File system in Linux enviroment. First principles of the C++ programming language.

Stanley B. Lippman, Josée Lajoie, Barbara E. Moo
C++ Primer, Fifth Edition
Addison-Wesley 2012

Any C++ programming language manual

see data sheet of the teacher in charge of the course

see data sheet of the teacher in charge of the course

see data sheet of the teacher in charge of the course

see data sheet of the teacher in charge of the course

see data sheet of the teacher in charge of the course

see data sheet of the teacher in charge of the course

see data sheet of the teacher in charge of the course

see data sheet of the teacher in charge of the course

Vectors in Euclidean Space. Reference and co-ordered systems. Orthogonal poijections, scalar, vector and mixed product. Parametric and Cartesian equations of lines and planes.
Linear systems. Linear equations, column vectors and matrices. Gauss elimination method: rank of a matrix, Cramer and Rouch ́e-Capelli theorems.

Algebra of Matrices. Sum and product for a scalar. Produced rows by columns. Invertible matrices, transposed matrix and symmetric matrices. The Gauss-Jordano algorithm for calculating the inverse. LU factorization. Product of block matrices.
Vector spaces and linear applications. Examples of vector spaces and linear applications. Generators and bases. Core, image. Linear independence and size; rank of a matrix. Nullity theorem plus rank and Grassmann's formula.
Determinant of a matrix and Gauss moves. Developments of Laplace. Binet's theorem.
Eigenvalues and eigenvectors. The characteristic polynomial of a linear operator. Similar matrices.
Scalar products. Schwartz inequality, orthogonal bases and matrices. Orthogonal projections and Grahm-Schmidt algorithm.
Quadratic shapes and self-added operators. The spectral theorem, quadratic forms. Classification of conics and quadrics.

Enrico Schlesinger, Algebra lineare e geomegtria. Zanichellii, (2017).
Luca Mauri, Enrico Schlesinger, Esercizi di algebra lineare e geomegtria. Zanichellii, (2020).

see the card of the teacher of the course

see the card of the teacher of the course

Classroom lectures
The scientific method: comparison between theory and experiment. Physical quantities and their measurement. The uncertainties in the measurements of physical quantities. Type A and Type B uncertainties. Measurement tools and their properties. Better estimate of the measure. Estimation of uncertainties.
Measurements, uncertainties and significant figures. Comparison between measure and expected value . Organization and presentation of data. Main properties of probability. Random events, random variables. Definition of probability: classical, frequentist, axiomatic. Total probability, conditional probability, compound probability. Bayes theorem. Statistical population. Sampling. Law of large numbers. Discrete and continuous random variables. Probability distributions. Expected value and variance. Bernoulli distribution. Poisson distribution. Gauss distribution. Probabilistic meaning of the standard deviation. Probability of obtaining a result in a measurement operation. The central limit theorem. Presentation of the result of a measure and confidence intervals. Hypothesis verification. Weighted average. Correlation between physical quantities and verification of the existence of a functional dependence: least squares method. Hypothesis test: Z test, T-Student test, Fisher test, Chi-square test.

Experiments:
Measurements of Lengths. Verification of Boyle-Mariotte law. Experiment for the determination of the spring constant. The pendulum. Measurement of gravitational acceleration with a reversible pendulum. Inclined plane. Verification of the central limit theorem (dice roll - repeated measurements). Verification of the law of radioactive decay (by means of simulation with dice). Verification of the probability distribution of Poisson (by means of Geiger).

For exam preparation, students,
in addition to consulting the teaching material made available to students on moodle (https://matematicafisica.el.uniroma3.it/):
they can consult the following texts:

C. Bini "Lezioni di Statistica per la Fisica Sperimentale" . Edizioni Nuova Cultura. Roma 2011.

Gaetano Cannelli, Metodologie sperimentali in Fisica, Introduzione al metodo scientifico, ed. EdiSES (ISBN: 978 88 7959 679 4)

GUM: Guide to the Expression of Uncertainty in Measurement - GM 100:2008
http://www.bipm.org/en/publications/guides/gum.html

see data sheet of the teacher in charge of the course

see data sheet of the teacher in charge of the course

see data sheet of the teacher in charge of the course

see data sheet of the teacher in charge of the course

see data sheet of the teacher in charge of the course

see data sheet of the teacher in charge of the course

Vectors and vector calculus: definition of a vector, its representation in cartesian and polar coordinates, carrier, properties, dot product, vector product, mixed product.

Point mass kinematics: position, velocity, scalar and vector acceleration of a point mass. Centripetal and tangential acceleration. Uniformly accelerated motion, uniform and not uniform circular motion, harmonic motion. Speed and acceleration in polar coordinates. Areolar speed.
Law of composition of speeds and accelerations; relative motion.

Mechanics of systems of points: the Galileo’s first principle of dynamics and Galileo’s relativity. Inertial reference frame. Second and third law of dynamics. Elastic forces, static and dynamic friction, viscosity; applications.
Transformation of coordinates and laws of composition of speeds and accelerations in general; acceleration of Coriolis.
Inertial reference frame and apparent forces: the centrifugal force and the Coriolis force.
Impulse of a force, momentum and their relationship. The moment of a force, the angular momentum and their relationship; central forces and pendulum.
The work of a force, kinetic energy and the theorem of kynetic energy. Conservative forces and potential energy, the law of conservation of mechanical energy.

