## Mechanics of Materials and Structures

OBJECTIVES

LEARNING OUTCOMES: The goal of this course is to provide the student with basic knowledge of the mechanics of linearly elastic structures and of the strength of materials. By completing this class successfully, the student will be able to compute simple structural elements and reasonably complex structures.

KNOWLEDGE AND UNDERSTANDING: At the end of this course, the student will be able to:

• compute constraint reactions and internal actions in rigid-body systems and beams subjected to point/distributed forces and couples
• compute centroid position and central principal second-order moments of area distributions
• understand the formal structure of the theory of linear elasticity for both discrete and continuous systems (beams and 3D bodies)
• analyze strain and stress states in 3D bodies
• compute the stress state in beams subjected to uniaxial bending, biaxial bending, eccentric axial force
• understand the behavior of beams subjected to shear with bending, and torsion
• understand how to compute displacements/rotations in isostatic beam systems, how to solve statically underdetermined systems, how to apply yield criteria, and how to design beams against buckling

APPLYING KNOWLEDGE AND UNDERSTANDING: The student will apply the knowledge and understanding skills developed during the course to the analysis of practical problems. This includes the analysis of linearly elastic structures and structural members in terms of strength and stiffness.

MAKING JUDGEMENTS: The student will have to demonstrate his awareness of the modeling assumptions useful to describe and calculate structural elements, as well as his critical judgment on the static response of elastic structures under loads, in terms of stresses, strains, and displacements.

COMMUNICATION SKILLS: The student will demonstrate, mostly during the oral test, his capacity of analyzing and computing the static response of linearly elastic structures, as well as his knowledge of the underlying theoretical models.

LEARNING SKILLS: The student will get familiar with the modeling of structures and structural elements in practical problems, mostly during the development of his skills for the written test. This mainly concerns discrete systems, beams, and three-dimensional bodies.

COURSE SYLLABUS

• Review of basic notions of vector and tensor algebra and calculus.
• Kinematics and statics of rigid-body systems.
• Geometry of area distributions.
• Discrete linearly elastic systems, static-kinematic duality, solution methods.
• Strain and stress in 3D continuous bodies and beam-like bodies.
• Virtual power and virtual work equation for discrete systems, beams, and 3D bodies.
• One-dimensional beam models: Bernoulli-Navier model, Timoshenko model, constitutive equations, governing differential equations.
• Constitutive equation for linearly elastic and isotropic bodies, material moduli.
• Hypothesis in linear elasticity, equilibrium problem for linearly elastic discrete systems, beams, and 3D bodies.
• Three-dimensional beam model: the Saint-Venant problem, uniaxial and biaxial bending, eccentric axial force, shear and bending, torsion.
• Elastic energy of beams and 3D bodies, work-energy theorem, Betti’s reciprocal theorem, Castigliano’s theorem.
• Yield criteria (maximum normal stress, maximum tangential stress, maximum elastic energy, maximum distortion energy).
• Buckling instability, bifurcation diagrams, load and geometry imperfections, Euler buckling load, design against buckling.
• Basic notions on the finite element method and structural analysis software.

## Feedback Control Systems

OBJECTIVES

LEARNING OUTCOMES:
The theory of differential equations is successfully used to gain profound insight into the fundamental mathematical control design techniques for linear and nonlinear dynamical systems.

KNOWLEDGE AND UNDERSTANDING:
Students should be able to deeply understand (and be able to use) the theory of differential equations and of systems theory, along with related mathematical control techniques.

APPLYING KNOWLEDGE AND UNDERSTANDING:
Students should be able to design feedback controllers for linear (and even nonlinear) dynamical systems.

MAKING JUDGEMENTS:
Students should be able to identify the specific design scenario and to apply the most suitable techniques. Students should be able to compare the effectiveness of different controls, while analyzing theoretical/experimental advantages and drawbacks.

