Elements of set theory. Maps between sets: invective, surjective, bijective maps.
Elements of propositional logic, truth tables. Equivalence and order relations.
Combinatorics. Binomial coefficients and binomial theorem. Permutations. The Integers: divisibility, GCD and Euclidean algorithm, Bézout identity, linear congruences.
Baiscs of algebraic structures: permutation groups, abstract groups, polynomials and finite fields.
Elements of graph theory.Lattices and Boolean algebras

Giulia Maria Piacentini Cattaneo
Matematica discreta e applicazioni
Zanichelli 2008

Elements of Set Theory.
Union, intersection, Cartesian product, set subtraction, complementary set, cardinality.

Set functions.
Domain, codomain, Range. Injective, surjective, bijective functions. Inverse function, Identity, Permutations.

Elements of logic.
Propositional calculus, Operations between propositions.

Relations.
Reflexive, symmetric, antisymmetric, transitive. Order and equivalence relations. Examples.
Equivalence relations and classes. Quotient set.

Integer numbers, Division and its properties.
Greatest common divisor. Euclidean algorithm. Prime numbers. Fundamental theorem of arithmetic.

Congruence mod n.
Basic modular arithmetic. Sum and multiplication in Zn. Linear congruence. Description of linear congruence solutions. Euler's totient function. Small Fermat Theorem, Euler’s Theorem

Combinatory algebra.
Dispositions and combinations with and without repetitions, binomial coefficient. Properties. Tartaglia's triangle.

Partially ordered sets
Hasse Diagram. Maximum and minimum, Sup and inf. Reticular formations. Properties of inf e sup. Boolean Algebra. The Boolean operators AND, OR and NOT.

Giulia Maria Piacentini Cattaneo
"Matematica discreta"
Edito da Zanichelli.

Lattices, Boolean algebras

Giulia Maria Piacentini Cattaneo
Matematica discreta e applicazioni
Zanichelli 2008

1. Linear equations and numbers
Systems of linear equations. Represent linear systems with matrix equations. Equivalent systems. Natural, integers, rational, real numbers and their properties. Pills of Graph Theory: subsets and set subtraction.

2. Matrixes and sets
Matrix with real coefficients. Square, triangular, diagonal matrixes. Transposed and symmetric matrix. Pills of Graph Theory: union and intersection.

3. Vector spaces and matrices
Matrix addition and scalar product and their properties.

4. Matrix product
Matrix product and its mathematical properties: associative and distributive. Example of how matrix product does not satisfy the commutative and simplification properties. Matrices and linear systems

5. Determinants
Formal definition of determinant and its properties. Transposed and triangular matrix determinants. Binet’s theorem.

6. Inverse of a matrix
Identity matrix. Inverse of a matrix and its properties. Cramer’s theorem.

7. Matrix rank
Definition and properties. Minor of a matrix.

8. System of linear equations.
Definition. Rouché-Capelli’s theorem. Rouché-Capelli’s method to solve a linear system.

9. Gaussian elimination and how to apply the Gaussian elimination
Elementary operation. Determinant and rank computations.

10. Geometric vectors
Vectors in 2 dimensions. Sum and scalar product of vectors. Vectors in 3 dimensions. Linear combination. Linear dependence and independence of vectors.

11. Vector spaces and Linear subspaces
Definition, examples and properties.

12. How to generate linear subspaces
Linear combination and generators.

13. Linear dependence and independence

14. Basis of a linear subspace
Basis. Dimensions. Solution set of an homogeneous system and its dimensions.

15. Vector subspaces sum and intersection
Grassmann formula.

16. Affine space
Lines in planes and space. Affine subspace.

17. Homomorphisms
Homomorphism between vector spaces. Represent an homomorphism as a matrix.

18. Image of a matrix
Properties of an homomorphism image and how to compute it. Surjective homomorphism.

19. Kernel of a matrix
Properties of an homomorphism kernel and how to compute it. Injectivity homomorphism.

20. Endomorphisms
Matrix representation of the endomorphisms. Change of basis.

21. Eigenvalues and Eigenvectors
Definition and properties. Eigenspaces. Characteristic polynomial. Diagonalizable matrix.

22. Diagonalizing a matrix
Rules and examples.

G. Accascina e V. Monti,
"Geometria"

1. Linear equations and numbers
Systems of linear equations. Represent linear systems with matrix equations. Equivalent systems. Natural, integers, rational, real numbers and their properties. Pills of Graph Theory: subsets and set subtraction.

2. Matrixes and sets
Matrix with real coefficients. Square, triangular, diagonal matrixes. Transposed and symmetric matrix. Pills of Graph Theory: union and intersection.

3. Vector spaces and matrices
Matrix addition and scalar product and their properties.

4. Matrix product
Matrix product and its mathematical properties: associative and distributive. Example of how matrix product does not satisfy the commutative and simplification properties. Matrices and linear systems

5. Determinants
Formal definition of determinant and its properties. Transposed and triangular matrix determinants. Binet’s theorem.

6. Inverse of a matrix
Identity matrix. Inverse of a matrix and its properties. Cramer’s theorem.

7. Matrix rank
Definition and properties. Minor of a matrix.

8. System of linear equations.
Definition. Rouché-Capelli’s theorem. Rouché-Capelli’s method to solve a linear system.

9. Gaussian elimination and how to apply the Gaussian elimination
Elementary operation. Determinant and rank computations.

10. Geometric vectors
Vectors in 2 dimensions. Sum and scalar product of vectors. Vectors in 3 dimensions. Linear combination. Linear dependence and independence of vectors.

11. Vector spaces and Linear subspaces
Definition, examples and properties.

12. How to generate linear subspaces
Linear combination and generators.

13. Linear dependence and independence

14. Basis of a linear subspace
Basis. Dimensions. Solution set of an homogeneous system and its dimensions.

15. Vector subspaces sum and intersection
Grassmann formula.

16. Affine space
Lines in planes and space. Affine subspace.

17. Homomorphisms
Homomorphism between vector spaces. Represent an homomorphism as a matrix.

18. Image of a matrix
Properties of an homomorphism image and how to compute it. Surjective homomorphism.

19. Kernel of a matrix
Properties of an homomorphism kernel and how to compute it. Injectivity homomorphism.

20. Endomorphisms
Matrix representation of the endomorphisms. Change of basis.

21. Eigenvalues and Eigenvectors
Definition and properties. Eigenspaces. Characteristic polynomial. Diagonalizable matrix.

22. Diagonalizing a matrix
Rules and examples.

G. Accascina e V. Monti,
"Geometria"

1. Linear equations and numbers
Linear equations systems. Matrix associated with a linear system. Equivalent systems. Natural, integer, rational numbers, real numbers and their property. Recall of set theory: inclusion of sets, difference between sets.
2. Matrices and sets
Matrices with real coefficients. Square, triangular, diagonal matrices. Transpose of a matrix and symmetric matrices. Recall of set theory: union and intersection of sets.
3. The vector space of the matrices
Addition between matrices and its properties. Multiplying a scalar for a matrix and its properties.
4. Product between matrices
Product between matrices with compatible dimensions. Properties of the product: associative property and distributive property. Examples showing that product between matrices does not satisfy the commutative property and the simplification property. Matrices and linear systems.
5. Determinants
Definition by induction of the determinant when using the first-row development. Determinant property: development according to any row or column, determinant of the transposed matrix, determinant of a triangular matrix. Binet theorem.
6. Reverse matrix
Unit matrix. Reverse matrix. Inverse property. Cramer's theorem.
7. Rank of a matrix
Definition. Property of the rank. Minors of a matrix. Theorem of Kronecker.
8. Linear equation systems
Definitions. Rouché-Capelli theorem. Rouché-Capelli method for solving a linear system.
9. Gauss method
10. Applications of Gauss method
Basic operations. Calculation of the determinant. Calculation of the rank.
11. Geometric vectors
Plan vectors. Addition between vectors. Product of a vector for a scalar. Space vectors. Lines and planes for the origin. Average point.
12. Linear combinations of geometric vectors
Linear combinations. Linearly dependent and independent vectors. Characterization of linearly independent vectors in V2(O) and V3(O).
13. Vector spaces on the real numbers
Definition of vector spaces. Examples of vector spaces. Basic properties of vector spaces.
14. Vector subspaces
Definition of vector spaces. Subspaces of V2(O) and V3(O).
15. Generators of vector spaces
Linear combinations and generators.
16. Linear dependency and independency
17. Basis of vector spaces
Basis. Dimension. Dimension of the set of solutions of a homogeneous system. Dimension of subspaces. Calculation of dimensions and basis.
18. Intersection and sum of subspaces
Intersection of vector subspaces. Sum of vector subspaces. Grassmann's formula.
19. Affine subspaces
The lines of the plane and of the space. Space planes. Affine subspaces. Set of system solutions.
20. Homomorphisms
Homomorphisms between vector spaces. Matrix associated with a homomorphism. Homomorphism associated with a matrix.
21. Image
Property of the image of a homomorphism. Calculation of the image of a homomorphism. Condition of surjectivity of a homomorphism.
22. Kernel
Property of the kernel of a homomorphism. Calculation of the kernel of a homomorphism. Injectivity condition of a homomorphism.
23. Endomorphisms
Matrix associated with an endomorphism. Change of basis.
24. Eigenvalues ​​and eigenvectors
Definitions and basic properties. Eigenspaces. Characteristic polynomial. Diagonalizable matrices.
25. Diagonalization
Diagonalizability conditions. Diagonalization procedure.