Material point systems: the cardinal equations of mechanics. Center of mass, definition, properties and the theorem of the center of mass.
The conservation of the momentum and of the angular momentum in isolated systems. Energy of a point system, the Koenig theorem. Two-point systems: reduced mass.
Collisions between material points: elastic and anelastic collisions.

Mechanics of rigid body: translation and rotation, characteristics and vector representation; decomposition of motion in translation and rotation. Momentum, angular momentum and kinetic energy of a rigid body. Moment of inertia, Steiner's theorem.
Relationship between angular momentum and angular velocity of a rigid body, main axes of inertia. Analysis of the motion of a systems in rotation around a fixed axis, around an axis moving parallel to itself or with a fixed point; gyroscope and trowel.

Universal law of gravitation, potential energy and applications. Inertial mass and gravitational mass. Kepler's laws and their explanation using Newton laws. Motion of a planet.

Elasticity: Hooke's law, Young's module and Poisson coefficient. Volume elasticity, shape elasticity; relationship between elastic constants. Plastic deformations.

Mechanics of fluids: pressure, definition and properties. Fluids at rest: law of Stevin, of Pascal, of Archimedes.
Fluids in motion: mass storage in stationary flow, Bernoulli equation.
Laminar motion, viscosity and the law of flow rate.
Touch upon the turbulent motion and the Reynolds number. The motion of a body in a fluid.

Thermodynamics: temperature and its microscopic meaning, heat, definitons and heat transmission: conduction, convection, irradiation.
Transformations of a thermodynamic system, reversible and irreversible transformations: the work in a transformation.
First law of thermodynamics, internal energy.
Perfect gases and their transformations, real gases, solids and liquids. Transformation between phase states of matter.
Second law of thermodynamics: classic statements, thermal engines; the Carnot engine, the Carnot’s theorem and its generalization; entropy, definition, properties and calculation in transformations of a gas or of simple systems.
Kinetic theory of gases: internal energy and entropy of the perfect gas. Third law of thermodynamics. Thermodynamic potentials: Helmotz free energy and Gibbs free enthalpy, applications. Equation of Clausius-Clapeyron

Waves: mathematical representation of waves. Transverse waves: waves in the strings; longitudinal waves: compression waves, the sound. Energy of the waves. Doppler effect.

The recommended textbook is:
S. Focardi, I. Massa, A. Uguzzoni, M. Villa:
Fisica Generale: Meccanica e Termodinamica
Casa Editrice Ambrosiana

Another recommended option is the book:
C. Mencuccini e V. Silvestrini:
Fisica: Meccanica e Termodinamica
Casa Editrice Ambrosiana

Vectors and vector calculus: definition of a vector, its representation in cartesian and polar coordinates, carrier, properties, dot product, vector product, mixed product.

Point mass kinematics: position, velocity, scalar and vector acceleration of a point mass. Centripetal and tangential acceleration. Uniformly accelerated motion, uniform and not uniform circular motion, harmonic motion. Speed and acceleration in polar coordinates. Areolar speed.
Law of composition of speeds and accelerations; relative motion.

Mechanics of systems of points: the Galileo’s first principle of dynamics and Galileo’s relativity. Inertial reference frame. Second and third law of dynamics. Elastic forces, static and dynamic friction, viscosity; applications.
Transformation of coordinates and laws of composition of speeds and accelerations in general; acceleration of Coriolis.
Inertial reference frame and apparent forces: the centrifugal force and the Coriolis force.
Impulse of a force, momentum and their relationship. The moment of a force, the angular momentum and their relationship; central forces and pendulum.
The work of a force, kinetic energy and the theorem of kynetic energy. Conservative forces and potential energy, the law of conservation of mechanical energy.

Material point systems: the cardinal equations of mechanics. Center of mass, definition, properties and the theorem of the center of mass.
The conservation of the momentum and of the angular momentum in isolated systems. Energy of a point system, the Koenig theorem. Two-point systems: reduced mass.
Collisions between material points: elastic and anelastic collisions.

Mechanics of rigid body: translation and rotation, characteristics and vector representation; decomposition of motion in translation and rotation. Momentum, angular momentum and kinetic energy of a rigid body. Moment of inertia, Steiner's theorem.
Relationship between angular momentum and angular velocity of a rigid body, main axes of inertia. Analysis of the motion of a systems in rotation around a fixed axis, around an axis moving parallel to itself or with a fixed point; gyroscope and trowel.

Universal law of gravitation, potential energy and applications. Inertial mass and gravitational mass. Kepler's laws and their explanation using Newton laws. Motion of a planet.

Elasticity: Hooke's law, Young's module and Poisson coefficient. Volume elasticity, shape elasticity; relationship between elastic constants. Plastic deformations.

Mechanics of fluids: pressure, definition and properties. Fluids at rest: law of Stevin, of Pascal, of Archimedes.
Fluids in motion: mass storage in stationary flow, Bernoulli equation.
Laminar motion, viscosity and the law of flow rate.
Touch upon the turbulent motion and the Reynolds number. The motion of a body in a fluid.

