Real numbers and functions, set theory, induction principle, infimum and supremum.
Sequences, definition of limit, operations with limits, comparison theorems, infinitives of increasing order.
Limits of function, continuity, link with the limits of sequences, theorems on continuous functions.
Derivatives, geometric meaning, theorems on differentiable functions, relative maximums and minimums, applications to the study of functions. Indefinite integrals, integration by parts and by substitution, definite integrals, fundamental theorem of integral calculus, improper integrals. Numerical series, simple and absolute convergence, convergence criteria.
Series of functions, point and total convergence. Complex numbers.

Marcellini, Sbordone - Elements of Mathematical Analysis 1,2.
Marcellini, Sbordone - Exercises in mathematics Vol. 1, 2.
Bertsch, Dall'Aglio, Giacomelli - Epsilon 1, A first course in Mathematical Analysis . McGraw Hill

Real numbers and functions, set theory, induction principle, infimum and supremum.
Sequences, definition of limit, operations with limits, comparison theorems, infinitives of increasing order.
Limits of function, continuity, link with the limits of sequences, theorems on continuous functions.
Derivatives, geometric meaning, theorems on differentiable functions, relative maximums and minimums, applications to the study of functions. Indefinite integrals, integration by parts and by substitution, definite integrals, fundamental theorem of integral calculus, improper integrals. Numerical series, simple and absolute convergence, convergence criteria.
Series of functions, point and total convergence. Complex numbers.

Marcellini, Sbordone - Elements of Mathematical Analysis 1,2.
Marcellini, Sbordone - Exercises in mathematics Vol. 1, 2.
Bertsch, Dall'Aglio, Giacomelli - Epsilon 1, A first course in Mathematical Analysis . McGraw Hill

The numbers refer to the chapters and paragraphs of the textbook:
Calcolo of P. Marcellini and C. Sbordone.

1) Real numbers and functions

Natural, whole and rational numbers; density of rationals (5). Axioms of real numbers (2). Overview of set theory (4).
The intuitive concept of function (6) and Cartesian representation (7).
Injective, surjective, bijective and invertible functions. Monotonic functions (8).
Absolute value (9). The principle of induction (13).

2) Complements to real numbers

Maximum, minimum, supremum, infimum.

7) Succession limits

Definition and first properties (56.57).
Limited successions (58). Operations with limits (59).
Indefinite forms (60).
Comparative theorems (61). Other properties of succession limits (62).
Notable limits (63). Monotone sequences, the number e (64).
Sequence going to infinity of increasing order (67).

8) Function limits. Continuous functions

Definition of limit and property (71,72,73).
Continuous functions (74). discontinuity (75).
Theorems on continuous functions (76).

9) Additions to the limits

The theorem on monotonic sequences (80).
Extracted successions; the Bolzano-Weierstrass theorem (81).
The Weierstrass theorem (82).
Continuity of monotonic functions and inverse functions (83).

10) Derivatives

Definition and physical meaning (88-89). Operations with derivatives (90).
Derivatives of compound functions and inverse functions (91).
Derivative of elementary functions (92).
Geometric meaning of the derivative: tangent line (93).

11) Applications of derivatives. Function study

Maximum and minimum relative. Fermat's theorem (95).
Theorems of Rolle and Lagrange (96).
Increasing, decreasing, convex and concave functions (97-98).
De l'Hopital theorem (99).
Study of the graph of a function (100).
Taylor's formula: first properties (101).

14) Integration according to Riemann

Definition (117). Properties of the defined integrals (118).
Uniform continuity. Cantor's theorem (119).
Integrability of continuous functions (120).
The theorems of the average (121).

15) Undefined integrals

The fundamental theorem of integral calculus (123).
Primitives (124). The indefinite integral (125). Integration by parts and by substitution
(126,127,128,129).
Improper integrals (132).

16) Taylor's formula

Rest of Peano (135).
Use of Taylor's formula in the calculation of limits (136).

17) Series

Numerical series (141).
Series with positive terms (142).
Geometric series and harmonic series (143.144).
Convergence criteria (145).
Alternate series (146).
Absolute convergence (147).
Taylor series (149).

P. Marcellini, C. Sbordone, Calcolo, Ed. Liguori, 1992
S. Lang, A First Course in Calculus, Springer Ed.
L.Chierchia, Corso di Analisi - Prima parte, McGraw Hill (2019)

The numbers refer to the chapters and paragraphs of the textbook:
Calcolo of P. Marcellini and C. Sbordone.

1) Real numbers and functions

Natural, whole and rational numbers; density of rationals (5). Axioms of real numbers (2). Overview of set theory (4).
The intuitive concept of function (6) and Cartesian representation (7).
Injective, surjective, bijective and invertible functions. Monotonic functions (8).
Absolute value (9). The principle of induction (13).

2) Complements to real numbers

Maximum, minimum, supremum, infimum.

7) Succession limits

Definition and first properties (56.57).
Limited successions (58). Operations with limits (59).
Indefinite forms (60).
Comparative theorems (61). Other properties of succession limits (62).
Notable limits (63). Monotone sequences, the number e (64).
Sequence going to infinity of increasing order (67).

8) Function limits. Continuous functions

Definition of limit and property (71,72,73).
Continuous functions (74). discontinuity (75).
Theorems on continuous functions (76).

9) Additions to the limits

The theorem on monotonic sequences (80).
Extracted successions; the Bolzano-Weierstrass theorem (81).
The Weierstrass theorem (82).
Continuity of monotonic functions and inverse functions (83).

10) Derivatives

Definition and physical meaning (88-89). Operations with derivatives (90).
Derivatives of compound functions and inverse functions (91).
Derivative of elementary functions (92).
Geometric meaning of the derivative: tangent line (93).

