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

October
Definition of a function, domain, codomain, image, graph. Injective, surjective, bijective functions, goniometric functions, inverse goniometric functions. Complex numbers: definition, properties, equations, power. Sequences: definition, theorems, limit of a sequence. Limits of functions.

November
Derivative: definition, geometrical meaning, derivative of elementary functions and by composition, derivative of the inverse function. Taylor polynomial, approximation of a function by Taylor polynomial, approximation error, limits using Taylor polynomials, o – notation. Function study in order to draw the graph: domain, simmetries, sign, intersection with the axis, limits and asymptotes, first derivative, monotonicity, minimum and maximum points, second derivative, convexity, inflection points.


December
Primitive functions, definition e theorems. Integrals of elementary functions and by composition, linear property. Techniques of integration: rational function, irrational function (Euler substitution), trigonometric substitution, substitution, by parts, fundamental theorem of calculus, definite integral. Improper integral with finite and infinite interval: solution by limit and by convergence tests.

January
Series, convergence tests: limit comparison test, ratio test, root test, integral test, Leibniz test, absolute convergence test.

Exercises on the syllabus topics, midterm exam simulations.

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

Flamini-Verra "Matrici e vettori" Carocci ed.

Basic concepts:
- Problems and algorithms
- Computer architecture
- languages and compilation
- I/O, variables, constants

Operations:
- Data types
- Expressions
- Boolean algebra

Control structures:
- Selection
- Iteration
- Functions

Data structures:
- Array
- Struct

Advanced topics:
- Libraries

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

Programming in Python
- Syntax
- Data structures
- Numerical computation (vectors and matrices)
- Data management (tables)
- Data Analysis

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

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.

Slides provided by the teacher

Taylor series and Fourier series. Ordinary differential equations: existence and local uniqueness; homogeneous and non-homogeneous linear ordinary differential equations.
Functions of several variables; continuity; partial derivatives; local maxima and minima, Hessian matrix. Lagrange multipliers. Integration according to Riemann;
multiple integrals. Curvilinear curves and integrals; surfaces and surface integrals. Divergence theorem and curl theorem.

T. Apostol, Calculus, vol. 2, Wiley

Teaching unit I – Fundamental tools and methods
Elements of vector algebra
Rotation matrix
ODE homogeneous and non-homogeneous
Spectral analysis of symmetric matrices
Eigenvalues problem and diagonalization
Conservative, potential and irrotational vector fields
Teaching unit II – Mechanics of a material particle
Fundamental properties of the motion of a particle
Dynamics of free and constrained material elements
Un-damped and damped oscillators
Mechanical work, power and energy
Stabilty of mechanical equilibrium
Teaching unit III – Mechanics of systems of particles
Internal forces
Conservation of momentum
Conservation of angular momentum
Kinetic energy, Koenig’s theorem
Teaching unit IV – Rigid-body motion and Galilean relativity
Two- and Three-dimensional rigid-body motion
Kinematics in non-inertial frames of reference
Dynamics in non-inertial frames of reference, fictitious forces
Derivative of vectors in moving frames of reference
Trasformazioni tra riferimenti in moto relativo
Derivata temporale di R
Teaching unit V – Statics and dynamics of rigid bodies
Dynamics
Conservation of momentum and angular momentum
Inertia tensor
Ellipsoid of inertia
Koenig’s theorem
Euler equations
Rotation about central axes
Gyroscopes and precessions
Statics
Equivalent forces
Central axis of a system of forces
Constraints reactions
Graphic methods for the analysis of equilibrium
Teaching unit VI – Elements of Lagrangean mechanics

• Lecture notes with solved problems

Aircraft components and their role in flight.
Elements of steady aerodynamics of fixed wings: lift and drag coefficients, polar curve of the aircraft; aerodynamic efficiency; finite wings.
Fixed-wing aircraft performance: power curve, range and endurance; climb performance, ceiling.
Glide performance and climb hodograph.
Maneuvers (steady turn, flare maneuver) and gust response.
Load factor, V-n diagram, gust envelope and flight envelope.
Take off and landing performance.
Aircraft trimmed flight conditions.
Aircraft static stability and corresponding characterizing parameters.

• Lecture notes
• Mc Cormick, B.W., Aerodynamics, Aeronautics, and Flight Mechanics. Wiley and Sons, 1995.
• Etkin, B., Dynamics of Flight-Stability and Control. John Wiley & Sons, Inc., 1996.