Thermodynamics: temperature and its microscopic meaning, heat, definitons and heat transmission: conduction, convection, irradiation.
Transformations of a thermodynamic system, reversible and irreversible transformations: the work in a transformation.
First law of thermodynamics, internal energy.
Perfect gases and their transformations, real gases, solids and liquids. Transformation between phase states of matter.
Second law of thermodynamics: classic statements, thermal engines; the Carnot engine, the Carnot’s theorem and its generalization; entropy, definition, properties and calculation in transformations of a gas or of simple systems.
Kinetic theory of gases: internal energy and entropy of the perfect gas. Third law of thermodynamics. Thermodynamic potentials: Helmotz free energy and Gibbs free enthalpy, applications. Equation of Clausius-Clapeyron

Waves: mathematical representation of waves. Transverse waves: waves in the strings; longitudinal waves: compression waves, the sound. Energy of the waves. Doppler effect.

S. Focardi, I. Massa, A. Uguzzoni, M. Villa:
Fisica Generale: Meccanica e Termodinamica
Casa Editrice Ambrosiana

In alternativa si può consultare il testo:
C. Mencuccini e V. Silvestrini:
Fisica: Meccanica e Termodinamica
Casa Editrice Ambrosiana

Part 1: Axiomatics of R and its main subsets Axiomatic definition of R.
Inductive assemblies; definition of N and induction principle. Definition of Z
and Q; Z is a ring, Q is a field.
Nth roots; rational powers.

Part 2: Theory of Limits
The extended line R*: intervals, neighbourhoods and accumulation points.
Limits of functions in R*.
Comparison theorems.
Lateral limits; limits of monotone functions.
Algebra of limits on R and R*.
Composition limit of functions.
Limits of inverse functions.
Notable limits. The number of Napier. Exponential and trigonometric functions.

Part 3: Continuous functions
Topology of R.
Theorem of existence of zeroes. Bolzano-Weierstrass theorems. Weierstrass’ Theorem.
Uniformly continuous functions.

Part 4: Differentiable functions
Rules of derivation. Derivatives of elementary functions.
Local minima and maxima and elementary theorems on derivatives (Fermat, Rolle, Cauchy,
Lagrange).
Bernoulli-Hopital theorem.
Convexity.
Taylor’s formulae.

Part 5: Riemann integral in R.
The Riemann integral and its fundamental properties.
Integration criteria. Integrability of continuous and monotone functions.
The fundamental theorem of calculus and its applications (integration by parts,
changes of variables in integration). Generalized ("improper") integrals and
related integrability criteria.

Luigi Chierchia: Corso di analisi. Prima parte. Una introduzione rigorosa all'analisi matematica su R
McGraw-Hill Education Collana: Collana di istruzione scientifica
Data di Pubblicazione: giugno 2019
EAN: 9788838695438 ISBN: 8838695431
Pagine: XI-374 Formato: brossura
https://www.mheducation.it/9788838695438-italy-corso-di-analisi-prima-parte

Testi di esercizi:
Giusti, E.: Esercizi e complementi di Analisi Matematica, Volume Primo, Bollati Boringhieri, 2000
Demidovich, B.P., Esercizi e problemi di Analisi Matematica, Editori Riuniti, 2010

1. Atomic theory and structure of the atom. Atoms, molecules, moles; atomic weight and molecular weight. Rutherford model, Bohr model, quantum theory, quantum numbers and energy levels; polyelectronic atoms, periodic system.

2. Chemical bond. Ionic bond. Covalent bond: σ bond and π bond. Polyatomic molecules. Molecular structure. Hybridization and resonance. Molecular orbital. Metallic bond. Intermolecular forces.

3. Nomenclature. Oxides, hydroxides, acids, salts, ions.

4. Chemical reactions. Balancing chemical reactions.

5. States of aggregation. Gaseous state and gas laws.

6. Thermodynamics. Matter, energy, heat. First and second principle. Enthalpy, entropy, free energy.

7. Solid state: ionic, molecular, metallic, covalent solids. Conductors, semiconductors, insulators.

8. Liquid and amorphous. State changes and state diagrams.

9. Solutions. Concentration of solutions. Colligative properties. Electrolyte solutions.

10. Chemical kinetics. Speed ​​of chemical reactions. Speed ​​constant. Influence of temperature on velocity: Arrhenius equation. Catalysts.

11. Chemical equilibrium. Equilibrium constant and speed constants. Constant of equilibrium and free energy. Equilibria in the gas and heterogeneous phase. Le Chatelier's principle. Van’t Hoff equation.

12. Equilibrium in solution. Acid-base equilibria: Acids and bases, pH, dissociation constants, polyprotic acids, hydrolysis, buffers; acid-base titrations, indicators.

13. Precipitation equilibria: solubility and solubility product, common ion effect.

14. Electrochemistry. Batteries, electrode potentials, Nernst equation.

15. Laboratory. Acid-base titrations and pH measurements.

Numerical exercises will be carried out on the topics covered during the lessons.
There will be two laboratory exercises that will take place at CeDiC (Via della Vasca Navale 79).

