium; heat capacity and specific heat.
First Principle of Thermodynamics: definition of state function; Internal Energy Function U; Energy transfers: heat and work; Mechanical work: expansion of a perfect gas, work for reversible and irreversible processes, graphical representation. Isochore and isobar transformations. Thermochemistry: definition of state function enthalpy H; the enthalpy of physical changes; Enthalpy of a chemical reaction; molar enthalpy and standard state; standard molar enthalpy of elements. Hess's law. Estimation of binding energy. Born-Haber cycle.
Second Principle of Thermodynamics: qualitative description; definition of Entropy; increase in entropy. Criterion for spontaneity (statistical interpretation). Definition of free energy G. Third principle of thermodynamics.
Liquid state: factors influencing aggregate state; vapor pressure: qualitative description and temperature dependence (Clapeyron's eq. and its thermodynamic demonstration). State diagrams for pure substances: transformations from one state to another, triple point, critical point, cooling curve at constant pressure, measurement of variance. Solutions: definition and types of solutions, Henry's law, definition of ideal liquid solution; measurement of concentration: molarity, molality, molar fractions, percentage by weight.
Properties of solutions: Raoult's law for mixtures of completely miscible liquids and temperature versus concentration state diagram (calculation of relative quantities); colligative properties for non-volatile solutes strong electrolytes and non-electrolytes, osmotic pressure, cooling curve for solutions.
Chemical equilibrium: definition of chemical equilibrium, equilibrium constant (Kp and Kc), thermodynamic definition of chemical equilibrium; reaction quotient, meaning of K, relationship between Kp and Kc, principle of mobile equilibrium (influence of pressure and concentrations), Van't Hoff's law (dependence of K on temperature); heterogeneous equilibrium. Dissociations: gas dissociation, degree of dissociation, weak electrolytes in solution.
Heterogeneous solid-liquid equilibrium in an aqueous environment: solubility of a salt, saturated solution, poorly soluble compounds, common ion effect.
Acids and bases according to Arrhenius and Brönsted-Lowry; strength of acids and bases; ionic product of water; definition of pH; conjugate acid-base pair and relationship between Ka and Kb; calculation of pH of a solution of a strong acid and a strong base (even very dilute), a weak acid and a weak base. Salt hydrolysis: calculation of pH for salts producing neutral solutions, salts producing acid solutions and salts producing basic solutions; buffer solutions.
Electrochemistry: galvanic cell, salt bridge, Nernst's Equation, calculation of cell potential, standard hydrogen electrode, standard reduction potentials, concentration cells and other types.

Road transport, Railway transport and elements of transportation Economy

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

Main principles of transportation infrastructures design
Physical and functional characteristics of transportation infrastructures
Constraints and limits for design
Transportation and mobility demand
Road transversal section design
Geometrical design
Horizontal and Vertical aligment
Safety
Road material and pavement design principles
Road hydraulics
Railways
Airports

A. Benedetto (2015) "Strade Ferrovie Aeroporti." UTET Università. De Agostini Scuola. Novara

- 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
- Moody's chart
- weir 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

- 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).
- Dimensional analysis and Buckingam theorem.
- Physical models and similitude.

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

The elastic equilibrium problem for the beam and its formulation.
Beam kinematics: displacement field and strain measurements.
Constitutive equations for the elastic beam. Axial behavior, flexural behavior, shear behavior. Uniform thermal variation, butterfly thermal variation, affine thermal variation.
Equation of the tensioned beam. Equation of the inflected beam (elastic line) in the Euler-Bernoulli model. Extension to Timoshenko's model. Fitting conditions and problem formulation for beam systems. Kinematic and static performance of internal constraints.
Identity of virtual works. Notion of congruent system. Notion of balanced system. External virtual work. Internal virtual work. Virtual Work Theorem, statement and proof. Application of the Virtual Work Principle to the calculation of displacements and rotations in statically determinate structures.
Method of forces. Notion of a principal system. Application of the method to repeatedly hyperstatic systems. Müller-Breslau equations. Flexibility matrix. Effect of yielding and thermal distortions.
Continuous beams. Equation of three moments.
Saint Venant's problem. Saint Venant's postulate. Simple and compound stresses. Semi-inverse method.
Centered normal force. Straight deflection. Deflection deflected. Tensoflexion, Pressoflexion. Central core of inertia. Torsion in circular sections. The compact circular section. The hollow circular section.
Torsion in compact sections of any shape. Neumann's problem. Elliptical section. Polygonal sections. The hydrodynamic analogy for tangential stresses. Thin rectangular section. Open sections composed of thin rectangles. Thin-walled hollow sections: Bredt's theory. Composite thin sections. Pluriconconnected sections.
Flexure and shear. Distribution of normal stresses. Distribution of tangential stresses: approximate treatment of Jourawsky. Applicability of Jourawsky's formula.
Open thin sections. Rectangular thin section. Double-T thin section. U and H thin sections. Closed thin sections. Symmetrical box section. Straight cut. Deviated cut. Symmetrical compact sections. Compound stresses of straight cut and twist. The center of shear. Tangential shear and torsion stresses. Determination of the center of shear.
Strength criteria. Strength criteria for brittle materials. Strength criteria for ductile materials.
The beam: structural analysis and verification. Extension of Saint Venant's theory. Strength criteria for Saint Venant's solid.