Introduction to the World of Materials
- Historical background, evolution of materials, an internal look at their structure, and an overview of transformations
- Properties and performance of components

Basic Properties and Elastic Behavior
- Intrinsic properties
- Extrinsic properties
- Mechanical stress systems: rigid body, deformable body, continuum mechanics; linear elasticity, Hooke's law, elastic behavior of isotropic solids

Composition and Structure of Matter at Different Dimensional Scales
- Composition: molecules, chemical bonding, Condon-Morse curves; ionic materials, molecular materials
- Thermodynamic origin of elasticity
- Structures: amorphous and crystalline, Bravais lattices, and Miller indices
- Defects in crystalline solids: point, line, and surface defects

Mechanical Behavior of Materials
- Influence of T (temperature) and t (time) on mechanical behavior depending on the nature of the material
- Static tensile stresses at low T: stress-strain curve (elastic field, plastic field, critical points)
- Mechanical properties: ductility, hardness, brittleness, resilience, and toughness (property measurement techniques)
- Fracture mechanics: Griffith's energy theory, stress intensity factor, fracture toughness
- Dynamic stresses: fatigue, Wohler curve, Paris-Erdogan law

Single-Phase and Multi-Phase Systems
- Thermodynamics of systems: thermodynamics of condensed states, basic concepts, first law, second law, equilibrium conditions, non-equilibrium states, combined first and second laws, characteristic state functions
- Solid-state solubility: cooling curves of single-component systems, aggregation state, Hume-Rothery rules, solid solutions, phases
- Solubility dependence on composition, temperature, and pressure: Gibbs rule and lever rule, Gibbs energy, Gibbs curves, phase equilibria in binary systems
- Solid-state phase transformations: diffusion mechanisms, activation energy, and Fick’s laws
- Solidification kinetics and microstructures: nucleation and growth, key thermodynamic transformations, microstructures

Introduction to the Main Classes of Metallic Materials
- Iron-based alloys: classification of steels and cast irons, main phase diagrams, classification of specific heat treatments; special steels, stainless steels, and applications
- Titanium alloys: properties, processes – applications
- Aluminum alloys: properties, processes – applications
- Superalloys: properties, processes – applications

Introduction to the Main Classes of Non-Metallic Materials
- Polymers and polymer matrix composites: properties, processes, applications
- Ceramics: properties, processes, an introduction to Weibull statistics – applications

Recap, Complements, In-Depth Topics, and Numerical Exercises for Each Subject

W.D. Callister, Jr. and D.G. Rethwisch
- Materials Science and Engineering
Publisher: Wiley

Vincenzo Casciaro and Carlo Mapelli
- Science and Technology of Metallic Materials
Publisher: CittàStudi Edizioni

Lucio Vergani, Maurizio Carboni
- Exercises in Materials Science and Technology
Publisher: Esculapio

Slides shown during lectures: available as PDFs on Moodle
Lecture notes: available online on the group's Teams site

Introductory concepts, deformation and motion of a particle, Cauchy theorem, Eurlerian and Lagrangian description, the Reynolds transport theorem, the material derivative. Forces and moments on airfoils. Buckingham theorem. General governing equations in integral and differential form. Constitutive relationships for Newtonian fluids. Navier-Stokes equations, Bernouilli equation. Vorticity dynamics. Potential flows and singular solutions (the case of the cylinder). Glauert theory for 2D airfoil. Finite wing theory. Low Reynolds number flows in ducts and Moody's diagram. Boundary layer concepts and theoretical approach for a 2D steady case. The separation of the boundary layer.

Notes provided by the teacher.
Graziani G., Aerodinamica, Univ. La Sapienza ed., 2010.
Anderson, Jr. J.D. , Fundamentals of Aerodynamics, 2nd Editino, McGraw Hill, 1991.

General concepts: airfoils and wings.
Potential flows in 2D and 3D, Green's theorem and Green's function, BEM methods.
The theory of infinite (Glauert) and finite (Prandtl) wings, the lifting line and surface.
Boundary layer theory: Falkner-Skan solutions and integral methods.
Fundamentals of Signal theory, Fourier series and Fourier transform. Fundamentals of the theory of probability and statistics, correlation functions and Power Spectral Density.
Turbulence: general equations for incompressible flows, modelling, Kolmogorov theory, turbulent boundary layer.
Computational Fluid Dynamics (CFD): discretization of the governing equations using Finite Difference method and Finite Volumes; Application of industrial codes.

- Notes distributed by the teacher
Further references are the following:
- Anderson, Jr. J.D. , Fundamentals of Aerodynamics, 2nd Editino, McGraw Hill, 1991.
- Mattioli E. Aerodinamica, Levrotto e Bella, Torino, 1989.