COMMUNICATION SKILLS: Students are expected to be able to read and capture the main results of a technical paper concerning the topics of the course, as well as to effectively communicate in a precise and clear way the content of the course. Tutor-guided individual projects (including Maple and Matlab-Simulink computer simulations as well as visits to labs) invite an intensive participation and ideas exchange.

LEARNING SKILLS:
Being enough skilled in the specific field to undertake following studies characterized by a high degree of autonomy.

COURSE SYLLABUS

Linear systems
The matrix exponential; the variation of constants formula. Computation of the matrix exponential via eigenvalues and eigenvectors and via residual matrices. Necessary and sufficient conditions for exponential stability: Routh-Hurwitz criterion. Invariant subspaces. Impulse responses, step responses and steady state responses to sinusoidal inputs. Transient behaviors. Modal analysis: mode excitation by initial conditions and by impulsive inputs; modal observability from output measurements; modes which are both excitable and observable. Popov conditions for modal excitability and observability. Autoregressive moving average (ARMA) models and transfer functions.
Kalman reachability conditions, gramian reachability matrices and the computation of input signals to drive the system between two given states. Kalman observability conditions, gramian observability matrices and the computation of initial conditions given input and output signals. Equivalence between Kalman and Popov conditions. Kalman decomposition for non-reachable and non-observable systems.
Eigenvalues assignment by state feedback for reachable systems. Design of asymptotic observers and Kalman filters for state estimation of observable systems. Design of dynamic compensators to stabilize any reachable and observable system. Design of regulators to reject disturbances generated by linear exosystems.
Introduction to adaptive control. Introduction to tracking control. Minimum phase systems and Proportional Integral Derivative (PID) control.
Bode plots. Static gain, system gain and high-frequency gain. Zero-pole cancellation. Nyquist plot and Nyquist criterion. Root locus analysis. Stability margins. Frequency domain design. Realization theory.

Introduction to nonlinear systems Nonlinear models and nonlinear phenomena. Fundamental properties. Lyapunov stability. Linear systems and linearization. Center manifold theorem. Stabilization by linearization.

## Analogue Electronics

OBJECTIVES

COURSE SYLLABUS

• Classification of electrical systems and requirements.
• Analysis of transitory and frequency behavior.
• Distortion in electronic systems and Bode diagrams.
• Diode semiconductor devices and circuit applications: clipper, clamper, peak detector, etc. Bipolar Junction and Field-Effect Transistors.
• Biasing techniques for Transistors. Amplifiers classification, analysis and circuit design.
• Frequency response of single and cascaded amplifiers.
• Differential amplifiers and Cascode.
• Current mirrors.
• Feedback amplifiers and stability issues. Power amplifiers.
• Operational amplifiers and related applications.
• Oscillator circuits. Integrated circuits and voltage waveform generators.

## Physics II

OBJECTIVES

LEARNING OUTCOMES: Learning the basic elements of Electromagnetism and fundamental physical principles of quantum mechanics.

KNOWLEDGE AND UNDERSTANDING:
Knowledge of the basic principles of electromagnetism and quantum mechanics useful for the own field of study. Understanding of advanced books on the arguments treated during the course.

APPLYING KNOWLEDGE AND UNDERSTANDING:
Capacity to develop autonomously basic conceptual ideas using arguments treated during the course.

MAKING JUDGEMENTS:
Capacity to evaluate autonomously ideas or project using the knowledge acquired in the course.

COMMUNICATION SKILLS:
Capacity to share informations and ideas on the basis of knwoledge acquired in the course.
Comprehension of specific problems and relative solutions proposed.

LEARNING SKILLS:
The knowledge acquired in the course must be of help for the student in future courses, improving the capacity of autonomous learning.