P. Casini, M. Vasta, "Scienza delle costruzioni", Città Studi Edizioni 2016.
Steen Krenk & Jan Høgsberg, "Statics and Mechanics of Structures", Springer 2013.
M. Capurso, Lezioni di Scienza delle Costruzioni, Pitagora Editrice, 1984.
E. Sacco, Lezioni di Scienza delle Costruzioni, 2016.
Solved problems.

The student will be introduced to the elements of probability calculus and the theory of random variables, through the notions of space of events and the axioms of probability. He will be introduced to the concept of conditional probability and its possible applications. The case of discrete and continuous random variables, scalar and vector, will be treated through the introduction of the concepts of probability distribution, mean value, variance, moments with integer exponent, correlation and covariance. The fundamental theorems of the theory of random numerical variables will be studied with a focus on the law of large numbers and the central limit theorem.
We will then move on to the introduction of the fundamental concepts of sample space statistics through the theory of statistical estimators and confidence intervals. The concept of statistical hypothesis tests will then be introduced, exposing the main cases and their field of applicability. Finally, some elements of descriptive statistics and the linear regression technique will be introduced.

1) Calcolo delle probabilità e statistica per le scienze e l'ingegneria, Pasquale Erto, McGraw-Hill (2008)
2) Probabilità e statistica per l'ingegneria e le scienze, Sheldon M. Ross, Maggioli editore (2023)

Introduction to the course

1. Characteristics of soils
• origin of natural soils, marine and continental environment
• identification and classification of soils

2. Porous continuous medium model
• review on stress analysis, Mohr circle
• review on strain analysis, volume change and distortion
• principle of effective stresses
• equations of equilibrium and compatibility

3. Distribution of pore pressures and stress in the soil
• hydrostatic conditions, capillary rise
• filtration motions (1D only) in soils
• tests for permeability measurement
• lithostatic stress state

4. Models of elastic and plastic material
• linear elasticity; drained and not drained conditions; ideal sampling
• elements of plasticity theory (1D conditions only)
• viscosity

5. Compressibility of soils
• mechanical laboratory tests
• edometric compression test
• analysis of the consolidation process

6. Deformability and resistance of soils
• mechanical behaviour of soils under drained and undrained conditions
• TD direct shear test; TX-CID drained triaxial tests
• criteria for shear strength, critical state, undrained shear strength
• TX-UU, TX-CIU undrained triaxial tests
• in-situ geotechnical tests; SPT standard penetration test, VT vane test

7. Introduction to analysis and design of geotechnical structures
• foundation structures, stress induced by foundation loads
• calculation of foundation settlements in coarse and fine grain soils
• calculation of soil pressure (active and passive yield conditions, Rankine)
• earth retaining structures, cantilever and gravity walls
• limit equilibrium methods (Coulomb)
• limit analysis methods
• bearing capacity of a foundation

- Lecture notes prepared by the lecturer and further suggested readings.

- Geotechnical engineering – Lancellotta, Ed. Balkema
- Foundation analysis and design - Bowles, Ed. McGraw-Hill

1. Safety of structures and Limit States approach
2. Actions on structures and their combinations
3. Steel structures
- Mechanical properties of steel
- Design of steel members under tensile loading
- Design of steel members under bending and shear
- Design of steel members under compression and bending (buckling)
- Design of bolted and welded joints
- Trusses
4. Reinforced concrete (r.c.) structures
- Mechanical properties of steel and concrete
- Design of r.c. beams under bending and shear
- Design of r.c. columns under compression and bending
- Design and representation of steel rebars and details

Main books and building codes:
- Giannini R, Teoria e Tecnica delle Costruzioni Civili, CittàStudi, 2011
- Norme tecniche per le costruzioni, DM 14/01/2008 – Cap 1, 2, 3, 4, 11
- Circolare sulle Nuove norme tecniche per le costruzioni di cui al DM 14/01/2008 (GU n.47 26/02/2009)

Other books:
- AICAP, Dettagli Costruttivi di Strutture in Calcestruzzo Armato, 2011
- AICAP, Costruzioni in Calcestruzzo, Costruzioni composte acciaio-calcestruzzo, Commentario alle Norme -Tecniche per le Costruzioni D.M. 14/1/2008, 2011.
- Mezzina M. Fondamenti di tecnica delle costruzioni. Cittàstudi, 2013
- Cosenza E, Manfredi G, Pecce M. Strutture in Cemento Armato. Basi della progettazione. Hoepli, 2015.
- Bernuzzi C. Progetto e verifica delle strutture in acciaio. Hoepli, 2011.