P.W.Atkins, L. Jones; CHEMISTRY: MOLECULES, MATTER, AND CHANGE

Electric charge. Coulomb force. Quantization of the c.e.
The electric field. The electrostatic potential. The electric dipole.

Gauss theorem. Electrostatic screen. Capacity'. Capacitors.
Series and parallel capacitors. The general problem electrostatics. Energy of the electrostatic field.

The dielectric constant. Polarization by deformation and orientation.
The vector Electric polarization. The equations of electrostatics in the presence of dielectrics. The vector D.

EMF Electric current and current density. Ohm's law.
Joule effect. Resistances. Series and parallel resistors.
Voltage generators. Kirchhoff's laws. Conduction in liquids and in gases.

Magnetic induction field. Lorentz force.
Magnetic field generated by a moving charge. Laplace's laws.
Divergence of B. Electrodynamic forces. Magnetic moment of a coil. Ampere's theorem. Electromagnetic induction.
Faraday-Neumann's law. Self and mutual induction. Displacement current.

Magnetic moment of an electron. Magnetic polarization.
Surface and volume current density. Fundamental equations magnetostatics in the presence of matter. the vector H. Materials dia-, para- and ferromagnetic. Larmor Precession. Polarization by orientation.

Electromagnetic waves. Wave equation. Plane waves.
Waves in dielectrics. Poynting vector. Doppler effect. Reflection and refraction. Light scattering. Huygens-Fresnel principle.
Interference. Diffraction. Geometric optics: mirrors, diopters, lenses.

Postulates. Time dilation and length contraction.
Lorentz transformations. Four vectors. Lorentz invariants.
Spatiotemporal distance. Speed'. Energy-impulse quadrivector.
Mass and energy. Minkowski's strength. Doppler effect. four-vector current density. Electromagnetic tensor.

Corrado Mencuccini, Vittorio Silvestrini.
Fisica 2. Elettromagnetismo-ottica. Corso di fisica per le facoltà scientifiche. Con esempi ed esercizi
Liguori Editore

Electrostatic. Fundamental phenomena. Electric charge. Coulomb force.
Quantization of the e.g. The electric field. The electrostatic potential. The dipole
electric.
Electrostatics and conductors. Gauss theorem. Electrostatic screen. Capacity. Capacitors. Capacitors in series and in parallel. The general problem
electrostatics. Energy of the electrostatic field.
Electrostatics in the presence of dielectrics. The dielectric constant. Polarization by deformation and orientation. The vector Electric polarization.
The electrostatic equations in the presence of dielectrics. The vector D ~.
Electric current. EMF Electric current and current density. Law of
Ohm. Joule effect. Resistances. Resistance in series and in parallel. Generators of
voltage. Kirchhoff's laws. Conduction in liquids and gases.
Magnetic field in a vacuum. Magnetic induction field. Lorentz force.
Magnetic field generated by a moving charge. Laplace's laws. Divergence of
B ~. Electrodynamic forces. Magnetic moment of a spire. Ampere theorem.
Electromagnetic induction. Faraday – Neumann law. Auto and mutual induction.
Displacement current.
Magnetic field in matter. Magnetic moment of an electron. Magnetic polarization. Surface and voluminous current density. Fundamental equations of magnetostatics in the presence of matter. the vector H ~. Dia-, materials
para- and ferromagnetic. Precession of Larmor. Polarization by orientation.
Optics. Electromagnetic waves. Wave equation. Flat waves. Waves in the
dielectrics. Poynting vector. Doppler effect. Reflection and refraction. Light scattering. Huygens-Fresnel principle. Interference. Diffraction. Optics
geometric: mirrors, diopters, lenses.
Introduction to restricted relativity. Postulates. Time dilation and length contraction. Lorentz transformations. Four vectors. Invariant
of Lorentz. Space-time distance. Speed. Energy-pulse four-vector.
Mass and energy. Minkowski's force. Doppler effect. Four-vector density
current. Electromagnetic tensor.

Fisica-Elettromagnetismo e Ottica (Corrado Mencuccini e Vittorio Silvestrini), ed. Ambrosiana

Esercizi di Fisica-Elettromagnetismo e Ottica (Corrado Mencuccini e Vittorio Silvestrini), ed. Ambrosiana

0. Number series
Definition and convergence criteria.

1. Sequences and series of functions
Pointwise convergence, uniform convergence.
Total convergence of series of functions.
Power series, Fourier series.

2. Functions of n real variables
Vector spaces. Scalar product (Cauchy-Schwarz inequality), norm, distance,
standard topology, compactness in Rn.

Continuous functions from Rn to Rm. Continuity and uniform continuity. Weierstrass theorem.
Definitions of partial and directional derivatives, differentiable functions,
gradient, Prop .: a continuous differentiable function and has all the directional derivatives.
Schwarz's Lemma total differential theorem. Functions
Ck, chain rule. Hessian matrix.
Taylor's formula at second order. Maximum and minimum stationary points
Positive definite matrices.
Prop: maximum or minimum points are critical points; the critical points in which the
Hessian matrix is ​​positive (negative) are minimum (maximum) points; the points
critics in which the Hessian matrix has a positive and a negative eigenvalue are saddles.
Functions that can be differentiated from Rn to Rm; Jacobian matrix. Jacobian matrix of the
composition.

