Fields. Real and complex numbers. Limits. Infinite Series. Continuity and differentiability. Integrals. Taylor's Polynomial.

1) Bramanti, Pagani, Salsa: Analisi Matematica I.
2) Bertsh, Dall'aglio, Giacomelli: Epsilon 1.
3) Amar Bersani: Analisi Matematica I (esercizi e richiami di teoria).
4 ) Salsa Squellati: Esercizi di analisi Matematica I.

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).

S. Lang, A First Course in Calculus, Springer Ed.

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).

S. Lang, A First Course in Calculus, Springer Ed.

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

1) Real numbers and functions
Natural, integer 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) Riemann integration
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 + exercises book

* 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 and algorithms
Computer architecture
Languages and Compilation
I / O, variables and constants

* Operations *
Types of data
Expressions
Boolean algebra

* Control structures *
Selection
Iteration
Functions

* Data structures *
Array
Strings
Matrices

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.

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

Any book dedicated to Engineering classes of Linear Algebra can be freely chosen.

SUGGESTED:
M. Abate Algebra Lineare McGraw-Hill Education con Marco Abate, Chiara de Fabritiis Esercizi di Geometria , McGraw-Hill Education

or:
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.
F. Bottacin Linear Algebra and Geometry Esculapio Soc. Ed.
F. Bottacin Exercises in Linear Algebra and Geometry Esculapio Soc. Ed.

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

Any book dedicated to Engineering classes of Linear Algebra can be freely chosen.

SUGGESTED:
M. Abate Algebra Lineare McGraw-Hill Education con Marco Abate, Chiara de Fabritiis Esercizi di Geometria , McGraw-Hill Education

or:
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.
F. Bottacin Linear Algebra and Geometry Esculapio Soc. Ed.
F. Bottacin Exercises in Linear Algebra and Geometry Esculapio Soc. Ed.

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

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.

• E. Chirone, S. Tornincasa, “DISEGNO TECNICO INDUSTRIALE”, Vol. 1, 2022 (Edizioni il Capitello);
• E. Chirone, S. Tornincasa, “DISEGNO TECNICO INDUSTRIALE”, Vol. 2, 2022 (Edizioni il Capitello);

English books:
• 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;

Online documentation on the Moodle site of the course.

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

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.

Bertsch, Dal Passo, Giacomelli, Analisi Matematica , McGraw Hill, II edizione
Gentile, Introduzione ai Sistemi Dinamici Volume 1, Springer
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 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

Ch. I : Electrostatics :
Electrostatic Field (i) : Electric charge, Coulomb's law.
Electrostatic Field (ii) : Electric field flux, Gauss's law for the electric field.
Electrostatic Field (iii) : Electric field line integral. Electrostatic potential.

Ch. II : Electric Field–Matter Interaction :
Electric Properties of Matter (i) : Conductors, dielectrics in electrostatic equilibrium.
Electric Properties of Matter (ii) : Conductors in dynamic equilibrium. Electric current. Ohm's law.

Ch III : Magnetostatics :
Magnetostatic Field (i) : Electric current. Ampère-Laplace law.
Magnetostatic Field (ii) : Magnetic field line integral, Ampère's law of the magnetostatic field.
Magnetostatic Field (iii) : Magnetic field flux. Gauss's law for the magnetic field. (Magnetic potential vector).

Ch. IV : Magnetic Field–Matter Interaction :
Magnetic Properties of Matter : Magnetic matter in magnetosttic equilibrium.

Ch V: ("slow") Electrodynamics :
Electromagnetic field (i) : Electric field line integral, Faraday's law.
Electromagnetic field (ii) : Magnetic field line integral, Ampère-Maxwell law. Maxwell equations.

P. Mazzoldi, M. Nigro, C. Voci, "Elementi di Fisica. Vol. II: Elettromagnetismo e Onde", 3rd ed., Edises.

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)

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.