11) Applications of derivatives. Function study

Maximum and minimum relative. Fermat's theorem (95).
Theorems of Rolle and Lagrange (96).
Increasing, decreasing, convex and concave functions (97-98).
De l'Hopital theorem (99).
Study of the graph of a function (100).
Taylor's formula: first properties (101).

14) Integration according to Riemann

Definition (117). Properties of the defined integrals (118).
Uniform continuity. Cantor's theorem (119).
Integrability of continuous functions (120).
The theorems of the average (121).

15) Undefined integrals

The fundamental theorem of integral calculus (123).
Primitives (124). The indefinite integral (125). Integration by parts and by substitution
(126,127,128,129).
Improper integrals (132).

16) Taylor's formula

Rest of Peano (135).
Use of Taylor's formula in the calculation of limits (136).

17) Series

Numerical series (141).
Series with positive terms (142).
Geometric series and harmonic series (143.144).
Convergence criteria (145).
Alternate series (146).
Absolute convergence (147).
Taylor series (149).

P. Marcellini, C. Sbordone, Calcolo, Ed. Liguori, 1992
S. Lang, A First Course in Calculus, Springer Ed.
L.Chierchia, Corso di Analisi - Prima parte, McGraw Hill (2019)

Systems of linear equations. Coefficient matrix. Matrix addition and scalar multiplication. Gauss-Jordan elimination. Row by Column multiplication. Determinant. Invertible matrices. Rank of a matrix and Rouche'-Capelli Theorem. Geometric vectors. Vector spaces and subspaces. Generators and linearly independent vectors. Basis and dimension. Linear maps. Kernel and image of a linear map. Rank plus nullity Theorem. Matrix associated with a linear map. Diagonalization of linear maps.

F. Flamini; A. Verra: “Matrici e vettori -Corso di base di geometria e algebra lineare” Carocci ed.

Linear Algebra:
Matrices. Determinants. Rank. Linear systems. Vector spaces. Linear applications. Eigenvalues ​​and eigenvectors.
Diagonalization. Scalar product. Symmetric operators. Spectral theorem.
Geometry:
Affine geometry of the plane and space. Euclidean geometry of the plane and space.

F. Flamini, A. Verra: Matrici e vettori. Corso di base di geometria e algebra lineare. Carocci.
Also suggested:
E. Schlesinger: Algebra lineare e geometria, Zanichelli.
L. Mauri e E. Schlesinger: Esercizi di algebra lineare e geometria, Zanichelli.

* Basic concepts *

Problems, algorithms, and programs
Computer architecture

Languages and Compilation
Style and conventions
I / O, variables and constants



* Operations *

Information representation
Binary arithmetic
Types of data
Expressions
Boolean algebra



* Control structures *

Selection
Iteration
Functions



* Data structures *

Array
Strings


* Advanced concepts *

Integrated development environments
Errors
Libraries

The course uses the C programming language

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

* Basic concepts *

Problems, algorithms, and programs
Computer architecture
Languages and Compilation
Style and conventions
I/O, variables and constants

* Operations *

Information representation
Binary arithmetic
Types of data
Expressions
Boolean algebra

* Control structures *

Selection
Iteration
Functions

* Data structures *

Array
Strings

* Advanced concepts *

Integrated development environments
Errors
Libraries

The course uses the C programming language

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

Learning outcomes
Students will acquire:
- basic knowledge in industrial design and drafting, with particular reference to the mechanical application field.

Course contents
The course aims at providing the students with the acquisition of basic skills for drawing all the main machine components and understanding drawings already made by others. After a brief introduction to the geometrical bases, it treats, according to the international standards, the rules and norms for the right representation of each component, by accounting for the function it plays into the device or assembly and for the cycle it experiences during its manufacturing.
Students follow a practical training performing hand sketches.

Testi/Bibliografia
CHIRONE, TORNINCASA, Disegno Tecnico Industriale, ed. Il Capitello, Torino.

1 Role of Engineering Drawing
• Introduction, Mechanical Drawing in the design workflow;
• Technical information, general, principles of drawings, Classification of Drawings;
• Layout of drawing sheets, Title Block, Layout of drawing sheets, scales, lines, Folding of drawing sheets;
• Part and assembly representation.
2 International Standards and normative
• Introduction and motivations;
• Standard code of practice for mechanical drawings.
3 Projections
• Projections: principles, definitions, Theories of projection;
• Orthographic projections: Principle of First Angle Projection, Methods of Obtaining Orthographic Views, Presentation of Views, Presentation of Views, Position of the Object, Selection of Views, Development of Missing Views.
4 Sections
• General principles, Section Views, Hatching of Sections, Cutting Planes, Revolved or Removed Section, Half Section, Local Section, Arrangement of Successive Sections.
5 Dimensioning
• General principles;
• Termination and Origin Indication, Method of Execution;
• Methods of Indicating Dimensions, Special Indications;
• Arrangement of Dimensions and Tolerances.
6 Limits, Tolerances, and fits
• Surface Roughness, indications and symbols;
• Fundamental tolerances, fundamental deviations, Method of Placing Limit Dimensions;
• Geometrical tolerance, Indicating Geometrical Tolerances on the Drawing;
• Indication of Feature Controlled, Standards Followed in Industry.
7 Threads
• Screw thread series, nomenclature, normative;
• Thread series and designation;
• Whitworth threads;
• Thread designation, bolted joints, nuts and studs.
8 Joints
• Temporary and Thread joints;
• keys, splines, cotters and pin joints;
• Welded Joints and Symbols;
• Permanent joints, rubber band fasteners.
9 Transmitting the power
• Introduction to motion guides and joints;
• Sliding and Rolling contact Bearings;
• motion guides and joints, transmission parts, gear box.