COURSE SYLLABUS

1) Electric Charge and Electric Field : Conductors, Insulators, and Induced Charges.
Coulomb’s Law. Electric Field and Electric Forces. Electric Field Lines. Charge and Electric Flux, Gauss’’ s Law. Charges on Conductors.
2) Electric Potential: Electric Potential Energy, Electric Potential, Equipotential Surfaces, Potential Gradient. Definition of electric dipole. Approximated formula for the electric potential of a dipole at large distances.
3) Capacitors and Capacitance. Capacitors in series and parallel configuration. Electrostatic Potential Energy of a Capacitor. Polarization in Dielectrics. Induced Dipoles. Alignment of Polar Molecules. Electric Field inside a dielectric material. Relative dielectric constant. Capacitors with dielectric materials.
4) Electric current, Vector current density J, Resistivity (ρ) and conductivity ( σ) of materials, Ohm’s law in vector and scalar form, Resistors and resistance, Microscopic theory of electric transport in metals (Drude model). Differences between thermal velocity and drift velocity of charge carriers. Thermal coefficient of resistivity for metal and semiconductors. Resistors in parallel. Kirchhoff current law and the conservation of charge. Resistors in series. Kirchhoff voltage law ( KVL) and the conservative nature of electric field. Resistor and capacitor in series. Charging a capacitor. Solving the equation for current and voltage in RC circuits, time constant.
5) Introduction to magnetism, historical notes. Magnetic Force on a moving charged particle in a Magnetic Field. Definition of the vector ( cross ) product. Vector product expressed by the formal determinant and calculated by Sarrus Rule. Thomson’s q/m experiment and the discovery of the electron. Magnetic force on a current carrying conductor. Local equation for the magnetic force, the second formula of Laplace. Introduction to current loops, the torque. Force and Torque on a current loop in presence of a constant magnetic field. The magnetic dipole moment. Torque in vector form. Stable and unstable equilibrium states. Equivalence between a magnetic dipole of a current loop and the dipole of a magnet. Potential energy of a dipole moment in a magnetic field. Force exerted on a magnetic dipole in a non-uniform magnetic field. Working principle of a dc motor. Generalization of a magnetic dipole to current loops with irregular area. Magnetic dipole of a coil consisting of n loops in series. The Hall effect.
6) Historical introduction to the Biot Savart Laplace equation. Electric current as sources of magnetic field, the current element. The Biot Savat Laplace (BSL) equation. BSL equation for an infinitely long wire with an electric current flow. The flux of the magnetic field B. The Gauss Law for the magnetic field. Forces acting on wires with electric current flow. Magnetic field on the axis of a current loop and a coil. Ampere Circuital Law. Definition of a Solenoid. Magnetic field from a long cylindrical conductor. Magnetic field from a toroidal coil. The Bohr magneton. Magnetic materials. Paramagnetism, Diamagnetism, Ferromagnetism.
7) Magnetic induction experiments. Faraday Law. Lenz Law. Flux swept by a coil and Motional Electromotive Force. Induced Electric Field. Displacement current. The four Maxwell equations in integral form. Symmetry of the Maxwell equation. Self induction. Inductors. Inductor as circuit element.Self inductance of a coil. Magnetic Field Energy. The R-L circuit. The LC circuit. The RLC series circuit.
8) The electromagnetic waves. Derivation of EM waves from Maxwell Equation. The electromagnetic spectrum. Electromagnetic energy flow and the Poynting vector. Energy in a sinusoidal wave. Electromagnetic momentum flow. Standing Electromagnetic waves.
9) Light waves behaving as particles. The photocurrent experiment. Threshold frequency and Stopping Potential. Einstein’s explanation of Light absorbed as “Photons”. Light Emitted as Photons: X-Ray Production. Light Scattered as Photons: Compton Scattering.
10) Interference and diffraction of waves. The Wave Particle Duality. De Broglie wavelength. The x-ray diffraction from a crystal lattice, the Bragg’s Law. The electron diffraction experiment of Davisson and Germer. The double slit experiment with electrons. Waves in one dimension: Particle Waves, the one-dimensional Schrödinger equation. Physical interpretation of the Wave Function. Wave Packets. Uncertainty principle. Particle in a box. Energy-levels and wave functions for a particle in a box. The tunneling effect.