G. Accascina and V. Monti, Geometry*
* This book is available for free at the following link: http://www.dmmm.uniroma1.it/accascinamonti/geogest/Geometria.pdf

1. Linear equations and numbers
Systems of linear equations. Represent linear systems with matrix equations. Equivalent systems. Natural, integers, rational, real numbers and their properties. Pills of Graph Theory: subsets and set subtraction.

2. Matrixes and sets
Matrix with real coefficients. Square, triangular, diagonal matrixes. Transposed and symmetric matrix. Pills of Graph Theory: union and intersection.

3. Vector spaces and matrices
Matrix addition and scalar product and their properties.

4. Matrix product
Matrix product and its mathematical properties: associative and distributive. Example of how matrix product does not satisfy the commutative and simplification properties. Matrices and linear systems

5. Determinants
Formal definition of determinant and its properties. Transposed and triangular matrix determinants. Binet’s theorem.

6. Inverse of a matrix
Identity matrix. Inverse of a matrix and its properties. Cramer’s theorem.

7. Matrix rank
Definition and properties. Minor of a matrix.

8. System of linear equations.
Definition. Rouché-Capelli’s theorem. Rouché-Capelli’s method to solve a linear system.

9. Gaussian elimination and how to apply the Gaussian elimination
Elementary operation. Determinant and rank computations.

10. Geometric vectors
Vectors in 2 dimensions. Sum and scalar product of vectors. Vectors in 3 dimensions. Linear combination. Linear dependence and independence of vectors.

11. Vector spaces and Linear subspaces
Definition, examples and properties.

12. How to generate linear subspaces
Linear combination and generators.

13. Linear dependence and independence

14. Basis of a linear subspace
Basis. Dimensions. Solution set of an homogeneous system and its dimensions.

15. Vector subspaces sum and intersection
Grassmann formula.

16. Affine space
Lines in planes and space. Affine subspace.

17. Homomorphisms
Homomorphism between vector spaces. Represent an homomorphism as a matrix.

18. Image of a matrix
Properties of an homomorphism image and how to compute it. Surjective homomorphism.

19. Kernel of a matrix
Properties of an homomorphism kernel and how to compute it. Injectivity homomorphism.

20. Endomorphisms
Matrix representation of the endomorphisms. Change of basis.

21. Eigenvalues and Eigenvectors
Definition and properties. Eigenspaces. Characteristic polynomial. Diagonalizable matrix.

22. Diagonalizing a matrix
Rules and examples.

G. Accascina e V. Monti,
"Geometria"

1. Linear equations and numbers
Systems of linear equations. Represent linear systems with matrix equations. Equivalent systems. Natural, integers, rational, real numbers and their properties. Pills of Graph Theory: subsets and set subtraction.

2. Matrixes and sets
Matrix with real coefficients. Square, triangular, diagonal matrixes. Transposed and symmetric matrix. Pills of Graph Theory: union and intersection.

3. Vector spaces and matrices
Matrix addition and scalar product and their properties.

4. Matrix product
Matrix product and its mathematical properties: associative and distributive. Example of how matrix product does not satisfy the commutative and simplification properties. Matrices and linear systems

5. Determinants
Formal definition of determinant and its properties. Transposed and triangular matrix determinants. Binet’s theorem.

6. Inverse of a matrix
Identity matrix. Inverse of a matrix and its properties. Cramer’s theorem.

7. Matrix rank
Definition and properties. Minor of a matrix.

8. System of linear equations.
Definition. Rouché-Capelli’s theorem. Rouché-Capelli’s method to solve a linear system.

9. Gaussian elimination and how to apply the Gaussian elimination
Elementary operation. Determinant and rank computations.

10. Geometric vectors
Vectors in 2 dimensions. Sum and scalar product of vectors. Vectors in 3 dimensions. Linear combination. Linear dependence and independence of vectors.

11. Vector spaces and Linear subspaces
Definition, examples and properties.

12. How to generate linear subspaces
Linear combination and generators.

13. Linear dependence and independence

14. Basis of a linear subspace
Basis. Dimensions. Solution set of an homogeneous system and its dimensions.

15. Vector subspaces sum and intersection
Grassmann formula.

16. Affine space
Lines in planes and space. Affine subspace.

17. Homomorphisms
Homomorphism between vector spaces. Represent an homomorphism as a matrix.

18. Image of a matrix
Properties of an homomorphism image and how to compute it. Surjective homomorphism.

19. Kernel of a matrix
Properties of an homomorphism kernel and how to compute it. Injectivity homomorphism.

20. Endomorphisms
Matrix representation of the endomorphisms. Change of basis.

21. Eigenvalues and Eigenvectors
Definition and properties. Eigenspaces. Characteristic polynomial. Diagonalizable matrix.

22. Diagonalizing a matrix
Rules and examples.

G. Accascina e V. Monti,
"Geometria"

1. Linear equations and numbers
Linear equations systems. Matrix associated with a linear system. Equivalent systems. Natural, integer, rational numbers, real numbers and their property. Recall of set theory: inclusion of sets, difference between sets.
2. Matrices and sets
Matrices with real coefficients. Square, triangular, diagonal matrices. Transpose of a matrix and symmetric matrices. Recall of set theory: union and intersection of sets.
3. The vector space of the matrices
Addition between matrices and its properties. Multiplying a scalar for a matrix and its properties.
4. Product between matrices
Product between matrices with compatible dimensions. Properties of the product: associative property and distributive property. Examples showing that product between matrices does not satisfy the commutative property and the simplification property. Matrices and linear systems.
5. Determinants
Definition by induction of the determinant when using the first-row development. Determinant property: development according to any row or column, determinant of the transposed matrix, determinant of a triangular matrix. Binet theorem.
6. Reverse matrix
Unit matrix. Reverse matrix. Inverse property. Cramer's theorem.
7. Rank of a matrix
Definition. Property of the rank. Minors of a matrix. Theorem of Kronecker.
8. Linear equation systems
Definitions. Rouché-Capelli theorem. Rouché-Capelli method for solving a linear system.
9. Gauss method
10. Applications of Gauss method
Basic operations. Calculation of the determinant. Calculation of the rank.
11. Geometric vectors
Plan vectors. Addition between vectors. Product of a vector for a scalar. Space vectors. Lines and planes for the origin. Average point.
12. Linear combinations of geometric vectors
Linear combinations. Linearly dependent and independent vectors. Characterization of linearly independent vectors in V2(O) and V3(O).
13. Vector spaces on the real numbers
Definition of vector spaces. Examples of vector spaces. Basic properties of vector spaces.
14. Vector subspaces
Definition of vector spaces. Subspaces of V2(O) and V3(O).
15. Generators of vector spaces
Linear combinations and generators.
16. Linear dependency and independency
17. Basis of vector spaces
Basis. Dimension. Dimension of the set of solutions of a homogeneous system. Dimension of subspaces. Calculation of dimensions and basis.
18. Intersection and sum of subspaces
Intersection of vector subspaces. Sum of vector subspaces. Grassmann's formula.
19. Affine subspaces
The lines of the plane and of the space. Space planes. Affine subspaces. Set of system solutions.
20. Homomorphisms
Homomorphisms between vector spaces. Matrix associated with a homomorphism. Homomorphism associated with a matrix.
21. Image
Property of the image of a homomorphism. Calculation of the image of a homomorphism. Condition of surjectivity of a homomorphism.
22. Kernel
Property of the kernel of a homomorphism. Calculation of the kernel of a homomorphism. Injectivity condition of a homomorphism.
23. Endomorphisms
Matrix associated with an endomorphism. Change of basis.
24. Eigenvalues ​​and eigenvectors
Definitions and basic properties. Eigenspaces. Characteristic polynomial. Diagonalizable matrices.
25. Diagonalization
Diagonalizability conditions. Diagonalization procedure.