• Nigel Cross, Engineering Design Methods: Strategies for Product Design, 4th Edition, John Willey & Sons, 2008;
• T.E. French, C. J. Vierck, R. J. Foster, “GRAPHIC SCIENCE AND DESIGN”, 4th edition, McGraw Hill, 1984;
• Giesecke, Mitchell, Spencer, Hill, Dygdon, Nocak and Lockhart, “TECHNICAL DRAWING WITH ENGINEERING GRAPHICS”, 14/e;

Introduction
- Physical quantities and units of measurement
- Elements of vector calculus

Kinematics of the material point
- Kinematic quantities in rectilinear motion
- Uniformly accelerated rectilinear motion
- Simple harmonic motion
- Kinematics in the plane and in space
- Trajectory of motion
- Tangential and normal components of acceleration
- Parabolic motion
- Circular motion
- Relative motions

Dynamics of the point
- Principles of dynamics and Newton's laws
- Momentum and momentum
- Equilibrium and constraint reactions
- Gravitational force
- Strength, weight and motion of the bodies
- Dynamic action of forces
- Sliding friction forces
- Inclined plane
- Elastic force and mass-spring system
- Thread tension
- Application to circular motions
- Viscous friction force
- Electric charge and Coulomb force
- The simple pendulum
- Inertial and non-inertial reference systems
- Forces of inertia

Work and energy
- Work and power
- Work of weight force, elastic force and sliding friction
- Work and kinetic energy theorem.
- Conservative forces. Potential energy
- Central forces
- Gravitational and electrostatic potential energy
- Law of conservation of mechanical energy.
- Conditions of equilibrium stability

Dynamics of systems of material points
- Point systems. Internal and external forces
- First cardinal equation of systems dynamics
- Center of mass and its motion
- Law of conservation of momentum
- Outline of shock phenomena
- Moment of force and angular momentum
- Second cardinal equation of systems dynamics
- Conservation law of angular momentum
- Koenig's theorems

Dynamics of the rigid body
- Definition of a rigid body and its properties
- Continuous bodies. Density and center of mass
- Kinematics of the rigid body. Angular speed
- Dynamics of the rigid body. Rotations around a fixed axis
- Moment of inertia
- Huygens-Steiner theorem
- Compound pendulum
- Rolling motion
- Equilibrium equations of a rigid body

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

Thermodynamics
- Introduction to the kinetic theory of ideal gases
- Temperature and pressure
- Systems and thermodynamic states
- Thermodynamic equilibrium
- Mechanical work and heat
- First law of thermodynamics
- Thermodynamic transformations (adiabatic, reversible, irreversible)
- Thermal capacity and specific heat
- State law of ideal gases
- Specific heats of ideal gases
- Cyclical transformations and the Carnot cycle
- Second law of thermodynamics
- Carnot's theorem
- Clausius theorem
- Entropy

- P. Mazzoldi, M. Nigro, C. Voci, “Elementi di Fisica. Vol. I: Meccanica – Termodinamica”, third edition, Edises
- Material provided by the teachers

Atom Structure: orbitals, poly-electron atoms, periodic table; covalent bond, delocalized bond.
Mass relationship in chemical reactions; redox and oxidation number.
Solids: metallic crystal, ionic crystal, molecular crystal, covalent crystal.
Gases: the ideal gas law, partial pressures.
Thermodynamics: nature and type of energy, the zero law of T.D., heat capacity, the first law of TD and Enthalphy, the second law of TD, entropy and free energy, equilibrium conditions.
Liquids: phase change, phase diagrams.
Chemical equilibrium: the equilibrium constant and the equilibrium law
Properties of liquid solutions: concentration units, the Raoult law and distillation, colligatives properties and freezing diagram, electrolytes.
Solutions of strong and weak electrolytes. Acids and bases, pH; Salt hydrolysis; buffer solutions.
Fundamentals of electrochemistry

Texts reported in class
Course slides on moodle site

Introduzione al mondo dei materiali
- Richiami storici, evoluzione dei materiali, uno sguardo al loro interno e un cenno alle trasformazioni
- Proprietà e prestazioni dei componenti
Proprietà di base e comportamento elastico
- Proprietà intrinseche
- Proprietà estrinseche
- Sistemi di sollecitazione meccanica: corpo rigido, corpo deformabile, meccanica del continuo; elasticità lineare, legge di Hooke, comportamento elastico del solido isotropo
Composizione e struttura della materia a diverse scale dimensionali
- Composizione: molecola, legame chimico, curve di Condon-Morse; materiali ionici, materiali molecolari
- Origine termodinamica dell’elasticità
- Strutture: amorfe e cristalline, reticoli di Bravais e indici di Miller
- Difetti nei solidi cristallini: reticolari di punto, di linea e di superficie
Comportamento meccanico dei materiali
- Influenza di T e t sul comportamento meccanico in funzione della natura del materiale
- Sollecitazioni statiche a trazione a bassa T: curva sforzo-deformazione (campo elastico, campo plastico, punti critici)
- Proprietà meccaniche: duttilità, durezza, fragilità, resilienza e tenacità (tecniche di misura delle proprietà)
- Meccanica della frattura: teoria energetica di Griffith, fattore di intensificazione degli sforzi, tenacità a frattura
- Sollecitazioni dinamiche: fatica, curva di Wohler, legge di Paris-Erdogan
Sistemi mono e plurifasici
- Termodinamica dei sistemi: Termodinamica degli stati condensati, concetti di base, primo principio, secondo principio, condizioni di equilibrio, stati di non equilibrio, I e II principio insieme, funzioni di stato caratteristiche
- solubilità allo stato solido: curve di raffreddamento di sistemi ad un componente, stato di aggregazione, regole di Hume-Rothery, soluzioni solide, fase
- dipendenza della solubilità da composizione, temperatura e pressione: regola di Gibbs e della leva, energia di Gibbs, curve di Gibbs, equilibri delle fasi nei sistemi binari
- trasformazioni di fase allo stato solido: meccanismi di diffusione, energia di attivazione e leggi di Fick
- cinetiche di solidificazione e microstrutture: nucleazione e accrescimento, principali trasformazioni termodinamiche, microstrutture
Introduzione alle principali classi di materiali metallici
- Leghe a base ferro: classificazione acciai e ghise, principali diagrammi di fase, classificazione trattamenti termici specifici; acciai speciali, inossidabili e applicazioni.
- Leghe di Titanio: proprietà, processi – applicazioni
- Leghe di alluminio: proprietà, processi – applicazioni
Introduzione alle principali classi di materiali non metallici
- Polimeri e compositi a matrice polimerica: proprietà, processi, applicazioni
- Ceramici: proprietà, processi, cenni alla statistica di Weibull – applicazioni
Richiami, complementi, approfondimenti ed esercitazioni numeriche previste per ogni argomento.