## Mathematical Analysis II

OBJECTIVES

LEARNING OUTCOMES:
One learns power series, differential calculus of several variables, line integral, multiple integral and surface and volume integral. One obtains the ability to calculate partial derivatives of elementary and composed functions, calculate various integrals and apply theorems of Green, Gauss and Stokes to facilitate the computations.

KNOWLEDGE AND UNDERSTANDING:
To know the definitions of basic conepts (convergence of series, partial derivatives, extremal points, multiple integral, line integal, surface integral and volume integral) and apply various theorems to execute concrete computations.

APPLYING KNOWLEDGE AND UNDERSTANDING:
To identify the theorems and techniques to apply to the given problems and execute computations correctly.

MAKING JUDGEMENTS:
To understand mathematical concepts for the given problems and to divide them into smaller problems that can be solved with the knowledge obtained during the course.

COMMUNICATION SKILLS:
To frame the problems in the obtained concepts, express the logic and general facts that are used during the computations.LEARNING SKILLS:

To know precisely basic mathematical concepts and apply them to some simple examples in physics.

COURSE SYLLABUS

• Sequences and series of functions, Taylor series
• Differential calculus of scalar and vector fields
• Applications of differential calculus, extremal points
• Basic differential equations
• Line integrals
• Multiple integrals
• Surface integrals, Gauss and Stokes theorems

## Electrical Network Analysis

Electrical quantities and SI units. Electrical energy and electrical power. Passive and active sign convention. Passive and active elements. Ideal voltage and current sources. Basic ideal electric components: resistance, inductance, capacitance. Models of real components. Ohm-s law. Series and Parallel connection of components. Topological circuital laws: Kirchhoff’s Voltage Law (KVL) and Kirchhoff’s Current Law (KCL). Mesh Current Method, Node Voltage Method. Sinusoidal functions: average and RMS (Root Mean Square) values.

Sinusoidal steady state circuit analysis. Phasors. Impedance and admittance. Analysis of circuits in AC steady state. Electrical power in the time domain and in sinusoidal steady state: active power, reactive power, complex power. Power factor correction. Maximum power transfer in AC. Application of superposition theorem in circuit analysis. Thevenin’s and Norton’s theorems.

Frequency response: first order electrical filters. Resonance: series and parallel resonant circuits.

Mutual inductance and ideal transformer. Three-Phase systems. Introduction to the power distribution and transportation grid. Time response and transient analysis. The unit step function, unit impulse function, exponential function, first-order circuits. Laplace transform method, Laplace transform of some typical functions, initial-value and final-value theorems, partial-fractions expansions, analysis of circuits in the s-domain. Network functions and circuit stability.

Electrical measurement bridges. Introductions to the electrical safety and electricity distribution system: description and prospects. Basics of designing a power plant. Effects of electricity on the human body and relative protection systems. Introduction to electrical machines: Tranformer and DC motor.

## Linear Algebra and Geometry

OBJECTIVES

LEARNING OUTCOMES: The course provides an introduction to linear algebra and euclidean geoemetry.

KNOWLEDGE AND UNDERSTANDING: The student will learn to solve simple geometric and algebraic problems using the tools provided by the course.

APPLYING KNOWLEDGE AND UNDERSTANDING: Ability to apply knowledge and understanding to concrete problems.

MAKING JUDGEMENTS: The student will learn how to interpret the data of an algebraic or geometric problem without following standard schemes.

COMMUNICATION SKILLS: The student will show, esapecially during the oral exam, her/his ability to describe the logical process that yields the theorems studied in the course.

LEARNING SKILLS: The student will learn to understand the exercises of the written exams, and to develop a method to solve them.