G. Accascina and V. Monti, Geometry*
* This book is available for free at the following link: http://www.dmmm.uniroma1.it/accascinamonti/geogest/Geometria.pdf

N and induction principle, Newton binomial; Z, integers modulo n; Q, axiomatic construction of R, Archimedean property, density of Q in R, powers with real exponent; complex numbers, polar representation and n-th roots of the unit; rudiments of topology of R (isolated and accumulation points, open / closed sets); real functions of a real variable, domain, co-domain, and inverse functions; Limits of functions and their properties, limits of monotone functions ; limits of sequences, significant limits, Nepero number, bridge theorem infinite series and convergence, geometric series, convergence tests for series with positive terms (comparison, asymptotic comparison, root, ratio, condensation) and for generic series (absolute convergence, Leibniz); continuous functions and their properties, continuity of elementary functions, types of discontinuities and monotone functions, fundamental theorems on continuous functions (zeros, intermediate values, Weierstrass); derivatives of a functions, derivatives of elementary functions, fundamental theorems of differential calculus (Fermat, Rolle, Cauchy, Lagrange, de l' Hospital, Taylor's formula), monotony and sign of the derivative , local maxima /minima, convex / concave functions; graph of a function; Riemann integral and its properties, integrability of continuous functions, primitive of elementary functions, I and II fundamental theorem of (integral) calculus; integration by substitution and by parts, rational functions, some special substitutions; improper integrals; Taylor series expansions, expansions of some elementary functions.

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

N and induction principle, Newton binomial; Z, integers modulo n; Q, axiomatic construction of R, Archimedean property, density of Q in R, powers with real exponent; complex numbers, polar representation and n-th roots of the unit; rudiments of topology of R (isolated and accumulation points, open / closed sets); real functions of a real variable, domain, co-domain, and inverse functions; Limits of functions and their properties, limits of monotone functions ; limits of sequences, significant limits, Nepero number, bridge theorem infinite series and convergence, geometric series, convergence tests for series with positive terms (comparison, asymptotic comparison, root, ratio, condensation) and for generic series (absolute convergence, Leibniz); continuous functions and their properties, continuity of elementary functions, types of discontinuities and monotone functions, fundamental theorems on continuous functions (zeros, intermediate values, Weierstrass); derivatives of a functions, derivatives of elementary functions, fundamental theorems of differential calculus (Fermat, Rolle, Cauchy, Lagrange, de l' Hospital, Taylor's formula), monotony and sign of the derivative , local maxima /minima, convex / concave functions; graph of a function; Riemann integral and its properties, integrability of continuous functions, primitive of elementary functions, I and II fundamental theorem of (integral) calculus; integration by substitution and by parts, rational functions, some special substitutions; improper integrals; Taylor series expansions, expansions of some elementary functions.

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

COURSE PROGRAM (First semester)

Computer operations and representation of information
-computer architecture
-operating systems
-binary arithmetic
-compilation and execution of programs

Algorithms
-program specification
-programming quality
-representation and algorithm design

Programming Fundamentals
-programming langauges
-variables
-Instructions
-types data
-Instructions structured
-style programming
-structure of the program
-functions

Software correctness
-testing methods
-debugging

Management of data sets
-arrays
-strings

COURSE PROGRAM (Second semester)

Pointers and dynamic memory allocation
Data structures, struct, files
Recursion
Sorting and searching algorithms
Computational cost of programs
- Big O, Omega and Theta notations
- best, average, and worst case analysis
Abstract data types and related structures
- lists
- queues
- stacks

- Author: Kernighan, Ritchie
Title: Il linguaggio C. Principi di programmazione e manuale di riferimento
Edition: Seconda edizione
Editor: Pearson
Year: 2004

COURSE PROGRAM (First semester)

Computer operations and representation of information
-computer architecture
-operating systems
-binary arithmetic
-compilation and execution of programs

Algorithms
-program specification
-programming quality
-representation and algorithm design

Programming Fundamentals
-programming langauges
-variables
-Instructions
-types data
-Instructions structured
-style programming
-structure of the program
-functions

Software correctness
-testing methods
-debugging

Management of data sets
-arrays
-strings

COURSE PROGRAM (Second semester)

Pointers and dynamic memory allocation
Data structures, struct, files
Recursion
Sorting and searching algorithms
Computational cost of programs
- Big O, Omega and Theta notations
- best, average, and worst case analysis
Abstract data types and related structures
- lists
- queues
- stacks

Author: Bellini, Guidi
Title: Linguaggio C - Una guida alla programmazione con elementi di Objective-C
Edition: 5-th edition
Editor: McGraw-hill
Year: 2013

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

Introduction to fields
- Gravitational field and electric field
- Gauss's law
- Electric potential
- Lorentz force and magnetic field
- Stationary electric currents
- Ohm's law

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)

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

Notes on selected arguments are also available on the course website, under the section "Complementi"

For further studies, the following is suggested:
- R. P. Feynman, "La Fisica di Feynman", volumes 1 and 2 (freely available at http://feynmanlectures.info/)

Non linear resistors: diode
small-signal model of a diode
Full-wave rectifier
Zener diode
Voltage stabilizer with zener diode
Transistor
small-signal model of a transistor
Transistor as a short-circuit or open-circuit
Logic gates: NOT,AND, OR
FLIP FLOP SR
Operational amplifier (OP.AMP.)
OP.AMP. Buffer
OP.AMP. Inverting
OP.AMP. Non Inverting
OP.AMP. Comparator
OP.AMP. Clock
OP.AMP. Integrator
OP.AMP. Differentiator
OP.AMP. Summing
Digital to Analog converter

Charles K. Alexander e Matthew N.O. Sadiku "Circuiti elettrici", McGraw-Hill Education

Antonino Laudano, Francesco Riganti Fulginei, "Quaderno di appunti di elettrotecnica. Esercizi sui circuiti elettrici", Pigreco Edizioni

From fields to circuits
Kirchhoff's circuit laws
Voltage and Current
Two-pole circuit
Electric Power
Passive, linear and time-independent circuit elements
Circuit elements with memory
Series and parallel circuit elements
Active circuit elements: voltage and current ideal sources (independent or controlled)
Passive circuit elements: resistor, capacitor and inductor
Series and parallel resistor
Equivalent models
Norton e Thevenin models
Brief notes of graph theory
Tableau method for the general analisys of electric circuits
Nodal analysis
Mesh analysis
Superposition principle
Thevenin's theorem
Steady and transient states
Steady state with sinusoidal signals
Frequency-domain analysis
Active, reactive, and apparent power
Three-phase electric systems
Balanced three-phase sources and loads
Three Phase Power
Measurement of Three Phase Power
Aron's insertion
Power factor correction

Charles K. Alexander e Matthew N.O. Sadiku "Circuiti elettrici", McGraw-Hill Education

Antonino Laudano, Francesco Riganti Fulginei, "Quaderno di appunti di elettrotecnica. Esercizi sui circuiti elettrici", Pigreco Edizioni

• Continuous and discrete signals and systems
Architecture of a communication system. Continuous and discrete signals: step and Dirac impulse signals, complex exponentials; elementary operations. Energy, power, periodicity of continuous and discrete signals; power of periodic signals. Linear, time-invariant, and causal systems. The impulse response. The Fourier series and its properties. Parseval theorem for periodic signals. The convolution and correlation of continue and discrete signals.

• Signals representation in the frequency domain
Fourier transform of continuous signals and its properties: linearity, time shift, frequency shift (modulation), product, duality, scale change, derivation, integration, convolution and correlation. Spectral energy density. Spectrum of periodic signals. Sampling theorem. Aliasing, energy and power of sampled signals. Reconstruction approaches of sampled signals. Fourier transform of discrete signals and its properties.

• Random signals
Basic concepts. Frequentist and axiomatic description. Continuous and discrete random variables. Cumulative distribution function, probability density (mass) function, characteristic function. Independent random variables. Joint, marginal and conditional probability density functions. Law of total probability. Bayes’ theorem. Gaussian, uniform, binomial, one-sides exponential statistics. Statistical moments of random variables: mean (expected value), variance, root mean square and their relations. Uncorrelated and statistically independent random variables. Functions of random variables and their probability density functions. Probability density function of the sum and the linear combination of independent random variables. Random processes and their statistics. Correlation and covariance. Stationary and ergodic processes. The harmonic process. The additive white Gaussian noise (AWGN). Random process through a system.