W.D. Callister, Scienza e Ingegneria dei Materiali
Scienza e tecnologie dei metalli - CittàStudi Edizioni
Esercitazioni: su dispense del docente e su Moodle
Slide proiettate a lezione: in pdf su Moodle
Dispense online sul sito Teams del gruppo
Gestione del corso: http://moodle.ing.uniroma3.it/

Introduction

Units of Measures

1. HEAT TRANSFERS

1) Conduction
phenomenology of heat transfers; general information on thermal fields; Fourier postulated. Fourier's equation, in Cartesian and cylindrical coordinates, with and without internal heat development. Examples of exact solutions: flatbed and cylindrical layer steady. Sull'adduzione limit signs on faces. The similarity of insulating critical elettrica.Raggio. Example variable regime: periodic regime stabilized in a semi-infinite half

2) Convection
Definition. Natural convection and forced convection. Schematic of the phenomenon. Definition of the heat exchange coefficient. dimensional analysis. Buckingham theorem. Method of indexes. Determination of dimensional characteristics of heat transfer variables. Applications.

3) Irradiation
Kirchhoff's law. Planck's law, Stefan-Boltzmann and Wien. gray bodies. Applications.

4) Complex Phenomena
Heat transfer by adduction. Applications.


2. Applied Thermodynamics

1) Thermodynamic systems
Thermodynamics principles. Temperature. thermodynamic equilibrium. Work in a closed system. Temperature concept.

2) First law
Conversion and energy transformation: the formulation of the first principle. internal energy. Specific heat.

3) Second law
Statements of the second law. Carnot cycle. Carnot's theorem. Thermodynamic temperature scale. Entropy. Reversible and irreversible transformation.


4) thermodynamic cycles
Cycle of the steam turbine (Rankine). Cycle of compression refrigerating machines saturated vapor.

5) Thermodynamics Air
gaseous mixtures. moist air. Absolute and relative humidity. dew point temperature. Enthalpy associated. Mollier diagram. moist air transformation. Psychrometer.
energy exchanges between man and environment. thermal comfort. wellness equations. Thermal comfort indices: actual temperature, PMV, PPD.

6) Quality and air treatment
The air quality in the neighboring environments. Heating equipment (outline) Air-conditioning systems (notes) Air-conditioning systems: all-air systems (notes). mixed systems (notes).


3. APPLIED ACOUSTICS

1) Definition fundamental physical quantities, sound fields and propagation of acoustic waves. Sound sources and their types. Characterization of the stimulus. Scale decibel

2) The auditory organ and psychophysical quantities. Normal Audiogram.

3) Hearing the sounds: Acoustic of a room, the reverberation time, the quality indexes of a room acoustic treatments.

4) Hearing noise: characterization of the phenomenon, the evaluation indices, current legislation.

5) Measurement Methods: description of the used instrumentation and measurement methodologies, current legislation.

4. LIGHTING

1) Definition fundamental physical quantities, basic laws of radiation. Characterization of the stimulus.

2) The visual organ and psychophysical quantities. Photometry and colorimetry principles.

3) Methods of measurement of photometric quantities: description of the used instrumentation and measurement methodologies.

4) Artificial light sources: incandescent lamps, discharge lamps, LEDs

5) Lighting fixtures: features and operation. Photometric curves and their construction.

6) artificial lighting technology: indoor lighting, outdoor lighting. Balance of luminance. Design principles and current legislation.

1. Yunus A. Çengel, “Termodinamica e trasmissione del calore”, McGraw-Hill Education (testo base in versione completa con compendio di Acustica ed Illuminotecnica)
2. Michael Moran et al., “Elementi di Fisica Tecnica per l’Ingegneria”, McGraw-Hill (per consultazione ed approfondimento)
3. Internal Booklet

Thermodynamics

Fundamentals: physical quantities and units of measurement, closed and open systems, forms of energy, properties of a thermodynamic system, transformations and thermodynamic cycles, temperature and zero principle of thermodynamics, pressure.
The first law of thermodynamics: the concept of conservation of energy, closed and open systems, enthalpy, energy conservation for stationary flow systems.
Properties of substances: pure substances, heat capacity and specific heats, phases of a substance, phase changes of pure substances, state diagrams, equation of state for ideal gases, transformations.
The second law of thermodynamics: statements of the second law of thermodynamics, heat engines, refrigeration machines and heat pumps, reversible and irreversible transformations, Carnot cycle, entropy.
Thermodynamics of humid air: dry air and atmospheric air, absolute humidity and relative humidity, dew temperature, psychrometric diagram, air conditioning, transformations for air conditioning.

Heat transfer

Steady-state thermal conduction: Fourier postulate, analogy with electrical flow, thermal conductivity, one-dimensional conduction in simple geometries, multilayer flat walls, cylindrical geometries, critical insulation radius.
Forced and natural convection: introduction, dimensionless numbers, classification of fluid motion, limit layer of velocity and temperature, natural convection on surfaces.
Irradiation: introduction, thermal radiation, black body radiation, radiative properties, view factors, heat transmission by radiation between black and gray diffusing surfaces, radiation screens.
Applications: thermal transmittance and conductance of walls, critical insulation radius.
Heat exchangers.