Suggested Textbooks
 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 made available on both Teams and Moodle web pages

Vector Space: definition of vectors; scalar and vector product.
Matrix algebra: tensor product and proiector.
Damped harmonic oscillator; study of mechanical power involved; phase plane.
Kinematics of material point.
Geometry of curves; velocity and acceleration in the moving frame.
Kinematics in polar coordinates; rigid motion; spin, angular speed and Poisson formulas.
Study of velocity field for rigid bodies.
Planar motions: center of rotation (CR)
Kinematics of constraints, points system; degrees of freedom.
Theoremes of Galileo and Coriolis
Principles of the mechanics of material point; notion of forces; friction forces.
Dynamics of material point.
Fundamental mechanical quantities.
Cardinal Equations; riduction of system of forces.
Power, Work, Energy, Potential
Kinetic energy theorem; balance of mechanical energy.
Center of mass and its properties.
Moment of inertia and its matrix representation
Momentum and angular momentum for CR
Statics; Euler’s Equations for 3D Rigid Body (cardial equations in Italian).
Statics of suspended cables.
Introduction to Analytics Mechanics;
Principle of Virtual Power
Lagrange equations for conservative system; analysis of stability
Small oscillations.
Elements of impulsive dynamics

Free pdf notes, comprehensive of exercises .

Reference text: Biscari, Ruggeri, Saccomandi, Vianello, “Meccanica Razionale per l’Ingegneria”, Monduzzi, (seconda edizione).

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).

S. Lang, A First Course in Calculus, Springer Ed.

Computer Architecture, Operative System, Problem, Algorithm, Software, Representation of information, Software compiling and execution, Python development environment, Languages - syntax and semantics, Types and expressions, Functions in Python, Conditional instructions, Repetitive instructions, Strings, Dictionaries, Tuples and Matrix in Python, Sorting algorithms, Basic notions of Specification and correctness of software, Computational complexity, Files and Exceptions, Linear Algebra, Linear equations and sets, Matrices in Algebra, Determinant, Reverse matrix, Rank of a matrix, Gauss, Algebraic functions, Vector spaces, Generators, Bases.

“Programmazione in Python”, di Lambert Kenneth, Maggioli Editore, Giugno 2018 (II Edizione).

“Geometria” di G. Accascina e V. Monti http://www.dmmm.uniroma1.it/accascinamonti/geogest/Geometria.pdf

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
- 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 elastic potential energies
- Conservation of mechanical energy. Applications
- Stability conditions for static equilibrium

- P. Mazzoldi, M. Nigro, C. Voci, "Elementi di Fisica. Vol. I: Meccanica e Termodinamica", terza edizione, Edises, Napoli

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.

• E. Chirone, S. Tornincasa, “DISEGNO TECNICO INDUSTRIALE”, Vol. 1, 2022 (Edizioni il Capitello);
• E. Chirone, S. Tornincasa, “DISEGNO TECNICO INDUSTRIALE”, Vol. 2, 2022 (Edizioni il Capitello);

English books:
• 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;

Online documentation on the Moodle site of the course.

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 electromagnetism
- Electric charge and Coulomb's law
- Electrostatic field
- Flux of a vector field and Gauss's law
- Electric potential
- Conductors and capacitors
- Stationary electric currents
- Ohm's law
- Magnetic interactions
- Lorentz force
- Magnetic force on current carrying conductors
- Magnetic field generated by a current
- Gauss's law for the magnetic field
- Ampere's law
- Dielectric and magnetic properties of materials (brief notes)

- P. Mazzoldi, M. Nigro, C. Voci, "Elementi di Fisica. Vol. II: Elettromagnetismo e Onde", terza edizione, Edises, Napoli

The course aims to 1) provide the basic geologic/geomorphologic concepts with a particular emphasis on those affect the evolution of coastal areas and the ocean floor; 2) present the main tools for direct and indirect analysis of the ocean floor; 3) understand the main physical and chemical mechanisms that regulate atmospheric circulation pattern and large scale oceanic currents; 4) evaluate natural risks with a focus on those occurring in the marine and coastal environments; 5) appreciate the conformation of the Italian coasts and the bathymeters of the seas that surround it.

General geology:
- Understanding Earth (Edition 7), Thomas H. Grotzinger and John, Jordan, Editor: W. H. Freeman, ISBN-13: 978-1464138744

Oceanography:
- Oceanography: An Invitation to Marine Science (Edition 9), Tom S. Garrison and Robert Ellis, Editor: Cengage Learning, ISBN-13: 9781305105164

Additional material will be provided during the class

Electric field and magnetic field. Electromagnetism fundamentals, basic principles and theorems for the analysis of electric and magnetic circuits. Electric circuits indc.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. Basic principles of staticpower conversion.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.