COURSE SYLLABUS

Linear equations and linear systems. Solutions. Consistency of a system. Basic and free variables. Matrix of coefficients. Augmented matrix. Row reduction to echelon matrix. Exercises on linear systems. Numerical vectors. Addition and multiplication by scalars. Linear combinations. Linear systems and vectors. Linearly independent vectors. Finding subsets of linearly independent vectors. Linear systems in matrix form. Exercises on linear systems in vector form. Canonical basis. Linear space. Basis and coordinates of vectors. Steinitz lemma. Dimension of linear spaces. Rank of a matrix. Linear spaces of rows and columns of a matrix. Null space of a matrix. Matrix transformations. Injectivity, surjectivity and rank. Linear transformations and matrices. Multiplication and addition of matrices and their linear transformations. Invertible matrices. Computing the inverse via row reduction Change of coordinates and matrices Vector (linear) spaces. Examples of polynomials and matrices. Linear subspaces. Intersection of linear subspaces. Sum of linear subspaces. Grassmann formula. Basis for intersections and sums of linear spaces. Determinants: definition, properties, computation. Computation of the rank using determinants. Computation of the inverse matrix using determinants. Determinant of a product. Cramer’s formula. Linear transformation between vector spaces. Image and kernel. Matrix of a linear transformation with respect to basis of the domain and of the range. Lines in the plane and in 3-dim. space. Planes in the 3-dim. space. Cartesian and parametric equations. Lines through 2 points. Plane through 3 non collinear points. Relative position of two planes. Relative position of two lines in 3-dimensional space. Inner product. Norm. Distances. Orthogonal vectors, lines, planes. Angles. Cross product in 3-dim. space. Mixed product. Area of parallelogram. Volume of parallelepiped. Eigenvalues and eigenvectors. Characteristic polynomial. Algebraic and geometric multiplicities. Diagonalization of endomorphisms and matrices. Orthogonal subspaces, orthonormal basis, orthogonal matrices.
Gram-Schmidt orthonormalization. Formula for the orthogonal projection. Matrix of orthogonal projections. Spectral theorem for symmetric matrices. Quadratic forms and their classification.Conic curves: classification Rotations and translations that put a conic in normal form.

## Fundamentals of Computing

OBJECTIVES

LEARNING OUTCOMES:
The course aims to provide students with knowledge and skills for an effective use of computer methodologies and tools in the field of engineering, expecially for the development of algorithms.

KNOWLEDGE AND UNDERSTANDING:
Acquire knowledge of the internals of computer architectures.
Acquire knowledge on data structures and algorithms.
Acquire knowledge on the principles of programming languages, including the object-oriented paradigm, and on tools and techniques for software development.

APPLYING KNOWLEDGE AND UNDERSTANDING:
Acquire ability to analyze problems and produce a design and implementation of software artifacts addressing them.
Acquire capability of group working on software development and documentation.

MAKING JUDGEMENTS:
Being able to choose appropriate languages and tools for software development.
Being able to evaluate the correctness and efficiency of a software implementation.

COMMUNICATION SKILLS:
Be able to describe and document software artifacts correctly and effectively.

LEARNING SKILLS:
Being able to use effectively the technical documentation and the reference manuals of systems, products and languages.

COURSE SYLLABUS

• Introduction to Computer Science; Von Neumann architecture; Computer Architectures; CPU and GPU; Programming Paradigms; Functional and Object Oriented Approaches; Principles of Software Engineering and Modeling; Basic concepts and comparison of Programming Languages; Variables; Control structures (Loops, Conditional Selection), Data structures and algorithms; Computational Complexity; Functions and parameters; Recursion; Sorting algorithms; Input/Output; Concurrency and Parallelism; Networking and Distributed Applications; Version Control; The Art of Documentation; Introduction to Safety, Security and Reliability concepts.
• The programming languages taught are C, Java and Rust

## Fundamentals of Chemistry

LEARNING OUTCOMES:
To provide students with basic chemical skills, in order to facilitate the understanding of the subsequent class of the course. To provide a solid basic knowledge of chemistry, preparatory to the understanding of a wide range of phenomena. To provide the tools for a proper interpretation of matter and its transformations, both at a microscopic (atomic/molecular) and macroscopic (phenomenological) level.