Electric field and magnetic field. Electromagnetism fundamentals, basic principles and theorems for the analysis of electric and magnetic circuits. Electric circuits in dc. Representation of sinusoidal electric quantities, definition of circuit impedance and analysis of single-phase and three-phase circuits; instantaneous power, active power and power factor in single-phase and three-phase circuits.
Methods for measuring current, voltage, active power, power factor and energy in single-phase and three-phase circuits.
Basic principle and operating characteristics of power transformers. Basic principles of static power conversion. Storage units and fuel cell generators.
Theory of the rotating magnetic field; basic structure and operating characteristics of induction and synchronous machines.
Components being used in electric systems; protection against either overvoltages or overcurrents; sizing of low-voltage secondary-network systems; power-factor correction; protective grounding and safety-related aspects in power distribution systems. Photovoltaic generating units and ground power units.

- G. Chitarin, F. Gnesotto, M. Guarnieri, A. Maschio, A. Stella - Elettrotecnica, 1 - Principi - Società Editrice Esculapio
- G. Chitarin, F. Gnesotto, M. Guarnieri, A. Maschio, A. Stella - Elettrotecnica, 2 - Applicazioni - Società Editrice Esculapio
- Additional Documents and Numerical Exercises available on either Moodle or Microsoft Teams

Kinematics of rigid bodies. Planar rigid displacements. Systems of rigid bodies.

Kinematic characterization of a constraint. External constraints and internal constraints.
Lability.

Statics of rigid bodies. External forces. Force, moment of a force, systems of forces, force density, distributed loads.
Static characterization of constraints. The static problem. Cardinal equations of statics. Static classification.

Evaluation of internal actions. Differential equilibrium equations in scalar and vector format. Direct method. Internal action diagrams.

Reticular trusses. Node method. Ritter method.

Beam kinematics. Displacement, rotation, hypothesis of small displacements. Kinematic conditions. Deformation measurements. Axial deformation. Angular scroll. Curvature. Equations of congruence. Model of Euler-Bernoulli. Vector representation of congruence equations. The kinematic problem for the beam.

Constitutive equations. Phenomenology of the response of a material. The uniaxial test. Elastic behavior. Plastic behavior and rupture. Ductile and fragile materials.

Constitutive equations for the elastic beam. Axial behavior, flexural behavior, shear behavior. Uniform thermal variation, affine thermal variation.

The elastic problem for the beam and its formulation.

Displacement method. Equation of the tension beam. Inflexion of a beam in the Euler-Bernoulli model. Extension to the Timoshenko model. Connection conditions and problem formulation for beam systems. Kinematic and static performance of internal constraints.

Three-dimensional continuous bodies. Cauchy's concept of traction. Partwise balance. Cauchy's Lemma. The stress tensor. Differential equations of equilibrium. Principal stresses and principal directions. Voltage states. Lamé's ellipsoid of tension. Isostatic lines. State of plane or biaxial tension. Purely tangential tension state. Uniaxial voltage state. Mohr's circles for the stress.


The problem of Saint Venant. Postulate of Saint Venant. The semi-inverse method. Normal force. Flexure. Torsion of compact and hollow circular sections. The Neumann problem. Elliptical sections. Polygonal sections. The hydrodynamical analogy. Thin rectangular section. Open sections composed of thin rectangles. Thin-walled sections: Bredt's theory.

Bending and shearing. Distribution of normal tractions. Distribution of tangential tractions: Jourawsky formula and its applicability.
Thin sections open. Thin rectangular section. Thin double T section. U and H shaped sections. Thin sections closed. Symmetrical closed section. Symmetrical compact sections. Determination of the shear center.

Rupture and yielding criteria for fragile materials and ductile materials.

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.

Kinematics of rigid bodies. Planar rigid displacements. Systems of rigid bodies.

Kinematic characterization of a constraint. External constraints and internal constraints.
Lability.

Statics of rigid bodies. External forces. Force, moment of a force, systems of forces, force density, distributed loads.
Static characterization of constraints. The static problem. Cardinal equations of statics. Static classification.

Evaluation of internal actions. Differential equilibrium equations in scalar and vector format. Direct method. Internal action diagrams.

Reticular trusses. Node method. Ritter method.

Beam kinematics. Displacement, rotation, hypothesis of small displacements. Kinematic conditions. Deformation measurements. Axial deformation. Angular scroll. Curvature. Equations of congruence. Model of Euler-Bernoulli. Vector representation of congruence equations. The kinematic problem for the beam.

Constitutive equations. Phenomenology of the response of a material. The uniaxial test. Elastic behavior. Plastic behavior and rupture. Ductile and fragile materials.

Constitutive equations for the elastic beam. Axial behavior, flexural behavior, shear behavior. Uniform thermal variation, affine thermal variation.

The elastic problem for the beam and its formulation.

Displacement method. Equation of the tension beam. Inflexion of a beam in the Euler-Bernoulli model. Extension to the Timoshenko model. Connection conditions and problem formulation for beam systems. Kinematic and static performance of internal constraints.