Testi Consigliati
- 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
- Materiale di Integrazione, Esercitazioni ed Esercizi d’esame - https://ingegneria.el.uniroma3.it/

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)

Physical properties of fluids
• Density and Compressibility
• Vapor pressure
• Viscosity
• Surface tension
Statics of Fluids
• Stress in one point and dependence on position
• Fundamental equation of fluid statics
• Equilibrium of a finite mass of fluid at rest
• Hydrostatic thrust on a flat surface
• Hydrostatic thrust on a curved surface
Fluid kinematics
• The material derivative
• Reynolds' theorem
• The velocity field around a point
Fluid dynamics
• Mass conservation equation
• Constitutive relationships
• Equation of conservation of momentum
• Conservation of total energy in a non-ideal fluid
• Angular-Momentum conservation equation
Applications of Bernoulli theorem and of the momentum conservation equation in integral form
• Applications of Bernoulli theorem
• Applications of the momentum conservation equation in integral form
Dimensionless form of the equations of motion
Ideal fluids
• Equations of motion
• Irrotational motion
• Flow around 2D and 3D bodies
Viscous fluids
Motions at low Reynolds numbers
• Motion between flat parallel plates
• Hydrodynamic lubrication
• Motion between concentric cylinders
Motions at moderate Reynolds numbers
• Boundary layer: Prandtl theory
• Separation of boundary layer
• Oseen equation
• Flow around a cylinder and a sphere as the Reynolds number increases
Compressible fluids
• Water Hammer and Surge Pressures

Cengel, Cimbala, fluid mechanics

Landau, Lifshitz, fluid mechanics

Physical properties of fluids
• Density and Compressibility
• Vapor pressure
• Viscosity
• Surface tension
Statics of Fluids
• Stress in one point and dependence on position
• Fundamental equation of fluid statics
• Equilibrium of a finite mass of fluid at rest
• Hydrostatic thrust on a flat surface
• Hydrostatic thrust on a curved surface
Fluid kinematics
• The material derivative
• Reynolds' theorem
• The velocity field around a point
Fluid dynamics
• Mass conservation equation
• Constitutive relationships
• Equation of conservation of momentum
• Conservation of total energy in a non-ideal fluid
• Angular-Momentum conservation equation
Applications of Bernoulli theorem and of the momentum conservation equation in integral form
• Applications of Bernoulli theorem
• Applications of the momentum conservation equation in integral form
Dimensionless form of the equations of motion
Ideal fluids
• Equations of motion
• Irrotational motion
• Flow around 2D and 3D bodies
Viscous fluids
Motions at low Reynolds numbers
• Motion between flat parallel plates
• Hydrodynamic lubrication
• Motion between concentric cylinders
Motions at moderate Reynolds numbers
• Boundary layer: Prandtl theory
• Separation of boundary layer
• Oseen equation
• Flow around a cylinder and a sphere as the Reynolds number increases
Compressible fluids
• Water Hammer and Surge Pressures

Download handouts from Teams

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. Sheet metal deformation processes. Formability of the plates. Shearing. Bending. Cupping.

Authors: Serope Kalpakjian, Steven R. Schmid
Editor: Pearson
Collection: Prentice Hall
Edition: 5
Year: 2008

Vector Space: definition of vectors; scalar and vector product.
Matrix algebra: tensor product and proiector.
Damped harmonic oscillator; study of mechanical power involved; phase plane.
Kinematics of material point.
Geometry of curves; velocity and acceleration in the moving frame.
Kinematics in polar coordinates; rigid motion; spin, angular speed and Poisson formulas.
Study of velocity field for rigid bodies.
Planar motions: center of rotation (CR)
Kinematics of constraints, points system; degrees of freedom.
Theoremes of Galileo and Coriolis
Principles of the mechanics of material point; notion of forces; friction forces.
Dynamics of material point.
Fundamental mechanical quantities.
Cardinal Equations; riduction of system of forces.
Power, Work, Energy, Potential
Kinetic energy theorem; balance of mechanical energy.
Center of mass and its properties.
Moment of inertia and its matrix representation
Momentum and angular momentum for CR
Statics; Euler’s Equations for 3D Rigid Body (cardial equations in Italian).
Statics of suspended cables.
Introduction to Analytics Mechanics;
Principle of Virtual Power
Lagrange equations for conservative system; analysis of stability
Small oscillations.
Elements of impulsive dynamics

Free pdf notes, comprehensive of exercises .
Reference text: Biscari, Ruggeri, Saccomandi, Vianello, “Meccanica Razionale per l’Ingegneria”, Monduzzi, (seconda edizione).