3. Normed spaces and Banach spaces
Examples. Converging and Cauchy sequences. Equivalent rules. Equivalence of the norms in Rn. The space of the
continuous functions with the sup norm a Banach space.
The fixed point theorem in Banach spaces.
Implicit and inverse function theorems.

Analisi Matematica II, Giusti - Analisi Matematica II, Chierchia

Conservative mechanical systems. Qualitative analysis of motion and Lyapunov stability. Planar systems and one-dimensional mechanical systems. Central motions and the two-body problem. Change of frames of reference. Fictitious forces. Constraints. Rigid bodies. Lagrangian mechanics: variational principles, cyclic variables, Routh method, constants of motion and symmetries. Hamiltonian mechanics: Liouville's theorem and Poincaré's recurrence theorem, canonical transformations, generating functions, Hamilton-Jacobi method and action-angle variables.

G. Gentile, Introduzione ai sistemi dinamici. 1. Equazioni differenziali ordinarie, analisi qualitativa e alcune applicazioni
G. Gentile, Introduzione ai sistemi dinamici. 2. Meccanica lagrangiana e hamiltoniana

ELECTRICAL CIRCUITS
Ideal components: Resistor, Capacitor, Inductor. Active components: current generator, voltage generator. Real components: Resistor, Capacitor, Inductor, Generator.
DC Circuits
Kirchhoff’s Laws, the method of nodes, the method of meshes. The Wheatstone's Bridge. Linear networks: Superposition theorem, Thevenin’s theorem, Norton's theorem, Reciprocity theorem.

MEASUREMENTS in DC Circuits
Current and Voltage Difference measurements, digital voltmeter, ohmmeter. Resistance measurements: voltmeter-ammeter method. Uncertainty in electrical measurements

Alternating Current Circuits
Periodic, alternating, sinusoidal signals. AC coupling. Components in AC circuits, solution of AC circuits: the symbolic method.

AC basic Circuits
RC circuits: low-pass, high-pass, RL circuits. Differentiator and integrator circuits. Resonant circuits: the RLC circuit, series and parallel. The compensated voltage divider.

The NI Educational Laboratory Virtual Instrumentation Suite (NI ELVIS)
Amplitude measurements, phase measurements. Measurement uncertainty.

Pulsed Circuits
Impulsive signals: step signal, pulse signal, rectangular waveform. RC circuits: high-pass, low-pass. Compensated voltage divider.

The transmission line
Model of the transmission line, telegrapher equation, lossless line. Reflection and transmission coefficients. The coaxial cable.

Basic statistical methods
Mean, standard deviation, propagation of errors, confidence limits of a measurement.
Chi-squared test. Graphs, fitting procedures. PHYTON basic.

Elementary optics
Basic geometrical optics. Optical interference. Optical diffraction.

Class Notes
R. Bartiromo, M. De Vincenzi - "Electrical Measurements in the laboratory Practice" - Springer
M. Severi - "Introduzione alla Esperimentazione Fisica" - Zanichelli
C.K. Alexander, M.N.O. Sadiku - "Circuiti Elettrici" - McGraw Hill
Young - "Elaborazione statistica dei dati sperimentali"
Taylor - "Introduzione all'analisi degli errori"
Any textbook on Physics, Electronics e Statistics for the degree course on Physic

ELECTRICAL CIRCUITS
Ideal components: Resistor, Capacitor, Inductor. Active components: current generator, voltage generator. Real components: Resistor, Capacitor, Inductor, Generator.
DC Circuits
Kirchhoff’s Laws, the method of nodes, the method of meshes. The Wheatstone's Bridge. Linear networks: Superposition theorem, Thevenin’s theorem, Norton's theorem, Reciprocity theorem.

MEASUREMENTS in DC Circuits
Current and Voltage Difference measurements, digital voltmeter, ohmmeter. Resistance measurements: voltmeter-ammeter method. Uncertainty in electrical measurements

Alternating Current Circuits
Periodic, alternating, sinusoidal signals. AC coupling. Components in AC circuits, solution of AC circuits: the symbolic method.

AC basic Circuits
RC circuits: low-pass, high-pass, RL circuits. Differentiator and integrator circuits. Resonant circuits: the RLC circuit, series and parallel. The compensated voltage divider.

The NI Educational Laboratory Virtual Instrumentation Suite (NI ELVIS)
Amplitude measurements, phase measurements. Measurement uncertainty.

Pulsed Circuits
Impulsive signals: step signal, pulse signal, rectangular waveform. RC circuits: high-pass, low-pass. Compensated voltage divider.

The transmission line
Model of the transmission line, telegrapher equation, lossless line. Reflection and transmission coefficients. The coaxial cable.

Basic statistical methods
Mean, standard deviation, propagation of errors, confidence limits of a measurement.
Chi-squared test. Graphs, fitting procedures. PHYTON basic.

Elementary optics
Basic geometrical optics. Optical interference. Optical diffraction.