Acoustics

Acoustic quantities: general information, sound pressure and sound pressure level, sound power and sound power level, sound intensity and sound intensity level, psychophysical acoustics, normal audiogram, weighting curves.
Free-field and indoor environment propagation: behavior of materials subjected to sound stresses, sound-absorbing and sound-insulating materials, sound-insulating power, sound insulation, Sabine theory.

Educational material provided by the Professor

Books:
Yunus A. Çengel, Giuliano Dall'Ò, Luca Sarto, “Fisica tecnica ambientale. Con elementi di acustica e illuminotecnica”, McGraw-Hill Education

Yunus A. Çengel, “Termodinamica e trasmissione del calore”, McGraw-Hill Education

Fabio Polonara, Gianni Cesini, Gianni Latini, “Fisica tecnica”, CittàStudi (only for in-depth analysis)

Linear first-order differential equations. General first order differential equations. Cauchy problem: local existence and uniqueness. Separation of variables. Systems of first-order equations: linearly independent solutions and Wronskian matrix. Variation of constants. Differential equations with constant coefficients and characteristic polynomial. Matrix exponential and computation for diagonalizable matrices. Some remarkable differential equations: Euler equation and Bernouilli equation.

Norm and distance in R^n. Functions of several variables. Continuous functions and Weierstrass theorem.
Partial derivatives, directional derivatives and gradient. Functions of class C^1 and C^2. Higher derivatives, Hessian matrix and Schwarz theorem. Differentiation of composed functions. Taylor expansion. Local maxima and minima. Method of Lagrange multipliers to compute local maxima and minima.

Riemann integration and Peano-Jordan measure. Integration of continuous functions, reduction formulae
and iterated integrals; area and volume. Change of variables in integrals and Jacobian matrix: polar, cylindrical and spherical coordinates. Gaussian integral.

Curves in R^n: parametrized and equivalent curves; length of a curve; curve integrals of scalar functions. Work and curve integrals of vector fields. Smooth surfaces in R^3: area of a surface and integrals on surfaces.

Teoria: Bertsch, Dal Passo, Giacomelli, Analisi Matematica , McGraw Hill, II edizione
Esercizi: Marcellini, Sbordone, Esercitazioni di Analisi Matematica Due (vol. I e vol. II), Zanichelli ed.

Linear first-order differential equations. General first order differential equations. Cauchy problem: local existence and uniqueness. Separation of variables. Systems of first-order equations: linearly independent solutions and Wronskian matrix. Variation of constants. Differential equations with constant coefficients and characteristic polynomial. Matrix exponential and computation for diagonalizable matrices. Some remarkable differential equations: Euler equation and Bernouilli equation.

Norm and distance in R^n. Functions of several variables. Continuous functions and Weierstrass theorem.
Partial derivatives, directional derivatives and gradient. Functions of class C^1 and C^2. Higher derivatives, Hessian matrix and Schwarz theorem. Differentiation of composed functions. Taylor expansion. Local maxima and minima. Method of Lagrange multipliers to compute local maxima and minima.

Riemann integration and Peano-Jordan measure. Integration of continuous functions, reduction formulae
and iterated integrals; area and volume. Change of variables in integrals and Jacobian matrix: polar, cylindrical and spherical coordinates. Gaussian integral.

Curves in R^n: parametrized and equivalent curves; length of a curve; curve integrals of scalar functions. Work and curve integrals of vector fields. Smooth surfaces in R^3: area of a surface and integrals on surfaces.

Teoria: Bertsch, Dal Passo, Giacomelli, Analisi Matematica , McGraw Hill, II edizione
Esercizi: Marcellini, Sbordone, Esercitazioni di Analisi Matematica Due (vol. I e vol. II), Zanichelli ed.

Health and Safety Fundamentals. Consulting, Control and Guide Lines Issuing Bodies. Hazards, Accidents, Injuries and Professional illness. Frequency and expectance indexes; technical thresholds, doses and damages; Risk and Risk assessment. Control Lists, PERT Techniques and Functional Analysis Space Techniques. Laws in force, Rights and Charges. Health at work Monitoring.
Structure and responsibility. Training, awareness and competence. Consultation and communication. Operational control. Emergency preparedness and response. Performance measuring, monitoring and improvement.
Italian Decree 81.01 and ISO 45001:018. The Italian DVR (Risk Assessment Document) and the art. 30. The OHSMS as a tool of promotion of safe and healthy working environment. Legislative compliance and overall performance improving.
The ISO 45001 compatibility with ISO 9001 and ISO 14001. The Plan – Do –Check – Act System. The Deming Wheel.

Lecture notes, texts, reference laws provided in the classroom by the teacher

Health and Safety Fundamentals. Consulting, Control and Guide Lines Issuing Bodies. Hazards, Accidents, Injuries and Professional illness. Frequency and expectance indexes; technical thresholds, doses and damages; Risk and Risk assessment. Control Lists, PERT Techniques and Functional Analysis Space Techniques. Laws in force, Rights and Charges. Health at work Monitoring.
Structure and responsibility. Training, awareness and competence. Consultation and communication. Operational control. Emergency preparedness and response. Performance measuring, monitoring and improvement.
Italian Decree 81.01 and BS OHSAS 18001:07. The Italian DVR (Risk Assessment Document) and the art. 30. The OHSMS as a tool of promotion of safe and healthy working environment. Legislative compliance and overall performance improving.
OHSAS 18001:07 e UNI INAIL Guide lines. The internationally recognized assessment specification for occupational health and safety management systems. The OHSAS 18001:07 compatibility with ISO 9001 and ISO 14001. The Plan – Do –Check – Act System. The Deming Wheel.