• Information theory and source coding
Basics of the information theory, self-information and entropy. Quantization. First Shannon theorem. Huffman coding.

• Baseband digital transmission
Binary and multi-level line encoding. Pulse amplitude modulation (PAM) and pulse coded modulation (PCM). Inter-symbol interference (ISI) and Nyquist theorem, Nyquist pulses. Noise and error probability in binary and multilevel PAM transmission. Matched filter and corresponding error probability.

• Passband digital transmission
Amplitude shift keying (ASK), quadrature amplitude modulation (QAM) and phase shift keying (PSK). Transmitter and receiver scheme. Constellations and distance between symbols. Symbol energy.

• Channel capacity and encoding
Second Shannon theorem. Channel capacity and encoding. Hard decoding and Hamming distance.

A.B. Carlson, P.B. Crilly, J.C. Rutledge, "Communication Systems: an introduction to signals and noise in electrical communication", McGraw-Hill international Edition publ.

Claudio Prati, "Segnali e Sistemi per le Telecomunicazioni", seconda edizione, McGraw-Hill, 2010.

1. INTRODUZIONE
SISTEMI AD EVENTI DISCRETI (SED)
MODELLI AD EVENTI DISCRETI (MED)
• MED LOGICI
• MED TEMPORIZZATI
2. ANALISI E REGOLAZIONE DEI FLUSSI PRODUTTIVI
TEORIA DELLE FILE D'ATTESA: RELAZIONI FONDAMENTALI
PROCESSI DI NASCITA E MORTE
TEORIA DELLE CODE E ANALISI DELLE PRESTAZIONI NEI SISTEMI A FLUSSO
RETI DI CODE APERTE
RETI DI CODE CHIUSE
3. MED LOGICI
AUTOMI
4. MED TEMPORIZZATI
RAPPRESENTAZIONE CON RETI DI PETRI DI SISTEMI DI CONTROLLO AD EVENTI DISCRETI:
ELEMENTI DELLE RETI DI PETRI: EVENTI , TRANSIZIONI; CONDIZIONI, POSTI, MARCHE; MARCATURA INIZIALE
MATRICI PRE , POST, DI INCIDENZA; RETI MARCATE: GRAFO DI STATO; EQUAZIONE DI STATO, DI TRANSIZIONE
CONFLITTI, MODELLO DI MAGAZZINO, ARCHI INIBITORI; CONCORRENZA, MODELLO DEI GUASTI; TEMPORIZZAZIONE; CONTROLLO SUPERVISORE
PROPRIETÀ DELLE RETI DI PETRI: CONSERVATIVITÀ, LIMITATEZZA, VIVEZZA, CICLICITÀ
INVARIANTI DI POSTO, DI TRANSIZIONE; GRAFI DI SINCRONIZZAZIONE.
RAPPRESENTAZIONE DEL CONTROLLO SUPERVISORE NELLE RETI DI PETRI

DI FEBBRARO A., GIUA A., SISTEMI AD EVENTI DISCRETI , MCGRAW-HILL, 2002
DISPENSE DISPONIBILI SUL SITO HTTP://ADACHER.DIA.UNIROMA3.IT

PART 1: Generalities and tools.
Definitions of computational problem, algorithm, data structure.
Random Access Machine and pseudocode.
Asympthotic study of functions (big-O, Omega, and Theta notations).
Asympthotic complexity of algorithms and problems.
Ammortized complexity.
Worst/average/best case analysis.
Recursion and recursion equalities.
Theorems for the analysis of recursion equalities.

PART 2: Abstract data types.
Abstract data types and their representations.
Already known examples: sets, stacks, queues, lists, etc.
Management of dynamic data structures.
Trees: binary trees; arbitrary degree trees; traversals of trees; binary search trees; red-black trees.
Hash tables.
Graphs: representations with adjacency matrix and adjacency lists. DFS and BFS. Graphs and connectivity. Connected components. Minimum-lengths paths.

PART 3: Algorithmic paradigms.
Greedy algorithms (example: selection sort).
Iterative algorithms (example: insertion sort).
Divide et impera algorithms (examples: merge-sort and quick-sort).

PART 4: The course requires (and sometimes recalls) the following notions of C Language.
Imperative programming.
Elementary data types.
Functions.
Arrays and pointers.
Strings.
Memory management: Heap and Stack.
Management of C projects: prototypes and implementations.
Recursion and memory.
Records and pointes.
Dynamic memory management.

Slides provided by the teacher and downloadable day by day from the course website: https://moodle1.ing.uniroma3.it/
In order to download the slides the usual userid-password pair of Roma Tre University is sufficient.

The course is a first level one in automatic control and provides methodological and practical knowledge about:
-Modelling, Simulating and analyze the behavior of physical systems, in particular those that are linear and time invariant;
-Basic concepts on the system dynamics, as stability, transient response and forced one;
-Frequency based design of feedback control systems;
-Digital implementations of linear controllers;
-Use of mainstream software tools to aid in the previous activities.

S. K. Bhattacharya, Control Systems Engineering, Pearson, 2008. [Kindle Edition]

Franklin, Powell, and Enami-Naeini, Feedback Control of Dynamical Systems, 5th Edition, Addison-Wesley, 2006. ISBN: 978-0136019695;

- Introduction to Computer Architecture
- Binary representation of numbers
- The general organization of a computer
- Digital circuits of a computer
- Bus and communication protocols
- The microarchitecture of a computer
- Programming in Assembler

A.S. Tanenbaum, T. Austin. Structured Computer Organization, 6th edition, Prentice Hall

Object Oriented Programming Paradigm
Classes and Objects
Code Quality
Polymorphism
Collections
Generics
Inheritance
Code reuse
Stream
Java Thread

Ken Arnold, James Gosling, David Holmes "Il linguaggio Java: Manuale Ufficiale" - Addison Wesley
Cay Horstmann "Concetti di informatica e fondamenti di Java" - APOGEO
Cay Horstmann, Gary Cornell "Core Java2 Vol I: Fondamenti" - Prentice Hall
Cay Horstmann, Gary Cornell "Core Java2 Vol II: Tecniche avanzate" - Prentice Hall

Introduction to Operations Research:
Formulations, the 5-step method
Preliminaries on Linear Algebra

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

Solving Linear Programming problems:
Linear programming geometry
Simplex algorithm
Fourier–Motzkin algorithm
Geometric interpretation of the simplex

Duality theory:
Construction of the dual problem
Fundamental PL theorem
Conditions of complementarity
Economic interpretation of the dual
Sensitivity analysis

Graph optimization:
Maximum flow
Shortest path
Minimum spanning tree

Caramia, Giordani, Guerriero, Musmanno, Pacciarelli, "Ricerca Operativa", Isedi, Italia, 2014.

Introduction to Operations Research:
Formulations, the 5-step method
Preliminaries on Linear Algebra

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

Solving Linear Programming problems:
Linear programming geometry
Simplex algorithm
Fourier–Motzkin algorithm
Geometric interpretation of the simplex

Duality theory:
Construction of the dual problem
Fundamental PL theorem
Conditions of complementarity
Economic interpretation of the dual
Sensitivity analysis

Graph optimization:
Maximum flow
Shortest path
Minimum spanning tree

Caramia, Giordani, Guerriero, Musmanno, Pacciarelli, "Ricerca Operativa", Isedi, Italia, 2014.

Database systems: general properties. Relational model. Relational algebra. SQL. Conceptual database design. Logical database design. Normalization.

P. Atzeni et al. Basi di dati 5/Ed. McGraw-Hill, 2018 (in alternative, any major database textbook, contact the instructor for advice)
Additional material available on the course site:
http://www.dia.uniroma3.it/~atzeni/didattica/BDN/BDNindex.html

Database systems: general properties. Relational model. Relational algebra. SQL. Conceptual database design. Logical database design. Normalization.

P. Atzeni et al. Basi di dati 5/Ed. McGraw-Hill, 2018 (in alternative, any major database textbook, contact the instructor for advice)
Additional material available on the course site:
http://www.dia.uniroma3.it/~atzeni/didattica/BDN/BDNindex.html

Elements of economic analysis
Demand and supply behavior: Budget constraint, demand elasticity; production decisions, profit maximization, technology and production function, cost functions (short and long term).