Class Notes
R. Bartiromo, M. De Vincenzi - "Electrical Measurements in the laboratory Practice" - Springer
M. Severi - "Introduzione alla Esperimentazione Fisica" - Zanichelli
C.K. Alexander, M.N.O. Sadiku - "Circuiti Elettrici" - McGraw Hill
Young - "Elaborazione statistica dei dati sperimentali"
Taylor - "Introduzione all'analisi degli errori"
Any textbook on Physics, Electronics e Statistics for the degree course on Physic

see card of the lecturer of the course

see card of the lecturer of the course

see data sheet of the teacher in charge of the course

see data sheet of the teacher in charge of the course

1. Riemann integral in Rn Review of the Riemann integral in one dimension. Rectangles
in R2, compact support functions, simple functions and their integral, function definition integrable according to Riemann in R2 (hence Rn).
Definition of measurable set, a set is measurable if and only if its boundary has zero measurement. Normal sets with respect to the Cartesian axes. A continuous function on a measurable and integrable set. Fubini reduction theorem.
Formula of change of variable in integrals (without size). Polar, cylindrical, spherical coordinates. Examples: calculation of some barycenters and moments of inertia.

2. Regular curves.
Regular curves in R ^ n. Tangent versor.
Two equivalent curves traveled in the same direction have the same tangent versor.
Length of a curve. It is greater than the displacement.
Two equivalent curves have the same length.
Curvilinear integrals.

3. Surfaces, flows and divergence theorem.
Recalls on the vector product. Definition of regular surface. Tangent plane and normal versor. Area of ​​a surface. Examples: graphs of functions and rotation surfaces. Surface integrals. Flow of a vector field through a surface. Examples. Statement of the divergence theorem. Demonstration of the divergence theorem (for normal domains with respect to the three Cartesian axes.

4. Differential forms and work.
1-Differential forms. Integral of a 1-differential form (work of a vector field), closed and exact forms. A form is exact if and only if the integral on any zero closed curve. Example of incorrect form closed.
Derived under the sign of integral. Starry sets; a closed form on a starred domain is exact.
Irrational and conservative fields, solenoidal and potential vector (on starry sets). The Green theorem in the plane. The Rotor theorem.

5. Series and sequence of functions

Series and sequence of functions: point, uniform and total convergence. Continuity of the limit, integration and derivation of uniformly convergent sequences of functions. Power series: convergence radius. Taylor series examples of elementary functions.

6. Fourier series
Fourier series, Fourier coefficients. Properties of Fourier coefficients, Bessel inequality, Lemem of Riemann Lebesgue. Pointwise convergence of the Fourier series (Dini test). Uniform convergence in the case of C1 functions. Equality of Parseval.

Analisi Matematica II, Giusti
Analisi Matematica II, Chierchia

Fundamental concepts of electronics used in the field of measurement of physical quantities. Introduction to semiconductor physics, junction diodes, BJT and MOS transistors. Introduction to the concept of amplification and the principles of feedback. Applications of operational amplifiers. Introduction to digital electronics and applications of logic gates.
The lessons are complemented by numerical and laboratory exercises (the latter with compulsory attendance).
The purpose of the laboratory exercises is to provide students with the necessary knowledge and practical skills, so as to enable them to use the electronic instruments and electronic components studied during the theoretical lessons. Students must carry out laboratory exercises and submit, at the end of the exercise, a report describing the activity carried out, the data collected and the numerical calculations carried out.
List of laboratory exercises: study of the resonance frequency of an RLC filter (introductory experience aimed at becoming familiar with the laboratory instrumentation); applications of operational amplifiers (three experiences); applications of circuits with junction diodes (two experiments); applications of BJT and MOS (two experiences); applications with logic gates (two experiences); use of the Geiger counter.

To prepare for the exam, in addition to consulting the teaching material provided by the teacher, students can consult the following texts:
(a) G. Schirripa Spanish, Applied Electronics, Efesto Editions, ISBN 978 88 9910 456 6
(b) Thomas C. Hayes and Paul Horowitz, Learning the Art of Electronics: A Hands-On Lab Course, Cambridge University Press (2016) ISBN 978 05 2117 7238

The crisis of classical physics. Waves and particles. State vectors and operators. Measurements, observables and uncertainty relation. The position operator. Translations and momentum. Time evolution and the Schrödinger equation. One-dimensional problems. Parity. Harmonic oscillator. Symmetries and conservation laws. Time independent perturbation theory. Time dependent perturbation theory. Rotations and angular momentum. Orbital angular momentum. Spin. Angular momentum composition. Identical particles. The hydrogen atom.

Lecture notes available on the course website

J.J. Sakurai, Jim Napolitano - Meccanica Quantistica Moderna - Zanichelli
An english version of the book is also available:
Sakurai J.J., Modern Quantum Mechanics - Addison-Wesley

Quantum mechanics: The crisis of classical physics. Waves and particles. State vectors and operators. Measurements, observables and uncertainty relation. The position operator. Translations and momentum. Time evolution and the Schrödinger equation. One-dimensional problems. Parity. Harmonic oscillator. Symmetries and conservation laws. Time independent perturbation theory. Time dependent perturbation theory. Rotations and angular momentum. Orbital angular momentum. Spin. Angular momentum composition. Identical particles. The hydrogen atom.