Lecture notes and texts distributed by the teacher

Teaching unit I – Fundamental tools and methods
Elements of vector algebra
Rotation matrix
ODE homogeneous and non-homogeneous
Spectral analysis of symmetric matrices
Eigenvalues problem and diagonalization
Conservative, potential and irrotational vector fields

Teaching unit II – Mechanics of a material particle
Fundamental properties of the motion of a particle
Dynamics of free and constrained material elements
Un-damped and damped oscillators
Mechanical work, power and energy
Stabilty of mechanical equilibrium

Teaching unit III – Mechanics of systems of particles
Internal forces
Conservation of momentum
Conservation of angular momentum
Kinetic energy, Koenig’s theorem

Teaching unit IV – Rigid-body motion and Galilean relativity
Two- and Three-dimensional rigid-body motion
Kinematics in non-inertial frames of reference
Dynamics in non-inertial frames of reference, fictitious forces
Derivative of vectors in moving frames of reference
Trasformazioni tra riferimenti in moto relativo
Derivata temporale di R

Teaching unit V – Statics and dynamics of rigid bodies
Dynamics
Conservation of momentum and angular momentum
Inertia tensor
Ellipsoid of inertia
Koenig’s theorem
Euler equations
Rotation about central axes
Gyroscopes and precessions
Statics
Equivalent forces
Central axis of a system of forces
Constraints reactions
Graphic methods for the analysis of equilibrium

Teaching unit VI – Elements of Lagrangean mechanics

• Lecture notes
• Problem set with solutions

Review of electromagnetism fundamentals, basic principles and theorems for the analysis of electric and magnetic circuits. Representation of sinusoidal electric quantities, definition of circuit impedance and analysis of single-phase and three-phase circuits; instantaneous power, active power and power factor in single-phase and three-phase circuits.
Instruments and methods for measuring current, voltage, active power, power factor and energy in single-phase and three-phase circuits.
Basic principle and operating characteristics of power transformers.
Theory of the rotating magnetic field; basic structure and operating characteristics of induction and synchronous machines.
Components and systems being used in power plants devoted to either generation or transportation or distribution of the electric energy; protection against either overvoltages or overcurrents; sizing of low-voltage secondary-network systems; power-factor correction; protective grounding and safety-related aspects in power distribution systems.

 G. Chitarin, F. Gnesotto, M. Guarnieri, A. Maschio, A. Stella - Elettrotecnica, 1 - Principi - Società Editrice Esculapio
 G. Chitarin, F. Gnesotto, M. Guarnieri, A. Maschio, A. Stella - Elettrotecnica, 2 - Applicazioni - Società Editrice Esculapio
 F. Iliceto, S. Rosati - Impianti di distribuzione dell'energia elettrica - Edizioni Efesto
 Additional Documents and Numerical Exercises - http://moodle1.ing.uniroma3.it

TEACHING PROGRAM

"ECONOMICS OF PRODUCTION SYSTEMS"

CONTENTS OF THE COURSE
Introduction - Economic science and the market
First part - Microeconomics
Second part - Introduction to the business system
Third part - Production management
Fourth part - Comparative Business Government-relations: Investment Analysis and Project Financing


EXTENDED PROGRAM

INTRODUCTION
ECONOMIC SCIENCE AND THE MARKET
Economic science
- Economics applied to Engineering (EAI)
- The economic problem
- The different economic disciplines and industrial economics
- Microeconomics and Macroeconomics
- The analysis of economic issues
The forms of the market
- The degree of competition
- Perfect competition
- Monopoly
- Monopolistic competition
- Oligopoly
- Price discrimination
- Game theory
- Market failures and public intervention

PART ONE - MICROECONOMICS
The supply-demand model
- The market
- Market supply and demand
- The determination of the price
- Market equilibrium
- The elasticity of supply and demand
The Consumer Theory
- Consumer preferences
- The budget constraint
- The marginal utility
- The utility function
- Consumer balance
Production: costs, revenues and profit
- The production function
- Short-term costs
- The long-term costs
- Revenues
- The maximization of profit
- The balance of the producer

SECOND PART - INTRODUCTION TO THE COMPANY SYSTEM
The company
- The company as an economic institution
- General characteristics: object of the company and subjects of the company ("legal entity" and "economic entity")
- Types of companies
- The company in its more general economic characteristics
- The aims of the business, economic equilibrium as a fundamental condition of life for the business, economic equilibrium and economy
- Business organization
- Business strategy

THIRD PART - PRODUCTION MANAGEMENT
- Operation supply chain management (OSCM)
- Product development process
- Business process redesign (BPR)
- Process performance measurement
- Total quality management
- Production capacity planning and management strategies

PART FOUR - COMPARATIVE BUSINESS-GOVERNMENT RELATIONS: INVESTMENT ANALYSIS AND PROJECT FINANCING
Investment analysis
- Choices and principles of equivalence and systems of choice
- Capital and Interest: Discounting and capitalization
- Investments and inflation
- Profit and profitability in investment choices
Project financing
- Public private partnership
- Definitions, characteristics and stakeholders involved
- Project financing models and risk management
- Sectors, type of works and economic and financial sustainability
- Project analysis: viability tests, economic-financial analysis and indicators
- Profitability in project finance
- Outline of ethical finance and non-conventional finance models
- Normative requirements