Management accounting: Full costs and their applications; Direct and indirect costs. Variable and fixed costs.
Accounting methods: traditional indirect allocation methods; job and process costing; activity based costing

Capital budgeting:
Discounted Cash flows: discount rate and its role as an opportunity cost; NPV, IRR and Payback rule; Compund and linear rate of return; Nominal and real discount rate; Project interaction.

“ECONOMIA APPLICATA ALL’INGEGNERIA”, MC GRAW HILL EDITOR “CREATE” BOOK

THE BOOK HAS BEEN MADE BY MERGING THE FOLLOWING BOOK CHAPTERS:

BERNHEIM, WHINSTON, “MICROECONOMIA”, 3/ED, MC GRAW HILL, 2017 – CAPITOLI DA 1 A 4 e da 6 a 8

ANTHONY, HAWKINS, MACRI’, MERCHANT, “SISTEMI DI CONTROLLO” 14/ED, MAC GRAW HILL, 2016 – CAPITOLI DA 1 A 6 E DA 14 A 17

Introduction to computer networks; The Iso-Osi reference model; The IEEE 802 Project: Architecture, MAC Layer, LLC Layer; CSMA/CD; ETHERNET and IEEE 802.3; Functions and technical features of Switches (Bridges); Evolution of Ethernet; Wireless networks and CSMA/CA; Line protocols; The Network layer and IP; ICMP, PING and TRACEROUTE; The Transport Layer, TCP, and UDP; The Domain Name System; HTML; HTTP; The Electronic mail service; The file transfer service.

SLIDES SUPPLIED BY THE PROFESSOR; THE STUDENTS MAY USE JAMES F. KUROSE, KEITH W. ROSS "INTERNET AND COMPUTER NETWORKS" PEARSON EDUCATION

- Computer System Overview: architecture, CPU, registers, instruction execution, interrupt, memory hierarchy, locality, I/O, procedures
- Operating Systems Overview: definitions, objectives, architecture, kernel/user mode, caratteristiche salienti
- Processes and Threads: dispatching, states, description and control, models and memory management
- Memory: allocators, partitioning, best/first/next fit, buddy algorithm, paging, segmentation, virtual memory and its hardware/software management/supports
- Scheduling: short-term and long-term scheduling, algorithms for cpu scheduling
- I/O and File Management: Disk scheduling, UNIX File Management, inode, Linux VFS, ext2
- Synchronization: primitives, RMW, mutex, semaphores
- Introduction to Linux: frequently-used commands (e.g., file and directory management), environment variables, piping, redirection, signals, regular expressions (sed e grep), scripting (bash, awk), linux filesystem management
- Debugger: gdb stepping, breakpoints, watching, backtrace, and commands.
- System programming: Linux process/thread management
- Virtualization: general concepts, containers, Docker

The course is partly based on

[t1] Operating Systems: Internals and Design Principles - William Stallings - Prentice Hall, fifth edition (or higher). Reference edition: ninth.
[t2] Operating Systems Concepts - Silberschatz Abraham, Galvin Peter Baer, Gagne Greg - Addison Wesley/Pearson, ninth edition (or higher). Reference edition: tenth global edition.

However, some topics are covered only on the slides published in the teaching material.

Software processes; Iterative and agile development.
Requirements; Use cases; User stories.
Object-oriented software analysis; Domain modeling; System operations; Operation contracts.
Object-oriented software design; Principles of software design; GRASP patterns; Use case realizations; Dynamic and static design; Design patterns; Layered architecture.
Software modeling; UML.

Craig Larman, APPLICARE UML E I PATTERN – ANALISI E PROGETTAZIONE ORIENTATA AGLI OGGETTI, PEARSON EDUCATION ITALIA, QUINTA EDIZIONE, 2020.
or
CRAIG LARMAN, APPLYING UML AND PATTERNS, PRENTICE HALL PTR, THIRD EDITION. 2004

Non linear resistors: diode
small-signal model of a diode
Full-wave rectifier
Zener diode
Voltage stabilizer with zener diode
Transistor
small-signal model of a transistor
Transistor as a short-circuit or open-circuit
Logic gates: NOT,AND, OR
FLIP FLOP SR
Operational amplifier (OP.AMP.)
OP.AMP. Buffer
OP.AMP. Inverting
OP.AMP. Non Inverting
OP.AMP. Comparator
OP.AMP. Clock
OP.AMP. Integrator
OP.AMP. Differentiator
OP.AMP. Summing
Digital to Analog converter

Charles K. Alexander e Matthew N.O. Sadiku "Circuiti elettrici", McGraw-Hill Education

Antonino Laudano, Francesco Riganti Fulginei, "Quaderno di appunti di elettrotecnica. Esercizi sui circuiti elettrici", Pigreco Edizioni

From fields to circuits
Kirchhoff's circuit laws
Voltage and Current
Two-pole circuit
Electric Power
Passive, linear and time-independent circuit elements
Circuit elements with memory
Series and parallel circuit elements
Active circuit elements: voltage and current ideal sources (independent or controlled)
Passive circuit elements: resistor, capacitor and inductor
Series and parallel resistor
Equivalent models
Norton e Thevenin models
Brief notes of graph theory
Tableau method for the general analisys of electric circuits
Nodal analysis
Mesh analysis
Superposition principle
Thevenin's theorem
Steady and transient states
Steady state with sinusoidal signals
Frequency-domain analysis
Active, reactive, and apparent power
Three-phase electric systems
Balanced three-phase sources and loads
Three Phase Power
Measurement of Three Phase Power
Aron's insertion
Power factor correction

Charles K. Alexander e Matthew N.O. Sadiku "Circuiti elettrici", McGraw-Hill Education

Antonino Laudano, Francesco Riganti Fulginei, "Quaderno di appunti di elettrotecnica. Esercizi sui circuiti elettrici", Pigreco Edizioni

• Continuous and discrete signals and systems
Architecture of a communication system. Continuous and discrete signals: step and Dirac impulse signals, complex exponentials; elementary operations. Energy, power, periodicity of continuous and discrete signals; power of periodic signals. Linear, time-invariant, and causal systems. The impulse response. The Fourier series and its properties. Parseval theorem for periodic signals. The convolution and correlation of continue and discrete signals.

• Signals representation in the frequency domain
Fourier transform of continuous signals and its properties: linearity, time shift, frequency shift (modulation), product, duality, scale change, derivation, integration, convolution and correlation. Spectral energy density. Spectrum of periodic signals. Sampling theorem. Aliasing, energy and power of sampled signals. Reconstruction approaches of sampled signals. Fourier transform of discrete signals and its properties.

• Random signals
Basic concepts. Frequentist and axiomatic description. Continuous and discrete random variables. Cumulative distribution function, probability density (mass) function, characteristic function. Independent random variables. Joint, marginal and conditional probability density functions. Law of total probability. Bayes’ theorem. Gaussian, uniform, binomial, one-sides exponential statistics. Statistical moments of random variables: mean (expected value), variance, root mean square and their relations. Uncorrelated and statistically independent random variables. Functions of random variables and their probability density functions. Probability density function of the sum and the linear combination of independent random variables. Random processes and their statistics. Correlation and covariance. Stationary and ergodic processes. The harmonic process. The additive white Gaussian noise (AWGN). Random process through a system.

• Information theory and source coding
Basics of the information theory, self-information and entropy. Quantization. First Shannon theorem. Huffman coding.

• Baseband digital transmission
Binary and multi-level line encoding. Pulse amplitude modulation (PAM) and pulse coded modulation (PCM). Inter-symbol interference (ISI) and Nyquist theorem, Nyquist pulses. Noise and error probability in binary and multilevel PAM transmission. Matched filter and corresponding error probability.

• Passband digital transmission
Amplitude shift keying (ASK), quadrature amplitude modulation (QAM) and phase shift keying (PSK). Transmitter and receiver scheme. Constellations and distance between symbols. Symbol energy.

• Channel capacity and encoding
Second Shannon theorem. Channel capacity and encoding. Hard decoding and Hamming distance.

A.B. Carlson, P.B. Crilly, J.C. Rutledge, "Communication Systems: an introduction to signals and noise in electrical communication", McGraw-Hill international Edition publ.

Claudio Prati, "Segnali e Sistemi per le Telecomunicazioni", seconda edizione, McGraw-Hill, 2010.