Energy and energy sources

Classification and general characteristics of fluid machines

Thermal and thermodynamic processes of machines and energy systems

Characteristics of operating fluids

Hydraulic power plants

Wind turbines and wave energy converters (WEC Systems)

Thermodynamics of machines

Fuels and combustion

Steam power plants

Gas turbine power plants

Reciprocating internal combustion engines

Combined plants and Cogeneration plants

Propulsion

Photovoltaic systems - overview

Pollutant emissions - emission factors

Introduzione allo studio delle machine, Oreste Acton, Carmelo Caputo, UTET 1979
Impianti motori, Oreste Acton, Carmelo Caputo, UTET 1992

Gli impianti convertitori di energia, Carmelo Caputo, Ed. Masson 1997 o successive

Mathematical theory of sea waves
Linear theory
wave characteristics (velocities, pressure, energy,...)
Wave propagation to shallow water
wind wave generation
Real wave field measures and analysis

Kinematic Structure of Mechanical Systems
Classification of kinematic pairs and their degrees of freedom, Lower pairs, Higher pairs, Shape and force closure pairs, Kinematic chains and mechanisms, Classical representation of kinematic chains and mechanisms, Introduction to the analysis and synthesis of mechanisms, Topological formulas for calculating the number of degrees of freedom (DoF), Mechanisms with lower pairs only. Correspondence between mechanism graphs. Enumeration of mechanisms with 1 DOF and 4 members.
Geometry of Constrained Systems
Introduction to graphical methods, Representation scales, Classical geometric approach to the problem of initial configuration, Slider-Crank mechanism, Grashof's rule for the planar four-bar linkages, four-bar parallelogram, anti-parallelogram, and rhomboid linkages. Analytical methods for determining the initial configuration, Numerical methods for determining the generic configuration of a mechanism, Dependent and independent coordinates, Solution of the problem of the initial configuration using the numerical method of Newton–Raphson, Application of Dini's theorem to the calculation of degrees of freedom: Instantaneous critical forms, Permanent critical forms, Graphical method for determining the configuration of an articulated quadrilateral given the crank angle and the length of the links, Methods for determining the configuration of an articulated quadrilateral given the crank angle and the length of the links: analytical, using complex numbers, and numerical, using constraint equations. Technograph, Pantograph, Use of the oscillating slider crank system, Hart's, Peaucellier's straight-line generator.

Geometry of Masses and Moments of Inertia
Static moments or first-order moments, Moments of inertia or second-order moments, Huygens-Steiner theorem, Principal axes and moments of inertia. Moment of inertia of the section about the neutral axis and polar moment of inertia of a shape. Analytical formulation based on matrices and vectors.

Introduction to Kinematic Analysis of Planar Systems
Review of kinematics of the material point, Review of kinematics of the rigid body, Motion law for a planar system and first-order centrodes, Fundamental formula of kinematics, Velocity center, First-order centrodes, Acceleration field. Euler-Savary formula in the first and second formulations. Inflexion circle, Curvature of trajectories, Null tangential acceleration circle, Review of the theorem of relative motions, Apparent wind velocity in a sailing boat with close-hauled and running reach, Aronhold-Kennedy theorem, Graphical methods of kinematic analysis. Graphical method based on vectors diagrams, vectors diagrams based on the fundamental formulas of kinematics, vectors diagrams based on the theorem of relative motions, Graphical determination of K, note F, Center points method, Graphical determination of the center of curvature of the trajectory of a point M of the mobile plane, knowing the centers of curvature of the first-order centrodes. Graphical determination of the first-order centrodes, Kinematic analysis of mechanisms, Kinematic analysis of mechanisms with higher pairs, Construction methods of conjugate profiles, The method of the envelope curve, The method of normal lines, The cycloid curve method with a point trajectory, The cycloid curve method with an auxiliary envelope curve, Assortment profiles. Justification of equivalent mechanisms with the cycloid curve method with a point trajectory, Center of curvature of the trajectory of a point, Kinematic analysis with the method of constraint equations, and with complex numbers. General case of a system with rehonomic constraints or time-dependent constraints Kinematic analysis of mechanisms with rolling or sliding bodies, Kinematic analysis of a planar four-bar linkages with numerical method based on constraint equations, Parametric equation of the involute curve, Parametric equation of the cycloid curve.