Reference didactic materials
- Slide by the teacher

External Seminars of Sector Experts

Slides and handouts by the teacher

The variety of the mechanisms in applications. Basic definitions. Degrees of freedom. Classification of the kinematic pairs. Kinematic chains and mechanisms. Kinematic analysis. Plane motion of a rigid body. Velocity and acceleration fields. Kinematic analysis of planar mechanisms. Characteristics of infinitesimal plane motion. Inflection and stationary circles. Euler Savary formula. Planar polodes theory. Pairs with unilateral contacts. Construction of conjugate profiles. Oldham and universal (Cardan) joints. Expression of the transmission ratio. Double cardan joint. Parallel and anti-parallel four bar linkages. Drafting table and pantograph mechanisms. Hart and Peaucellier exact straight lines mechanism generators. Disaggregation principle in statics. Free body static force and torque analysis of complex systems. Applications of the theorem of the virtual works. Basic topics in Tribology. Surface analysis and characterization. Hertz formulae. Friction. An elementary model of adhesive friction. Friction basic mechanisms. Adhesion, abrasion, fretting, surface fatigue. Experimental classification of the worn surfaces: scuffing, scoring, spalling, case crushing, pitting, galling. Predictive models of wear and friction. Energy dissipated “Reye” method, Archard equation. Ball bearings: static force and fatigue modeling, Striebeck formula. Introduction to lubrication. Viscosity and viscosity index. Petroff’s law. One-dimensional Reye theory of hydro-dynamic lubrication. Lubrication of the Rayleigh step bearing. Film with linearly decreasing thickness. Kingsbury – Mitchell bearings. Hydro-static lubrication in the thrust bearing. Hydrostatic compensation. Journal bearings with hydrodynamic lubrication. Work, power and energy. Principles of energy conservation. Power flow analysis in the mechines. Efficiency. Dynamics of the material point. Dynamic of the rigid body. Newton Euler formulation of the dynamic problems. Dynamic analysis by means of the generalized principle of the virtual works. Traction coefficient in transmission. Gearings. The geometrical characteristics of gears with involute profiles. The mechanical interference in gearings. Advanced methods in kinematics: analytical and numerical methods. Dynamic analysis of multibody systems by means of the coordinate partitioning method and the elimination of the Lagrange’s multipliers. Vibration of systems with one degree of freedom. Free oscillation, damped oscillations and excited vibrations. Rayleigh method for the case of the free undamped oscillator. The function of the flywheel in machines. Flexural and torsional vibration in transmission shafts. Vibrations of system with n degrees of freedom. Dynamic problems and wear in breaks. Cams. Construction of cams with prescribed law of motion. Dynamic problems in cams. Constant acceleration cam. Exercises. Kinematic analysis of the slider crank and four bar linkages. Centrodes of the coupler motions. Static balance in different mechanisms. Lubrication. Kingsbury – Michell hydrodynamic bearings. Geometry of involute gearings. Evaluation of the efficiency of simple mechanisms. Analytical and numerical methods in the kinematic analysis of simple mechanisms. Inverse and direct dynamic problems in simple mechanisms. The application of the methods of Lagrange’s multipliers to the solution of direct dynamic analysis of Multibody systems.

Belfiore, N.P., Di Benedetto, A., Pennestrì, E., Fondamenti di meccanica applicata alle macchine, SECONDA
EDIZIONE, CEA Casa Editrice Ambrosiana, Milano, 2011.

Di Benedetto, A., Belfiore, N.P., Fondamenti di Teoria delle vibrazioni meccaniche, CEA Casa Editrice
Ambrosiana, Milano, 2007.

Materials available from Moodle and Teams platforms.

Kinematic analysis of planar mechanisms (graphical and numerical methods)
Direct motion
Hydrodynamic lubrication
Mechanical efficiency
Spur gears
Multibody dynamics
Vibrations of systems with a single degree of freedom

William T. Thomson, Marie Dillon Dahleh, Theory of Vibration with Applications, Prentice Hall

Kinematics of rigid bodies. The rigid body model. Rigid displacements. General formula of infinitesimal rigid displacement. Scalar representation of the rigid displacement field. Planar rigid displacements. Systems of rigid bodies.

Kinematic characterization of a constraint. External constraints and internal constraints.
The cinematic problem. Kinematic classification.

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

Beam kinematics. Displacement, rotation, hypothesis of small displacements. Kinematic conditions.

Deformation measurements in the Timoshenko model. Axial deformation. Angular scroll. Bowing. Equations of congruence. Model of Euler-Bernoulli. Vector representation of congruence equations. The kinematic problem for the beam. Statics of the beam. External actions and internal actions. Partwise balance. Differential equilibrium equations in scalar and vector format. The static problem. Internal action diagrams.

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

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

The elastic problem for the beam and its formulation.

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

Principle of virtual work. The concept of congruent system. Notion of a balanced system. External virtual work. Internal virtual work. Theorem of virtual works, statement and proof. Application of the Virtual Works Principle to the calculation of displacements and rotations in statically-determined structures.

Force method. Released structure. Application of the method to the general case. Müller-Breslau equations. Flexibility matrix. Effect of constraint displacement and thermal distortions.

Reticular trusses. Internal isostaticity of the triangular mesh. Canonical nodes. Node method. Canonical sections. Ritter method.

Continuous beams. The three-moment equation.

Three-dimensional continuous bodies: analysis of the deformation. The strain tensor. Geometrical interpretation of the components of the strain tensor.
State of triaxial deformation. State of cylindrical deformation. Spherical or hydrostatic deformation state. Mohr's circles.

Three-dimensional continuous bodies. Cauchy's concept of traction. Partwise balance. Cauchy's Lemma. The stress tensor. Differential equations of equilibrium.

Principal stresses and principal directions. Voltage states. Lamé's ellipsoid of tension. Isostatic lines. State of plane or biaxial tension. Purely tangential tension state. Uniaxial voltage state. Mohr's circles for the stress.

Linearly elastic constitutive equations. Experimental determination of elastic constants. Traction test. Torsion test. Isotropic materials: the generalized Hooke law.

The problem of elastic balance. The Virtual Works Theorem. Partial solutions to the problem of elastic equilibrium. Deformation work. Clapeyron's theorem. Betti's theorem. Theorem of the minimum total potential energy. Theorem of the minimum total complementary potential energy

The problem of Saint Venant. Postulate of Saint Venant. The semi-inverse method.

Normal force. Flexure.

Torsion of compact and hollow circular sections.