1. INTRODUZIONE
SISTEMI AD EVENTI DISCRETI (SED)
MODELLI AD EVENTI DISCRETI (MED)
• MED LOGICI
• MED TEMPORIZZATI
2. ANALISI E REGOLAZIONE DEI FLUSSI PRODUTTIVI
TEORIA DELLE FILE D'ATTESA: RELAZIONI FONDAMENTALI
PROCESSI DI NASCITA E MORTE
TEORIA DELLE CODE E ANALISI DELLE PRESTAZIONI NEI SISTEMI A FLUSSO
RETI DI CODE APERTE
RETI DI CODE CHIUSE
3. MED LOGICI
AUTOMI
4. MED TEMPORIZZATI
RAPPRESENTAZIONE CON RETI DI PETRI DI SISTEMI DI CONTROLLO AD EVENTI DISCRETI:
ELEMENTI DELLE RETI DI PETRI: EVENTI , TRANSIZIONI; CONDIZIONI, POSTI, MARCHE; MARCATURA INIZIALE
MATRICI PRE , POST, DI INCIDENZA; RETI MARCATE: GRAFO DI STATO; EQUAZIONE DI STATO, DI TRANSIZIONE
CONFLITTI, MODELLO DI MAGAZZINO, ARCHI INIBITORI; CONCORRENZA, MODELLO DEI GUASTI; TEMPORIZZAZIONE; CONTROLLO SUPERVISORE
PROPRIETÀ DELLE RETI DI PETRI: CONSERVATIVITÀ, LIMITATEZZA, VIVEZZA, CICLICITÀ
INVARIANTI DI POSTO, DI TRANSIZIONE; GRAFI DI SINCRONIZZAZIONE.
RAPPRESENTAZIONE DEL CONTROLLO SUPERVISORE NELLE RETI DI PETRI

DI FEBBRARO A., GIUA A., SISTEMI AD EVENTI DISCRETI , MCGRAW-HILL, 2002
DISPENSE DISPONIBILI SUL SITO HTTP://ADACHER.DIA.UNIROMA3.IT

PART 1: Generalities and tools.
Definitions of computational problem, algorithm, data structure.
Random Access Machine and pseudocode.
Asympthotic study of functions (big-O, Omega, and Theta notations).
Asympthotic complexity of algorithms and problems.
Ammortized complexity.
Worst/average/best case analysis.
Recursion and recursion equalities.
Theorems for the analysis of recursion equalities.

PART 2: Abstract data types.
Abstract data types and their representations.
Already known examples: sets, stacks, queues, lists, etc.
Management of dynamic data structures.
Trees: binary trees; arbitrary degree trees; traversals of trees; binary search trees; red-black trees.
Hash tables.
Graphs: representations with adjacency matrix and adjacency lists. DFS and BFS. Graphs and connectivity. Connected components. Minimum-lengths paths.

PART 3: Algorithmic paradigms.
Greedy algorithms (example: selection sort).
Iterative algorithms (example: insertion sort).
Divide et impera algorithms (examples: merge-sort and quick-sort).

PART 4: The course requires (and sometimes recalls) the following notions of C Language.
Imperative programming.
Elementary data types.
Functions.
Arrays and pointers.
Strings.
Memory management: Heap and Stack.
Management of C projects: prototypes and implementations.
Recursion and memory.
Records and pointes.
Dynamic memory management.

Slides provided by the teacher and downloadable day by day from the course website: https://moodle1.ing.uniroma3.it/
In order to download the slides the usual userid-password pair of Roma Tre University is sufficient.

The course is a first level one in automatic control and provides methodological and practical knowledge about:
-Modelling, Simulating and analyze the behavior of physical systems, in particular those that are linear and time invariant;
-Basic concepts on the system dynamics, as stability, transient response and forced one;
-Frequency based design of feedback control systems;
-Digital implementations of linear controllers;
-Use of mainstream software tools to aid in the previous activities.

S. K. Bhattacharya, Control Systems Engineering, Pearson, 2008. [Kindle Edition]

Franklin, Powell, and Enami-Naeini, Feedback Control of Dynamical Systems, 5th Edition, Addison-Wesley, 2006. ISBN: 978-0136019695;

- Introduction to Computer Architecture
- Binary representation of numbers
- The general organization of a computer
- Digital circuits of a computer
- Bus and communication protocols
- The microarchitecture of a computer
- Programming in Assembler

A.S. Tanenbaum, T. Austin. Structured Computer Organization, 6th edition, Prentice Hall

Object Oriented Programming Paradigm
Classes and Objects
Code Quality
Polymorphism
Collections
Generics
Inheritance
Code reuse
Stream
Java Thread

Ken Arnold, James Gosling, David Holmes "Il linguaggio Java: Manuale Ufficiale" - Addison Wesley
Cay Horstmann "Concetti di informatica e fondamenti di Java" - APOGEO
Cay Horstmann, Gary Cornell "Core Java2 Vol I: Fondamenti" - Prentice Hall
Cay Horstmann, Gary Cornell "Core Java2 Vol II: Tecniche avanzate" - Prentice Hall

Introduction to Operations Research:
Formulations, the 5-step method
Preliminaries on Linear Algebra

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

Solving Linear Programming problems:
Linear programming geometry
Simplex algorithm
Fourier–Motzkin algorithm
Geometric interpretation of the simplex

Duality theory:
Construction of the dual problem
Fundamental PL theorem
Conditions of complementarity
Economic interpretation of the dual
Sensitivity analysis

Graph optimization:
Maximum flow
Shortest path
Minimum spanning tree

Caramia, Giordani, Guerriero, Musmanno, Pacciarelli, "Ricerca Operativa", Isedi, Italia, 2014.

Elements of economic analysis
Demand and supply behavior: Budget constraint, demand elasticity; production decisions, profit maximization, technology and production function, cost functions (short and long term).

Management accounting: Full costs and their applications; Direct and indirect costs. Variable and fixed costs.
Accounting methods: traditional indirect allocation methods; job and process costing; activity based costing

Capital budgeting:
Discounted Cash flows: discount rate and its role as an opportunity cost; NPV, IRR and Payback rule; Compund and linear rate of return; Nominal and real discount rate; Project interaction.

“ECONOMIA APPLICATA ALL’INGEGNERIA”, MC GRAW HILL EDITOR “CREATE” BOOK

THE BOOK HAS BEEN MADE BY MERGING THE FOLLOWING BOOK CHAPTERS:

BERNHEIM, WHINSTON, “MICROECONOMIA”, 3/ED, MC GRAW HILL, 2017 – CAPITOLI DA 1 A 4 e da 6 a 8

ANTHONY, HAWKINS, MACRI’, MERCHANT, “SISTEMI DI CONTROLLO” 14/ED, MAC GRAW HILL, 2016 – CAPITOLI DA 1 A 6 E DA 14 A 17

Introduction to computer networks; The Iso-Osi reference model; The IEEE 802 Project: Architecture, MAC Layer, LLC Layer; CSMA/CD; ETHERNET and IEEE 802.3; Functions and technical features of Switches (Bridges); Evolution of Ethernet; Wireless networks and CSMA/CA; Line protocols; The Network layer and IP; ICMP, PING and TRACEROUTE; The Transport Layer, TCP, and UDP; The Domain Name System; HTML; HTTP; The Electronic mail service; The file transfer service.

SLIDES SUPPLIED BY THE PROFESSOR; THE STUDENTS MAY USE JAMES F. KUROSE, KEITH W. ROSS "INTERNET AND COMPUTER NETWORKS" PEARSON EDUCATION

Decision making process. Introduction to Integer Linear Programming (ILP): relation between ILP and LP, equivalent formulations, relaxations, totally unimodular matrices, standard techniques for ILP modelling. Typical ILP formulations: plant location, investment problem, sequencing problems, network optimization, transportation problems, set covering, set partitioning, set packing, crew scheduling. Exact algorithms: Branch and Bound, Cutting Planes, dynamic programming. Exact algorithms for binary and integer knapsack problems. Optimization on graphs: matching, vertex cover, max flow, independent set, Eulerian graphs and bipartite graphs. Use of an ILP commercial solver.

[1] M. FISCHETTI, "LEZIONI DI RICERCA OPERATIVA", EDIZIONI LIBRERIA PROGETTO PADOVA, ITALIA, 1995. (CHAP. 2, 5, part of 6 and 7).
[2] R. AHUJA, T. MAGNANTI, J. ORLIN, "NETWORK FLOWS", PRENTICE HALL, 1993. (PG. 189-191, 473-475, 494-496)
[3] Lecture notes.