Recap of Statics
Newton-Euler equations of Statics, Elementary cases of equilibrium, Body subjected only to two forces, Body subjected only to three forces, Examples, Body subjected only to four forces in the plane, The principle of fragmentation, Equivalent force systems, The principle of virtual work, Static equilibrium of mechanisms with one degree of freedom.

Dynamics of Planar Mechanisms
Classifications of dynamic actions, External and internal forces, Driving and resisting forces, Active and reaction forces. Review of the dynamics of the point mass, d'Alembert's principle, Application of d'Alembert's principle to systems of lumped point masses. Review of the dynamics of the rigid body, Equation of motion of a translating body, Equations of motion of a body rotating about an axis, Equivalent force system, Body subjected to generic planar motion, Newto-Euler equations in space, Dynamics of systems through the Principle of the Virtual Work PLV. Direct and indirect dynamic problems, Application of PLV, Scotch-yoke mechanism, Lifting hoist, Dynamics of the planar four-bar likage, Kinematics and Dynamics of the slider crank mechanism. Analysis of the main dynamic actions, Static and dynamic balancing of rotors, Static balancing of the slider crank mechanism. Examples of direct or inverse dynamic problems.

Analytical Dynamics
Dynamic analysis with the method of Lagrange multipliers, the role of reactions in the method of Lagrange multipliers. The setting up of the dynamic problem, Integration of equations using initial conditions, Approach based on minimizing the constraint equations, Approach based on the partitioning of coordinates, Lagrange multipliers and reaction forces.

Friction and Wear
Elements of surface mechanics, Ideal and real surfaces, Contact between two real surfaces, Stresses and deformations in surface contacts, Hertz's Formulas. Typology of dissipative phenomena, Types of friction, Types of wear, Models for calculating tangential dissipative forces in direct contacts, Determination of the coefficient of sliding friction in adhesive wear regime. Experimental determination of tribological characteristics of a pair of materials, Models for wear calculation, Models for the case of predominantly abrasive wear, Friction in the revolute pair, axial revolute pair and journal bearings. Friction circle. Classification of friction based on the relative motion between bodies in contact, Rolling friction due to material hysteresis. Rolling friction parameter, Loaded and Unloaded driving wheel. First definition of rolling friction coefficient for material hysteresis, Driven wheel: further definition of rolling friction coefficient for material hysteresis, Rolling friction due to impacts, Rolling bearings, Friction circle for rolling bearings, Design of axial and journal rolling bearings in Static and fatigue conditions.

Basics of Lubrication Theory
Viscosity in lubricating fluids, Other characteristics of lubricating oils, Additives for lubricating oils, Classification of lubrication types, friction in lubricated prismatic pair. Expression of the flow rate of a fluid in a fluid film. Pushing rolling pair, Hydrostatic lubrication with constant flow rate or pressure, Circuits with hydrostatic compensation, Hydrodynamic lubrication: need for a film with variable thickness. Film with constant height, Film with constant height in sections: step bearing, Hydrodynamic lubrication in a gap with variable thickness, Film with linearly variable thickness. Effect of lateral leaks, Kingsbury-Michell bearings, Axial revolute pair with lubrication, journal bearing, Half-Somerfield Theory. Geometric meaning of the mediated friction angle in the lubricated rolling pair, Inverse problem. Lubricated flat sliding pair, Direct problem. Michell bearings with self-aligning pads, Direct problem. Michell bearing with fixed orientation.

Work and Energy
Kinetic energy, Variation of kinetic energy, Potential energy, Conservation of mechanical energy, Energy balance and efficiency, Instantaneous and average efficiencies, Backward (reverse) motion efficiency, Other expressions of efficiency, efficiency of mechanisms, Force and torque reduction, Mass reduction, Reduction of masses in a crank mechanism, Reduction of stiffness, Design of a Flywheel.