Torsion of compact sections of arbitrary shape. The Neumann problem. Elliptical sections. Polygonal sections. The hydrodynamical analogy. Thin rectangular section. Open sections composed of thin rectangles. Thin-walled sections: Bredt's theory.

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

Rupture criteria for fragile materials and ductile materials.

The phenomenon of structural instability. Stability analysis in rigid beams with elastic restraints. Stable branches. Unstable branches. Sensitivity to initial imperfections. Euler's Elastica. Dependence of the critical load on the constraint conditions. Inflection plans. Curves of stability, slenderness.

The beam: structural analysis and verification. Extension of the Saint Venant theory. Resistance criteria for the Saint Venant solid.

P. Casini & M. Vasta, "Scienza delle costruzioni", Città Studi Edizioni 2016.
Steen Krenk & Jan Høgsberg, "Statics and Mechanics of Structures", Springer 2013.

Design of elements subjected to static loading: stress and strain state, simple loadings, Mohr circles, ideal stress, hypotheses of failure.
Principles for designing or choosing of: rolling and sliding bearings, springs, non-permanent and permanent joints.
Elastic instability, surface to surface contact, impact stresses.

AIM OF THE COURSE. The course in Manufacturing Technology provides the student with the basic knowledge of the main mechanical processing technologies. Specifically, the course aims to illustrate, transversely, the traditional processes of transformation and mechanical processing, starting from the study of the properties of the materials and related techniques of characterization and arriving at a detailed analysis of the technologies and related processing parameters, as well as the productive context in which they fit. The course aims to provide the student with all the tools to define the processing cycle of a component and to highlight the links between the parameters of the process, the properties of the raw material and the final properties of the semi-finished / finished product. The contents of the course will pour, in a first introductory part, on the study and understanding of the micro / macroscopic properties of the materials and related analysis techniques. Subsequently, the main processing technologies will be examined, such as the manufacturing processes for casting, the processing by plastic deformation and machining processes. Every single processing technology will be analyzed in terms of operating principle, type of production context and technological criticality.

DETAILED PROGRAM OF THE COURSE. Introduction to the course. Overview of production processes and transformation technologies. Metrology and dimensional control. Dimensional accuracy and tolerance, geometric tolerance. Main properties of materials of technological interest. Tests for the determination and measurement of the mechanical properties of materials: Traction, Compression, Flexion, Fatigue. Milling processes. The casting and solidification of the castings. Foundry defects. Casting processes in transitional form. Permanent casting processes. Forming in earth, in shell, in vacuum, die-casting, centrifugal and lost wax. Notes on the design of anime and models. Notes on the sizing of the power supply system. Coolers. Allowances. Technical and economic aspects of foundry processes. The workings for plastic deformation. The theory of plasticity. Massive deformation processes. Forging and molding. Slab method. Molding cycle. Forging defects. Design of the molds. Presses and knits. Lamination. The mechanics of the flat rolling process. The defects of laminated products. Extrusion: general information and equipment. Drawing: general information and equipment. Machining processes: general information. Tool angles. Wear and principle of tool angles selection. Mechanic of machining process. Turning. Milling. Drilling. Other machining processes.

Text: Mechanical technology. Ediz. MyLab. With e-text. With online expansion by Serope Kalpakjian, Steven R. Schmid
Publisher: Pearson
Necklace: Engineering
Edition: 2
Publication Date: September 2014
EAN: 9788865183748
ISBN: 8865183748
Pages: XIV-872
Format: produced in several parts of different sizes

Machines and Heat exchangers: Classifications;
• State functions and process-dependent entities. Equations of state;
• Fundamental laws of thermodynamics: conservation, equivalence, and evolution of a thermodynamic system;
• Energy conservation;
• Irreversible processes;
• Thermodynamic processes and diagrams. Relevant thermodynamic processes (e.g., isentropic, polytropic, isothermal, isobaric, isochoric processes)
• Compression and expansion processes: adiabatic processes, intercooled compression, re-heated expansion)
• Thermodynamic laws applied to the analysis of energy conversion systems: relevant case studies
• Combustion processes
- Combustion: generalities;
- Combustion at constant volume;
- Combustion at constant pressure for open and closed systems.
• Thermodynamic cycles and periodical processes
- Ideal, limit and real cycles;
- Direct and inverse cycles;
- Performance of thermodynamic cycles: power, efficiency, COP and other relevant indexes
- Relevant cycles: Brayton/Joule, Rankine, Hirn, Stirling, Ericsson, Beau de Rochas, Diesel, Sabathé
- Combined cycles
- Periodical processes and related diagrams

• Introduction to applied fluid-dynamics:
- Control volume analysis;
- 1D, 2D, and 3D analyses;
• Conservation of mass, momentum, and energy. The entropy.
• The effect of fluid viscosity and compressibility:
• Definition of Mach Number and equations for gasses in terms of Mach Number;
• Subsonic, transonic and supersonic flows;
• Fanno Flow;
• Rayleigh Flow;
• Varying-area isentropic flows: Hugoniot equations for nozzles and diffusers;
• Converging-diverging nozzles;
• Nozzles, diffusers, and converging-diverging nozzles in real conditions.
• Evaluation of thrust, work, power, and efficiency in simple cases.
• Cavitation in hydraulic machines: generalities, Net Positive Suction Head (NPSH),
• Relevant applications for energy conversion and propulsion systems
• Cavitation: generalities, Net Positive Suction Head available and required
• Relevant cases in hydraulic plants

• C. Caputo, "Gli impianti convertitori d’energia", Casa Editrice Ambrosiana;
• C. Caputo, "Le turbomacchine", Casa Editrice Ambrosiana;
• R. D. Zucker, O. Biblarz, “Fundamentals of Gas Dynamics”, Ed. John Wiley & Sons, 2002, ISBN 0-471-05967-6
• Specific documents uploaded on Moodle