Introduction to Digital Control System
-Discrete time system representation
-Mathematical modelling of sampling process
-Data reconstruction
Modeling discrete time systems
-Pulse transfer function
-Mapping of s-plane to z-plane
Stability analysis of discrete time system
-Routh Hourwitz stability test
-Jury stability test
Time response of discrete systems
-Transient and steady state responses
-Time response parameters of a prototype second order system
Design of sampled data control systems
-Bode plot
-Steady state compensator
-Discretization of Continuous Controllers
-Difference Approximations
-Impulse/Step Discretization
-Zero-Pole Matching
-Compensator design in w domain
PID controllers
-PID actions
-System identification
-PID parameters tuning
Quantization errors
Introduction to microcontroller: the Arduino board

Charles L. Phillips, Troy Nagle, Aranya Chakrabortty, "Digital Control System Analysis & Design", Pearson Education,2014

1. INTRODUCTION
1.1. Historical background
1.2. Current Scenario and trends
1.3. Some basics of organizational theory
1.4. Project definition and properties
1.5. Project Management
1.6. Project Management Body of Knowledge

2. PROJECT LIFE CYCLE
2.1. Project Life Cycle concept
2.2. Project Life Cycle phases
2.3. Project planning
2.4. The Projects Planning & Control cycle and tools

3. LOGICAL PROJECT PLANNING
3.1. Work Breakdown Structure
3.2. Elementary tasks
3.3. Work Package Description
3.4. Responsibility Matrix

4. TECHNICAL SPECIFICATION AND CONTROL
4.1. Specifying
4.2. Technical control (Design Reviews, Tests and Audits)

5. TIME/RESOURCES PLANNING & CONTROL
5.1. Milestones
5.2. Bar Charts
5.3. Activity networks
5.4. Scheduling

6. COST PLANNING & CONTROL
6.1. Project budgeting process
6.2. Cost estimating
6.3. Project account opening process and spending authorization
6.4. Forecast of Project spending vs time (C-S CSC concept)
6.5. Earned Value
6.6. Indexes
6.7. Cost at Completion forecast
6.8. Allocated founds vs commitments

7. RISK MANAGEMENT BASICS
7.1. Risk Identification
7.2. Risk Evaluation
7.3. Risk contrast and planning
7.4. Risk Control
7.3. Decision trees
8. REPORTING
8.1. Project progress
8.2. Completion indexes
8.3. Progress meetings and reports

9. TECHNICAL DOCUMENTATION
9.1. Technical Documentation System Structure
9.2. Technical documents
9.3. Configuration Control

10.ORGANIZATIONAL AND BEHAVIORAL ISSUES
10.1. The Project Office
10.2. The Project Manager Role and skills
10.3. Team behavior, leadership types and characteristics

• INTERPERSONAL COMMUNICATION BASICS (optional)

Dispense a cura del docente
Stefano Protto “Concetti e strumenti di Project Management” II ed. 2006 Franco Angeli

1. INTRODUCTION
1.1. Historical background
1.2. Current Scenario and trends
1.3. Some basics of organizational theory
1.4. Project definition and properties
1.5. Project Management
1.6. Project Management Body of Knowledge

2. PROJECT LIFE CYCLE
2.1. Project Life Cycle concept
2.2. Project Life Cycle phases
2.3. Project planning
2.4. The Projects Planning & Control cycle and tools

3. LOGICAL PROJECT PLANNING
3.1. Work Breakdown Structure
3.2. Elementary tasks
3.3. Work Package Description
3.4. Responsibility Matrix

4. TECHNICAL SPECIFICATION AND CONTROL
4.1. Specifying
4.2. Technical control (Design Reviews, Tests and Audits)

5. TIME/RESOURCES PLANNING & CONTROL
5.1. Milestones
5.2. Bar Charts
5.3. Activity networks
5.4. Scheduling

6. COST PLANNING & CONTROL
6.1. Project budgeting process
6.2. Cost estimating
6.3. Project account opening process and spending authorization
6.4. Forecast of Project spending vs time (C-S CSC concept)
6.5. Earned Value
6.6. Indexes
6.7. Cost at Completion forecast
6.8. Allocated founds vs commitments

7. RISK MANAGEMENT BASICS
7.1. Risk Identification
7.2. Risk Evaluation
7.3. Risk contrast and planning
7.4. Risk Control
7.3. Decision trees
8. REPORTING
8.1. Project progress
8.2. Completion indexes
8.3. Progress meetings and reports

9. TECHNICAL DOCUMENTATION
9.1. Technical Documentation System Structure
9.2. Technical documents
9.3. Configuration Control

10.ORGANIZATIONAL AND BEHAVIORAL ISSUES
10.1. The Project Office
10.2. The Project Manager Role and skills
10.3. Team behavior, leadership types and characteristics

• INTERPERSONAL COMMUNICATION BASICS (optional)

Dispense a cura del docente
Stefano Protto “Concetti e strumenti di Project Management” II ed. 2006 Franco Angeli

Computer Integrated Manufacturing. Market standards for automation networks: information networks, control networks and field buses. Supervisory control and data acquisition systems (SCADA). Structure of a Programmable Logic Controller (PLC). Programming packages for Ladder Logic and SCADA systems. Sequential Functional Chart (SFC) and its translation into Ladder Logic. Control examples of simple plants. Graphic language programming for motion control. Remote monitoring using fieldbus and general purpose LAN. Sensors for industrial applications. Motion Control. Interprocess communications and distributed services. IT security and SCADA systems.

W. Bolton, Programmable Logic Controllers, Fifth Edition, Newnes, 2009 ISBN 978-1-85617-751-1

Lattices, Boolean algebras

Giulia Maria Piacentini Cattaneo
Matematica discreta e applicazioni
Zanichelli 2008

Lattices, Boolean algebras

Giulia Maria Piacentini Cattaneo
Matematica discreta e applicazioni
Zanichelli 2008

1. Linear equations and numbers
Linear equations systems. Matrix associated with a linear system. Equivalent systems. Natural, integer, rational numbers, real numbers and their property. Recall of set theory: inclusion of sets, difference between sets.
2. Matrices and sets
Matrices with real coefficients. Square, triangular, diagonal matrices. Transpose of a matrix and symmetric matrices. Recall of set theory: union and intersection of sets.
3. The vector space of the matrices
Addition between matrices and its properties. Multiplying a scalar for a matrix and its properties.
4. Product between matrices
Product between matrices with compatible dimensions. Properties of the product: associative property and distributive property. Examples showing that product between matrices does not satisfy the commutative property and the simplification property. Matrices and linear systems.
5. Determinants
Definition by induction of the determinant when using the first-row development. Determinant property: development according to any row or column, determinant of the transposed matrix, determinant of a triangular matrix. Binet theorem.
6. Reverse matrix
Unit matrix. Reverse matrix. Inverse property. Cramer's theorem.
7. Rank of a matrix
Definition. Property of the rank. Minors of a matrix. Theorem of Kronecker.
8. Linear equation systems
Definitions. Rouché-Capelli theorem. Rouché-Capelli method for solving a linear system.
9. Gauss method
10. Applications of Gauss method
Basic operations. Calculation of the determinant. Calculation of the rank.
11. Geometric vectors
Plan vectors. Addition between vectors. Product of a vector for a scalar. Space vectors. Lines and planes for the origin. Average point.
12. Linear combinations of geometric vectors
Linear combinations. Linearly dependent and independent vectors. Characterization of linearly independent vectors in V2(O) and V3(O).
13. Vector spaces on the real numbers
Definition of vector spaces. Examples of vector spaces. Basic properties of vector spaces.
14. Vector subspaces
Definition of vector spaces. Subspaces of V2(O) and V3(O).
15. Generators of vector spaces
Linear combinations and generators.
16. Linear dependency and independency
17. Basis of vector spaces
Basis. Dimension. Dimension of the set of solutions of a homogeneous system. Dimension of subspaces. Calculation of dimensions and basis.
18. Intersection and sum of subspaces
Intersection of vector subspaces. Sum of vector subspaces. Grassmann's formula.
19. Affine subspaces
The lines of the plane and of the space. Space planes. Affine subspaces. Set of system solutions.
20. Homomorphisms
Homomorphisms between vector spaces. Matrix associated with a homomorphism. Homomorphism associated with a matrix.
21. Image
Property of the image of a homomorphism. Calculation of the image of a homomorphism. Condition of surjectivity of a homomorphism.
22. Kernel
Property of the kernel of a homomorphism. Calculation of the kernel of a homomorphism. Injectivity condition of a homomorphism.
23. Endomorphisms
Matrix associated with an endomorphism. Change of basis.
24. Eigenvalues ​​and eigenvectors
Definitions and basic properties. Eigenspaces. Characteristic polynomial. Diagonalizable matrices.
25. Diagonalization
Diagonalizability conditions. Diagonalization procedure.