Gears
Transmission by higher kinematic pairs, Levers with constant transmission ratio, Friction wheels, Types of gears, Nomenclature of gears. Involute profiles, Line of action and action line, Drawing of the involute profile, Tooth thickness, Calculation of slip between teeth, Specific slips. Interference phenomenon, Methods to overcome interference, Rack-wheel pair with involute profile, gear cutting, Helical gears for parallel axes, characteristics of teeth on normal and front planes, Transmission from rotation to translation using gears, Efficiency of gear pair with involute profiles, Worm wheel pair.

Transmission Joints
Analysis of kinematic structure, Homokinetic joints, Oldham joint, Cardanic joints, Cardan joint and double Cardan joint. Overview of other types of joints.

Cam-Follower Mechanisms
Classification of cam-follower mechanisms, Classification by absolute motion type of driver. Classification by contact type between driver and follower, Classification by absolute motion type of driver and follower, Classification by combination of operating phase sequences. Classification by member contact mode, Conical or spherical eccentrics, Followers. Cam profiling: graphical method, centric roller follower, centric plate follower, Eccentric roller follower, Standard motion profiles, Constant velocity profile, Constant acceleration profile (parabolic), Harmonic profile, Cycloidal profile, Polynomial profiles.

Brakes
The dynamic problem of braking, Reye's hypotheses, Determination of braking force, Mechanical clutch engagements, Cone clutch engagements. Brake shoe with rigid and free approach motion. Jamming and partialization.

Introduction to Mechanical Vibrations
Preliminary concepts and definitions. Free vibrations of linear systems with one degree of freedom. Equation of motion: Newtonian deduction and energy criterion. Study of undamped free oscillations using the method of complex numbers. Rayleigh's method. Damped free vibrations of linear systems with one degree of freedom. Viscous damping, Logarithmic decrement. Forced vibrations of linear systems with one degree of freedom. Resonance and dynamic amplification, applications. Forced and damped vibrations of linear systems with one degree of freedom, analytical, vector and complex number-based approaches, dynamic amplification coefficient and phase, Influence of the ratio n, quasi-static, resonance, and seismographic regions. Vibration isolation. Forced and damped vibrations, vector approach, transmissibility coefficient. Introduction to systems with multiple degrees of freedom.

Flexural Vibrations and Torsional Pulsations
Flexural vibrations. Self-centering of a rotating shaft with a keyed flywheel in the middle. Torsional pulsations, torsional pendulum. Elements of rotordynamics: Jeffcott rotor.

Hoists
Lifting organs. Direct and reverse hoist. Applications. Operation in the ideal case. Static analysis of forces. Optional: Witt hoist. Differential hoist. Efficiency of the single pulley.

Practical Exercises
1. Kinematic analysis of a planar four-bar linkage with graphical method based on the properties of points belonging to the same rigid system.
2. The centrodes of the coupler link with respect to the frame in a centered slider-crank mechanism using the graphical method.
3. Kinematic analysis of mechanisms having glyphs, higher pairs, and links; Divided into two parts: Fairbairn's guide and Cam-follower mechanism.
4. Kinematic analysis with graphical method based on the determination of the centers of the first and second orders, First Part Planar four-bar linkage, Second Part Sider Crank mechanism.
5. Involute and cycloid. Study of the trajectory of a point tracking attached to a body for assigned centrodes of the motion (graphical method). Point tracking a cycloid curve. Point tracking an involute curve.
6. Study of the static force balance of mechanisms using graphical methods in the ideal case. First part. Graphical method of the free body for calculating ideal reactions in a mechanism in static/stationary equilibrium. Second part. Ideal constraints. Absence of weight force. Application of the principle of virtual work for calculating driving actions (forces/torques) acting on a mechanism in static/stationary equilibrium under the simultaneous action of a load Q.
7. Practical method for calculating the instantaneous efficiency of a mechanism.
8. Inverse Dynamic Problem. Free body method.
9. Geometry of gears. First Part. Gear geometry. Second Part. Interference in gears.