Lecture notes available on the course website

J.J. Sakurai, Jim Napolitano - Meccanica Quantistica Moderna - Zanichelli
An english version of the book is also available:
Sakurai J.J., Modern Quantum Mechanics - Addison-Wesley

Section I: Complex variable functions

- Complex numbers
- Analytic functions
- Integration of complex functions
- Power series
- Integration using the Residue theorem
- Asymptotic expansions
- Distributions

Section II: Vector spaces and eigenvalue problems

- Vector spaces
- Euclidean spaces
- Eigenvalue problems in N and infinite-dimensional vector spaces
- Function of a matrix
- Fourier transform

Section III: Integral and differential operators

- Integral operators and integral equations
- Sturm-Liouville operators
- First order partial differential equations

C. Bernardini, O. Ragnisco and P.M. Santini
Metodi matematici della Fisica, NIS 1993

B. Chabat, M. Lavrentiev
Methodes de la Theorie des fonctions d'une variable complexe, MIR 1972

A. I. Markusevic
Elementi di teoria delle funzioni analitiche, Editori Riuniti 1988

F. Bagarello
Fisica Matematica, Zanichelli, 2007

P. A. Grassi
Esercizi di metodi matematici, Casa Editrice Ambrosiana, 2018

Section I: Complex variable functions

- Complex numbers
- Analytic functions
- Integration of complex functions
- Power series
- Integration using the Residue theorem
- Asymptotic expansions
- Distributions

Section II: Vector spaces and eigenvalue problems

- Vector spaces
- Euclidean spaces
- Eigenvalue problems in N and infinite-dimensional vector spaces
- Function of a matrix
- Fourier transform

Section III: Integral and differential operators

- Integral operators and integral equations
- Sturm-Liouville operators
- First order partial differential equations

C. Bernardini, O. Ragnisco and P.M. Santini
Metodi matematici della Fisica, NIS 1993

B. Chabat, M. Lavrentiev
Methodes de la Theorie des fonctions d'une variable complexe, MIR 1972

A. I. Markusevic
Elementi di teoria delle funzioni analitiche, Editori Riuniti 1988

F. Bagarello
Fisica Matematica, Zanichelli, 2007

P. A. Grassi
Esercizi di metodi matematici, Casa Editrice Ambrosiana, 2018

First module:
The proton, cathode rays, the electron, mass and electric charge.
Black body radiation, Planck constant, photoelectric effect, X rays, Compton effect, the photon. Bohr atomic model, atomic spectra, electron magnetic moment and spin.
Special relativity, Lorentz transforms, four-vectors and relativistic invariants, energy and momentum, relativistic kinematics.
Cross section, absorption coefficient. Coulomb scattering, Rutherford cross section. Scattering of electromagnetic radiation by a charge, Thomson cross section.
Quantum mechanics and perturbation theory, transition probability, phase space. Decay low, electromagnetic interaction, emission and absorption,
electric and magnetic dipole radiation, selection rules. Rutherford scattering, electric form factor, scattering of a charge by a magnetic
moment, electric and magnetic form factor of proton and neutron. Potential scattering, partial waves, scattering and
absorption cross section.

Second module:
Properties of nuclei, atomic and mass number, stability band, measurement of charge, mass and nuclear radius. Statistics, spin and parity of nuclei, the neutron. Electromagnetic energy of nuclei, magnetic dipole and electric quadrupole moments.
Fermi gas model, kinetic energy of nucleons. Liquid drop model, Bethe-Weizsaeker mass formula, mirror nuclei. Magic numbers, shell model, spin-orbit interaction, energy levels and spin-parity states. The neutron-proton system, the deuteron.
Nuclear decays, activity. Phenomenology of gamma decay, multipole radiation, Weisskopf coefficients. Phenomenology of alpha decay, kinematics, stability curve, potential barrier and Gamow factor, lifetime. Phenomenology of beta decay, the neutrino hypothe
sis, Fermi theory, Kurie plot, lifetime, Fermi and Gamow-Teller transitions. Weak interaction and Fermi constant.
Discovery of the neutrino.

Third module:
Nuclear reactions, Fission, energy balance of the Uranium fission, neutron-induced fission,
nuclear reactor.
Fusion, cycles of the Sun, energy balance, nucleo-synthesis, fusion in the laboratory.
Nuclear forces, Yukawa model. Cosmic rays, primary and secondary components, the positron.
Discovery and properties of elementary particles, meson and baryons, anti-particles. Elementary particle interactions: nuclear, electromagnetic, weak. The quark model, discovery of quarks.