G. Accascina and V. Monti, Geometry*
* This book is available for free at the following link: http://www.dmmm.uniroma1.it/accascinamonti/geogest/Geometria.pdf

1. Linear equations and numbers
Linear equations systems. Matrix associated with a linear system. Equivalent systems. Natural, integer, rational numbers, real numbers and their property. Recall of set theory: inclusion of sets, difference between sets.
2. Matrices and sets
Matrices with real coefficients. Square, triangular, diagonal matrices. Transpose of a matrix and symmetric matrices. Recall of set theory: union and intersection of sets.
3. The vector space of the matrices
Addition between matrices and its properties. Multiplying a scalar for a matrix and its properties.
4. Product between matrices
Product between matrices with compatible dimensions. Properties of the product: associative property and distributive property. Examples showing that product between matrices does not satisfy the commutative property and the simplification property. Matrices and linear systems.
5. Determinants
Definition by induction of the determinant when using the first-row development. Determinant property: development according to any row or column, determinant of the transposed matrix, determinant of a triangular matrix. Binet theorem.
6. Reverse matrix
Unit matrix. Reverse matrix. Inverse property. Cramer's theorem.
7. Rank of a matrix
Definition. Property of the rank. Minors of a matrix. Theorem of Kronecker.
8. Linear equation systems
Definitions. Rouché-Capelli theorem. Rouché-Capelli method for solving a linear system.
9. Gauss method
10. Applications of Gauss method
Basic operations. Calculation of the determinant. Calculation of the rank.
11. Geometric vectors
Plan vectors. Addition between vectors. Product of a vector for a scalar. Space vectors. Lines and planes for the origin. Average point.
12. Linear combinations of geometric vectors
Linear combinations. Linearly dependent and independent vectors. Characterization of linearly independent vectors in V2(O) and V3(O).
13. Vector spaces on the real numbers
Definition of vector spaces. Examples of vector spaces. Basic properties of vector spaces.
14. Vector subspaces
Definition of vector spaces. Subspaces of V2(O) and V3(O).
15. Generators of vector spaces
Linear combinations and generators.
16. Linear dependency and independency
17. Basis of vector spaces
Basis. Dimension. Dimension of the set of solutions of a homogeneous system. Dimension of subspaces. Calculation of dimensions and basis.
18. Intersection and sum of subspaces
Intersection of vector subspaces. Sum of vector subspaces. Grassmann's formula.
19. Affine subspaces
The lines of the plane and of the space. Space planes. Affine subspaces. Set of system solutions.
20. Homomorphisms
Homomorphisms between vector spaces. Matrix associated with a homomorphism. Homomorphism associated with a matrix.
21. Image
Property of the image of a homomorphism. Calculation of the image of a homomorphism. Condition of surjectivity of a homomorphism.
22. Kernel
Property of the kernel of a homomorphism. Calculation of the kernel of a homomorphism. Injectivity condition of a homomorphism.
23. Endomorphisms
Matrix associated with an endomorphism. Change of basis.
24. Eigenvalues ​​and eigenvectors
Definitions and basic properties. Eigenspaces. Characteristic polynomial. Diagonalizable matrices.
25. Diagonalization
Diagonalizability conditions. Diagonalization procedure.

G. Accascina and V. Monti, Geometry*
* This book is available for free at the following link: http://www.dmmm.uniroma1.it/accascinamonti/geogest/Geometria.pdf

N and induction principle, Newton binomial; Z, integers modulo n; Q, axiomatic construction of R, Archimedean property, density of Q in R, powers with real exponent; complex numbers, polar representation and n-th roots of the unit; rudiments of topology of R (isolated and accumulation points, open / closed sets); real functions of a real variable, domain, co-domain, and inverse functions; Limits of functions and their properties, limits of monotone functions ; limits of sequences, significant limits, Nepero number, bridge theorem infinite series and convergence, geometric series, convergence tests for series with positive terms (comparison, asymptotic comparison, root, ratio, condensation) and for generic series (absolute convergence, Leibniz); continuous functions and their properties, continuity of elementary functions, types of discontinuities and monotone functions, fundamental theorems on continuous functions (zeros, intermediate values, Weierstrass); derivatives of a functions, derivatives of elementary functions, fundamental theorems of differential calculus (Fermat, Rolle, Cauchy, Lagrange, de l' Hospital, Taylor's formula), monotony and sign of the derivative , local maxima /minima, convex / concave functions; graph of a function; Riemann integral and its properties, integrability of continuous functions, primitive of elementary functions, I and II fundamental theorem of (integral) calculus; integration by substitution and by parts, rational functions, some special substitutions; improper integrals; Taylor series expansions, expansions of some elementary functions.

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

N and induction principle, Newton binomial; Z, integers modulo n; Q, axiomatic construction of R, Archimedean property, density of Q in R, powers with real exponent; complex numbers, polar representation and n-th roots of the unit; rudiments of topology of R (isolated and accumulation points, open / closed sets); real functions of a real variable, domain, co-domain, and inverse functions; Limits of functions and their properties, limits of monotone functions ; limits of sequences, significant limits, Nepero number, bridge theorem infinite series and convergence, geometric series, convergence tests for series with positive terms (comparison, asymptotic comparison, root, ratio, condensation) and for generic series (absolute convergence, Leibniz); continuous functions and their properties, continuity of elementary functions, types of discontinuities and monotone functions, fundamental theorems on continuous functions (zeros, intermediate values, Weierstrass); derivatives of a functions, derivatives of elementary functions, fundamental theorems of differential calculus (Fermat, Rolle, Cauchy, Lagrange, de l' Hospital, Taylor's formula), monotony and sign of the derivative , local maxima /minima, convex / concave functions; graph of a function; Riemann integral and its properties, integrability of continuous functions, primitive of elementary functions, I and II fundamental theorem of (integral) calculus; integration by substitution and by parts, rational functions, some special substitutions; improper integrals; Taylor series expansions, expansions of some elementary functions.

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

COURSE PROGRAM (First semester)

Computer operations and representation of information
-computer architecture
-operating systems
-binary arithmetic
-compilation and execution of programs

Algorithms
-program specification
-programming quality
-representation and algorithm design

Programming Fundamentals
-programming langauges
-variables
-Instructions
-types data
-Instructions structured
-style programming
-structure of the program
-functions

Software correctness
-testing methods
-debugging

Management of data sets
-arrays
-strings

COURSE PROGRAM (Second semester)

Pointers and dynamic memory allocation
Data structures, struct, files
Recursion
Sorting and searching algorithms
Computational cost of programs
- Big O, Omega and Theta notations
- best, average, and worst case analysis
Abstract data types and related structures
- lists
- queues
- stacks

- Author: Kernighan, Ritchie
Title: Il linguaggio C. Principi di programmazione e manuale di riferimento
Edition: Seconda edizione
Editor: Pearson
Year: 2004

COURSE PROGRAM (First semester)

Computer operations and representation of information
-computer architecture
-operating systems
-binary arithmetic
-compilation and execution of programs

Algorithms
-program specification
-programming quality
-representation and algorithm design

Programming Fundamentals
-programming langauges
-variables
-Instructions
-types data
-Instructions structured
-style programming
-structure of the program
-functions

Software correctness
-testing methods
-debugging

Management of data sets
-arrays
-strings

COURSE PROGRAM (Second semester)

Pointers and dynamic memory allocation
Data structures, struct, files
Recursion
Sorting and searching algorithms
Computational cost of programs
- Big O, Omega and Theta notations
- best, average, and worst case analysis
Abstract data types and related structures
- lists
- queues
- stacks

Author: Bellini, Guidi
Title: Linguaggio C - Una guida alla programmazione con elementi di Objective-C
Edition: 5-th edition
Editor: McGraw-hill
Year: 2013

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

Introduction to fields
- Gravitational field and electric field
- Gauss's law
- Electric potential
- Lorentz force and magnetic field
- Stationary electric currents
- Ohm's law

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)

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

Notes on selected arguments are also available on the course website, under the section "Complementi"

For further studies, the following is suggested:
- R. P. Feynman, "La Fisica di Feynman", volumes 1 and 2 (freely available at http://feynmanlectures.info/)