Exercises based on computer Lab Activities
Any programming environment can be used, for example, Python, MatLab (recommended), Mathematica, etc. However, during the exam, you must be able to explain the functioning of the code from a methodological (mechanical) point of view.
1. Elementary example of direct dynamic problem: rectilinear motion of an accelerated mass (with assigned function for force) First Part (analytical method) Second Part (numerical integration methods)
2. Application of the Newton Raphson numerical method for determining the configuration of a planar articulated four-bar linkage and an ordinary centered slider-crank mechanism. First Part - Planar four-bar linkage Second Part – Slider Crank mechanism Third Part (optional) – Slider Crank mechanism with secondary slider-coupler rods.
3. Involute and cycloid - Study of the trajectory of a point tracking solid with a body for assigned centrodes of the motion; Analytical method. Point tracking a cycloid curve. Point tracking an involute curve. Development with analytical approach.
4. Numerical method based on constraint equations for kinematic analysis of mechanisms Second part (optional) – Sider Crank mechanism and Slider Crank mechanism with secondary slider-coupler rods.
5. Study of hydrodynamic lubrication. First Part. Inverse Problem. Second Part. Direct Problem.
6. Multibody Systems Dynamics (MBS Dynamics). Direct Dynamic Problem.
7. Free mass-spring-damper system (use the provided MatLab code PCLAB7.m). Direct Dynamic Problem. Analytical and numerical solution.

Nicola Pio Belfiore, Augusto Di Benedetto, Ettore Pennestrì, Fondamenti di meccanica applicata alle macchine, Terza Edizione, Editore CEA (distribuzione Zanichelli), Pagine 912, 2024, ISBN 9788808220158
Materiale pubblicato sulla piattaforma Moodle e Teams.

Elements of Algebra and Vector and Tensor Calculus
Kinematics of Rigid Bodies
The Rigid Body Model
Rigid Displacements
General Formula for Infinitesimal Rigid Displacement
Planar Rigid Displacements
Systems of Rigid Bodies
Kinematic Characterization of Constraints
Kinematic Characterization of External Constraints
Kinematic Characterization of Internal Constraints
Settlement Constraints
The Kinematic Problem
Kinematic Classification by Analytical Means
Kinematic Classification by Direct Means
Graphical Method for Solving the Kinematic Problem
Definitions. Kinematic Chains.
Statics of Rigid Bodies
Static Characterization of Constraints
Static Characterization of External Constraints
Static Characterization of Internal Constraints
The Static Problem
Cardinal Equations of Statics
Position of the Problem
Static Classification
Static-Kinematic Duality
Kinematics of Beams
The Deformation Process
Displacements and Rotations
Displacement
Rotation of Sections
Small Displacement Assumption
Boundary Conditions on Displacements and Rotations
External Constraints: Kinematic Characterization
Strain Measurements
Axial Strain
Angular Slip
Bending Curvature
Implicit Equations of Compatibility
Timoshenko Model
Euler-Bernoulli Model
Kinematic Problem
Discontinuities in the Kinematic Problem
Statics of Beams

Position of the Problem
External Forces
Internal Actions
Indeterminate Equations of Equilibrium
Static Problem
Laws and Diagrams of Stress Characteristics
Discontinuities in the Static Problem
General Rules for Plotting Stress Characteristic Diagrams

Linear Elastic Link for One-Dimensional Beams
Axial Behavior
Bending Behavior
Shear Behavior
Thermal Distortions
Uniform Thermal Variation
Butterfly Thermal Variation
Linear Thermal Variation
Constitutive Equations for One-Dimensional Beams

The Elastic Problem for Beams
Euler-Bernoulli Model
Timoshenko Model
Beam Systems
Displacement Method: The Elastic Line
Elastic Line
Axial Problem
Bending Problem: Euler-Bernoulli Model
Elastic Line in Beam Systems
Kinematic and Static Performance of Internal Constraints

Virtual Work Identity. Duality.
Work
Congruent System
Equilibrium System
External Virtual Work
Internal Virtual Work
Virtual Work Theorem
Calculation of Displacements and Rotations in Isostatic Structures

Force Method
Once Hyperstatic Systems
Multiple Hyperstatic Systems
Müller-Breslau Equations

Truss Structures and Continuous Beams.
Truss Structures
Node Method
Ritter's Section Method
Continuous Beams: Three-Moment Equation

Continuum Mechanics: Deformation Analysis
Deformation Process
Deformation Analysis in the Vicinity: Strain Tensor
Mechanical Interpretation of ε Components
Meaning of Diagonal Components εx, εy, εz
Meaning of Off-Diagonal Components γxy, γxz, γyz
Decomposition of the Deformation Process
Volumetric Dilatation
Cauchy's Formula for Deformation - Principal Directions of Deformation
Triaxial Deformation State
Cylindrical Deformation State
Principal Reference - Mohr's Circles
Compatibility Equations