• W. E. Burcham and M. Jobes, Nuclear and Particle Physics, Pearson Education, 1994.
• The notes of the course of Institutions of Nuclear and Subnuclear Physics of Prof. Ceradini will be made available on the course website

The teaching material is available in double copy on the moodle platforms https://matematicafisica.el.uniroma3.it/course/view.php?id=51 and in sharepoint https://uniroma3.sharepoint.com/sites/ElementidiFisicaNucleareeSubnucleareAA201920. Students are asked to register on moodle and on teams (https://teams.microsoft.com/l/team/19%3a57c8fc1e646a489894614511aea22a8c%40thread.tacv2/conversations?groupId=b5330848-367f-43b5-ae3c-bdb-fdb f464-458c-a546-00fb3af66f6a)

CONTENTS OF THE LECTURES: the numbers in round brackets refer to the chapter and section of the textbook adopted.
Kinetic theory of gases. Boltzmann equation and H theorem. (1, Par.2.1,2.2,2.3,2.4)
Maxwell-Boltzmann distribution. (1, Par. 2.5)
Phase space and Liouville theorem. (1, Par. 3.1,3.2)
Gibbs ensembles. Micro canonical ensemble. Definition of entropy. (1, Par. 3.3,3.4)
The ideal gas in the micro canonical ensemble. (1, Par. 3.6)
The equipartition theorem. (1, Par. 3.5)
The canonical ensemble. (1, Par.4.1).
The partition function and the free energy. Fluctuations of energy in the canonical ensemble. (1 Par. 4.4)
The grand canonical ensemble. The grand potential. The ideal gas in the grand canonical ensemble. (1 Par. 4.3).
Fluctuations of the particle number. (1 Par. 4.4)
Classical theory of the linear response and fluctuation-dissipation theorem. (1, Par. 8.4).
Einstein and Langevin theories of the Brownian motion. (Par. 1 par. 11.1,11.2).
Johnson-Nyqvist theory of thermal noise. (1 Par. 11.3).
Quantum statistical mechanics and the density matrix. (1, Par. 6.2,6.3,6.4)
Fermi-Dirac and Bose-einstein quantum statistics. ( 1, Par. 7.1)
The Fermi gas. The Sommerfeld expansion and the electron specific heat. (1, Par. 7.2)
The Bose gas. The Bose-Einstein condensation. (1, Par. 7.3)
Quantum theory of black-body radiation. (1, Par. 7.5)

e-Learning Moodle Platform with Supplementary Material

Suggested textbook:
1) C. Di Castro and R. Raimondi, Statistical Mechanics and Applications in Condensed Matter, Cambridge University Press, 2015.

Further reading:
2) K. Huang, Meccanica Statistica, Zanichelli, 1997.
3) L. Peliti, Appunti di Meccanica Statistica, Bollati Boringhieri, 2003.
4) Joel L. Lebowitz, Statistical mechanics: A selective review of two central issues, Reviews of Modern Physics, 71, S346 (1999).

1- Bohr model for hydrogenoid atoms. Spectroscopic series in absorption and emission.
Quantum theory for the hydrogenoid atom. The Schoedinger equation of an electron in the Coulomb field.
Eigenfunctions and energy levels. Classification of states. Some properties of radial atomic functions.

2- Interaction of the hydrogenoid atom with the e.m. The interaction
electron-field e.m. treated with the theory of dependent perturbations
from time. Term of absorption and term of issue.
Transition probability for absorption and stimulated emission.
Cross section for absorption. Spontaneous emission.
Dipole approximation. Selection rules.

3- Grotrian's diagram. Radiation polarization and helicity of the photons. Einstein coefficients.
Shape of lines due to lifetime levels.

4- Relativistic corrections. Spin-orbit interaction. Darwin term.
Fine structure corrections to the hydrogenoid atoms.

5- Effects of static electric and magnetic fields. Stark effect. Effect Normal Zeeman. Paschen-Back effect. Abnormal Zeeman effect.

6- Definition of atomic units. Two-electron atoms.
Independent electron approximation. Interaction
electron-electron as perturbation. Variational method. Excited states.
Coulomb energy and exchange for states with two electrons. Levels of energy immersed in the continuous.

7- Atoms with many electrons. Central field approximation. scheme
of levels. Many particle wave function, Slater determinant.
Hartree-Fock equations and exchange term.

8- Hund scheme of levels and rules. LS coupling Rules of Hund in the presence of the term spin-orbit. Examples of energy levels for non-equivalent electrons and for equivalent electrons. Coupling j-j.

9- Selection rules for atoms with many electrons in the approximation of dipole. Spectra of alkaline atoms, quantum defect. Spectra of the atom of He is an alkaline earth.

10- Molecular Physics. Born-Oppenheimer approximation. Problem of Schroedinger for electrons. Equation for nuclei.

11- Molecular hydrogen ion. Application of the LCAO method.
Symmetry properties of diatomic molecules. Hydrogen molecule with the molecular orbitals method. LCAO method in general.
Binding and anti-binding states. Covalent bond and ionic bond.

12- Dynamics of nuclei. Rotational and vibrational levels. Moment total angular of nuclei and electrons.

13- Potential of Morse. Anharmonic corrections. Centrifugal corrections to the potential of Morse.

14- Transitions between vibrational and rotational levels. Selection rules.
Examples for diatomic etronuclear molecules.
Raman effect. Electronic transitions.

15- Franck-Condon principle.

B. H. Bransden and C. J. Joachain "Physics of Atoms and Molecules" (I-st or II-nd edition)