Three-dimensional continuous bodies. Cauchy's concept of traction. Partwise balance. Cauchy's Lemma. The stress tensor. Differential equations of equilibrium. Principal stresses and principal directions. Voltage states. Lamé's ellipsoid of tension. Isostatic lines. State of plane or biaxial tension. Purely tangential tension state. Uniaxial voltage state. Mohr's circles for the stress.


The problem of Saint Venant. Postulate of Saint Venant. The semi-inverse method. Normal force. Flexure. Torsion of compact and hollow circular sections. The Neumann problem. Elliptical sections. Polygonal sections. The hydrodynamical analogy. Thin rectangular section. Open sections composed of thin rectangles. Thin-walled sections: Bredt's theory.

Bending and shearing. Distribution of normal tractions. Distribution of tangential tractions: Jourawsky formula and its applicability.
Thin sections open. Thin rectangular section. Thin double T section. U and H shaped sections. Thin sections closed. Symmetrical closed section. Symmetrical compact sections. Determination of the shear center.

Rupture and yielding criteria for fragile materials and ductile materials.

. Fundamental concepts of control systems
• Continuous-time dynamic systems and differential equations
• The Laplace transform
• Transfer function
• Stability and canonical responses
• Block diagrams
• Root locus
• The permanent polynomial regime
• The harmonic response and representations and the permanent sinusoidal regime
• Frequency behavior of the closed loop
• Sensitivity to parametric variations
• Compensating networks
• Standard regulators
• High gain loop control
• Direct synthesis of the controller in the frequency domain
• Stability of nonlinear systems and linearization
• Modeling and control of a quadcopter

• Teacher’s notes on lectures
• Teacher’ s exercices

The Aircraft Structures and Technologies course is part of the activities of the Construction and Aerospace Structures (ING-IND/04 SSD).

The teaching program is structured to provide students with knowledge and skills in the structural design of aeronautical components, using methods widely used in the aircraft conceptual and preliminary design phases.

The teaching program is divided into 36 lectures (equal to 9 CFU) divided into the following four main sections:

Introduction to aircraft design and semi-monocoque structures: loads acting on aircraft, regulations for aircraft design, box-wing concept, fuselage structure, and landing gear. Review of aeronautical materials and failure criteria of fragile and ductile materials. Structural design criteria: safe life, fail-safe, and damage tolerance.

Stress and strain analysis on beams: a review of bidirectional bending, torsion, and shear of open and closed thin-walled beams. Torsion and shear in multicell thin-walled beams.

Structural analysis of semi-monocoque structures: beam theory for torsion and shear of multicell thin-walled beams, stiffened and tapered. Structural idealization. The fuselage and box-wing stress and strain analysis. Cut-outs in wings and fuselages. Joints and connections.

Introduction to structural instability: buckling of beams (Euler's critical load); buckling on aeronautical structures.

- T.H.G. Megson, Aircraft Structures for Engineering Students, Arnold, London, 1999 (for all the contents of the syllabus)

- Lecture notes by the teacher (for all the contents of the syllabus)

The educational material used by the teacher from time to time is indicated during lectures. The lecture notes are available on the Moodle platform to facilitate their use for attending and non-attending students. On the same platform, are also made available the specifications of the project the students have to perform during the year, as well as a collection of written tests of previous exams, to provide students with a valid and realistic test bench for the final exam.

Introduction to Operations Research

Formulation of typical optimization problems:
Allocating resources
Inventory management
Assignment
Task planning
Other formulations

Solving Linear Programming problems:
Linear programming geometry

Difference between linear, integer and mixed optimization problems

Airline Operations and Delay Management
Cheng-Lung Wu

S.M. Pollock et al., Eds., Handbooks in OR & MS

PART 1: FUNDAMENTALS of THERMODYNAMICS ELEMENTS OF GAS-DYNAMICS/THERMO-DYNAMICS
General definitions; laws of thermodynamics; calculation of entropy variation; ideal and real thermodynamic cycles
PART 2: FUNDAMENTALS of GASDYNAMICS
Introductory concepts; governing equations for compressible flows; inviscid compressible flows; quasi-1D model for compressible flows; isentropic flows; 1D model for compressible flows; normal shocks; evolution of compressible flows in convergent and divergent ducts; entropy evaluation in a compressible flow; standard atmosphere
PART 3: PROPULSIVE SYSTEMS
Introductory concepts and classification. Performance parameters. Definition of thrust and power. Definition of efficiencies. Simple turbojet; turbofan; turboprop. Propellers and blade element theory. Nozzles and diffusers (subsonic and supersonic flows).

Notes provided by the professor
HILL P., PETERSON C., “MECHANICS AND THERMODYNAMICS OF PROPULSION”, ADDISON WESLEY PUBL., 2ND ED., 1992.
CUMPSTY N., “JET PROPULSION”, CAMBRIDGE UNIV. PRESS, 1997.