KNOWLEDGE AND UNDERSTANDING:
At the end of the lectures, the student must have acquired the knowledge necessary to understand and apply general chemistry concepts, in particular concerning reactivity and structure of matter in its different states of aggregation, with specific regard to relevant issues of Engineering Science. The acquired skills will be employed by the student to carry out more advanced studies.

APPLYING KNOWLEDGE AND UNDERSTANDING:
At the end of the teaching period the student must have matured the ability to apply the theory of basic chemistry to the resolution of exercises and problems, with specific reference to engegneering science.

MAKING JUDGEMENTS:
Judgment skills are developed through individual or group works. The student will have to self-evaluate (self assessment-test) and compare with colleagues.

COMMUNICATION SKILLS:
At the end of the teaching sessions the student will be able to use a rigorous chemical language, both in written and oral form, together with the use of graphic and formal languages to represent the descriptive models of the matter.
Inoltre lo studente avrà la possibilità di dimostrare di saper operare efficacemente nel gruppo di pari utilizzando supporti informatici per raccogliere e divulgare informazioni.
In addition, the student will have the opportunity to demonstrate that he / she can work effectively in the peer group using IT support to collect and disseminate information.

LEARNING SKILLS:
At the end of the teaching sessions the student will be able to understand and predict the outcome of the most common inorganic reactions, as well as correlate structure-reactivity properties of the fundamental inorganic compounds and of selected simple organic molecules

COURSE SYLLABUS

• The scientific method. Elements and compounds. Chemical formulas. The balancing of chemical reactions. Chemical nomenclature (notes). Stoichiometric calculations. The principal chemical reactions. Atomic Theory. Sub-atomic particles. Isotopes. Quantum Theory. Particles and waves. Quantum numbers. Atomic orbitals. Pauli and Hund principles. Electronic structures of atoms. The periodic system and periodic properties.
• Chemical bonds. Ionic and covalent bonds. Valence bond theory: hybridization and resonance. Determinationof meolecular structuresbased on the repulsion of the valence electron pairs (VSEPR). Molecular orbitals theory (LCAO-MO). Application of MO theory for homo- ed heteronuclear diatomic molecules of the I and II period. Dipolar interactions. Hydrogen bond. Metallic bond. Band theory. Structure and conductivity.
• Solid state. Crystal and amorphous solids. Metals. Ionic crystals and lattice energy. Insulators and semiconductors.
• The gaseous state. Ideal gas laws. Ideal gas equation. Dalton law. Real gases: van der Waals equation.
• First principle of thermodynamics. State functions: Internal Energyand Enthalpy. Thermochemistry. Hess law. Secondand third principleofthermodynamics. Entropyand Free Energy. Equilibrium and spontaneity criteria. Molar free energy: activityand standard states.
• Vapour pressure. Clapeyron equation.
• Solutions: Phase equilibria. State diagrams. Fractional distillation.Colligative properties for ideal solutions.
• Chemical equilibrium: Le Chatelier principle. Equilibrium constant. Law of mass action. Gaseous dissociation equilibria.
• Electrolytic systems: electrolytic dissociation equilibria, electric conductivity. Colligative properties of electrolytic solutions. Low soluble electrolytes: solubility product.
• Acid-base equilibria. Autoionizationof water: pH. Monoprotic and polyprotic acids and bases. Buffer solutions. Indicators. Titrations. pH dependent solubility.
• Chemical kinetics: Chemical reactions rate, activation energy, catalysis.
• Red-ox systems: electrode potentials. Galvanic cells: Nernst equation. Electrolysis: Faraday law; electrode discharge processes.
• Electrochemical applications: Fuel cells, batteries. Metal corrosion.
• Nuclear Chemistry. Notes of Organic chemistry. Polymers.