Continuum Mechanics: Stress Analysis
Cauchy Stress
Cauchy's Lemma
Decomposition of the Cauchy Stress Vector
Cauchy's Formula
Indeterminate Equations of Equilibrium
Stresses and Principal Directions
Principal Reference
Stress States
Isostatic Lines
Mean Stress, Deviatoric Stress, and Octahedral Stress
Mohr's Circles
Plane or Biaxial Stress State
Purely Shear Stress State
Monoaxial Stress State
Linear Elastic Link
Isotropic Materials: Generalized Hooke's Law
The Problem of Elastic Equilibrium: Direct Formulation and Energy Aspects

Saint-Venant Problem
Saint-Venant Postulate
Simple and Combined Stresses
Semi-Inverse Method
Indeterminate Equations of Equilibrium
Compatibility and Constitutive Equations
Concentrated Normal Force. Straight Bending
Concentrated Normal Force
Uniform Straight Bending
Deflected Bending. Tensile Bending, Compressive Bending
Uniform Deflected Bending
Compressive (Tensile) Deflected Bending
Eccentric Normal Force
Uniform Torsion
Torsion in Circular Sections
Compact Circular Section
Hollow Circular Section
Torsion in Any Shape Compact Sections
Hydrodynamic Analogy for Shear Stresses
Thin Rectangular Section
Open Sections Made of Thin Rectangles
Thin-Walled Hollow Sections: Bredt's Theory
Composite Thin Sections
Bending and Shear
Distribution of Normal Stresses
Distribution of Shear Stresses: Approximate Treatment by Jourawsky
Problem Equations
Jourawsky's Formula
Applicability of Jourawsky's Formula
Open Thin Sections
Thin Rectangular Section
Thin Double-T Section
Thin U and H Sections
Closed Thin Sections
Symmetrical Hollow Section
Straight Shear according to y
Deflected Shear
Symmetrical Compact Sections
Combined Shear and Torsion Stress
Shear Center
Shear and Torsion Shear Stresses

Strength Criteria and Introduction to Plasticity
Ductile and Brittle Materials
Linear Elastic Model and Plastic Behavior
The Concept of Yielding
Elasto-Plastic Constitutive Relationship
Yielding Mechanisms and Plasticity Criteria
Stress-Strain Diagrams for Elasto-Plastic Materials
Plasticity in Bending: Yield Moments
Effects of Plastic Behavior in Beams and Structural Elements
Calculation of Safety Factors in Plastic Regime
Limit Analysis of Structures
Methods for Determining Plastic Hinges in Hyperstatic Structures
Structural Verification in Plastic Field

The Phenomenon of Structural Instability
Stability Analysis in Rigid Beams with Elastic Constraints
Euler's Column
Stability Curves, Slenderness

Structural Verifications
Verification of Beams under Operating Conditions
Extension of Saint-Venant Theory
Strength Criteria for Saint-Venant Solids
Operational Procedure for Structural Verification

Geometry of Areas
Area and Centroid
Moments of Inertia
Transport Formulas (without Rotation Formulas)
Principal Moments of Inertia
Central Inertia Ellipse
Notable Cases

Recurring Static Schemes
Cantilever
Simply Supported Beam
Fixed-Supported Beam
Beam Fixed at Both Ends
Continuous Beam
Frame

Hibbeler, R. C. (2017). Mechanics of Materials (SI Units). Boston: Pearson.

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.

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. Sheet metal deformation processes. Formability of the plates. Shearing. Bending. Cupping. Machining by chip removal. Cutting mechanics. Single-cutting tools and cutting angles. Wear and duration of tools. Materials for cutting tools. Optimization of cutting parameters. Turning. Milling. Drilling. Straight cut. Operation and grinding machines. Joining techniques. Weldings: classification and general information. Structure of welded joints. Welding defects. Flame welding. Arc welding. Resistance welding. Solid state welding. Welding with unconventional techniques. Mechanical junctions. Bonding.

Authors: Serope Kalpakjian, Steven R. Schmid
Editor: Pearson
Collection: Prentice Hall
Edition: 5
Year: 2008