Other standards:
- Eurocode 2: Design of concrete structures – Part 1-1: General rules and rules for buildings (prEN 1992-1-1) December 2003 – Italian Annex
- Consiglio Superiore dei Lavori Pubblici, Servizio Tecnico Centrale. Linee guida per la messa in opera del calcestruzzo strutturale. Settembre 2017
- Consiglio Superiore dei Lavori Pubblici, Servizio Tecnico Centrale. Linee guida per la valutazione delle caratteristiche meccaniche del calcestruzzo indurito mediante prove non distruttive. Settembre 2017

Software:
VCASLU (free software for the analysis of reinforced concrete sections under ocmpression and bending)

The course is made of two parts. The first part provides the students with the main notions of applied hydrology for water management and flood risk management; the second is dedicated to the design of urban water supply and sewer systems.
Part 1 – Hydrology
1.1) Rainfall: rainfall genesis, rainfall measurements, rainfall regimes, intense rainfall, rainfall amount at the catchment scale.
1.2) Evapotranspiration: phenomenology and measures.
1.3) Catchment and hydrogeological basin definitions: water balance.
1.4) Groundwater hydrology: unsaturated zone, aquifers and spring classification.
1.5) Surface water storage: lakes.
1.6) Surface water flow: flow discharge measurements, river regimes, probabilistic models.
1.7) Hydrologic losses and runoff generation mechanisms.
1.8) Rainfall-runoff models: lumped linear models, kinematic model.
Parte 2 – Water supply and sewer systems
2.1) Water use, sustainable water use.
2.2) Water-intake hydraulic structures for surface water.
2.3) Artificial lakes and dams.
2.4) Water transport, open channel flow.
2.5) Water transport, aqueducts, network configurations, manufactures, pumping stations.
2.6) Urban reservoirs.
2.7) Sewer systems.

(in Italian)
Calenda, G. (2016). Infrastrutture Idrauliche. Vol. 1 – Idrologia e Risorsa Idrica, Edizioni Efesto, Roma.
Calenda, G. Introduzione alla statistica (dispense).
Calenda, G. Fognature (dispense).

The course will lead to an understanding of the fundamental principles governing the design of road engineering projects including technical and environmental constraints by carrying out the calculations and producing the required drawings of the different geometrical design of the road project. Moreover, the course covers the required knowledge for the full design of all required geometrical characteristics of a road project including horizontal layout, vertical layout, and speed diagram. Theoretical information will be provided on cross sections, section areas calculations, earthwork volume diagrams and volume calculations, and super elevation diagrams.

A. Benedetto “Strade Ferrovie Aeroporti” - Utet editore;
Italian road design regulations and Public procurement code;
Handouts and slides provided by the professor.

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.

Specifically, the lectures concern:
• Transport systems
• Demand and supply
• Design of infrastructures
• Highway Capacity Manual – Exercises
• Transport supply model: graph construction
• Four steps demand model
• Emission model: origin/destination model
• Distributional model: uniform factor model, average factor model, Detroit model, gravitational model
• Route choice model
• Algorithms to compute the minimum path: Bellman teorem and Dijkstra model
• Assignment model
• Benefit/cost analysis
• Exercises with Excel and EMME software
• Project with Excel and EMME software

Lecture notes 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 staircase, 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
• Cinuzzi, Gaudiano, Progetto di Strutture in c.a. – ESA ed.

Identification of the primary structures of a building and consequent preliminary design choices. Identification of the static schemes for the calculation of stresses in structural elements and their design: the design of beams and columns (types, preliminary sizing criteria, load analysis, reinforcement calculation), the design of the staircase, the calculation of foundations (footings and inverted beams).
Validation of structural calculations.
Graphical representation of a project.

• Giannini R., Teoria e Tecnica delle Costruzioni Civili, 2011
• Cinuzzi, Gaudiano, Progetto di Strutture in c.a. – ESA ed.

EXTERNAL AQUEDUCT SYSTEMS
1. Water needs assessment
2. Tank, regulation, control room
3. identification of the of the optimal pipeline system
4. Design of the pipeline (external aqueduct)
5. Verification of the external Aqueduct
6. Materials, structural verification
7. Artifacts
8. Preparation of reports;

DRAINAGE NETWORK SYSTEMS
9. Introduction to drainage systems, rainfall
10. Hydrological losses
11. Design of the drainage network
12. pumping systems
13. The water quality problem, green infrastructures

- Seminars on aqueducts
- Seminar on Drainage systems

Fondamenti di Costruzioni Idrauliche, Becciu G e Paoletti A. , Utet Scienze Tecniche, ISBN: 8859805228;
Infrastrutture Idrauliche Vol. 1, Calenda G., Edizioni Efesto, Roma (2015), ISBN: 978-88-99104-13-9.