REAL NUMBERS AND OTHER INTRODUCTORY SUBJECTS
The rationals; $\sqrt 2$ is irrational. The real numbers contain the rationals and have the sup property. A distance on the reals; functions and sequences; limits of sequences. Monotone sequences always admit a limit; series with positive terms; the comparison test, the condensation test, the root and ratio test. Cauchy sequences; series with non-positive terms; absolute convergence and convergence. The Leibnitz convergence theorem. power series and convergence radius. Definition of sine, cosine, exponential and logarithm through their series; important limits.

REAL FUNCTIONS
Definition of the limit of a function; continuous functions; power series are continuous; uniform continuity; a continuous function in a closed and bounded interval is uniformly continuous. The intermediate value theorem; the theorem of Weierstrass. The derivative; differentiability implies continuity; the derivative in the point of maximum is zero. The chain rule and the derivative of the inverse. The theorems of Rolle and Lagrange. Convex functions; the slope of their chords is increasing; if they are differentiable, the derivative is increasing. Inequalities among the means and Young's inequality. Two versions of L'Hopital's theorem. Taylor's formula with the remainder in the forms of Lagrange and of Peano. Convergence of Taylor series: counterexamples and examples. The relationship between convergence of sequences and of functions.

INTEGRATION
Riemann's integral; integration by parts and by substitution; fundamental theory of calculus. The complex numbers; the complex plane and Euler's representation. Integration of rational functions. Taylor's formula with integral remainder. Improper integrals; absolute integrability. Uniform convergence for sequences and series of functions. Limits of Riemann integral under uniform convergence. Power series can be integrated and differentiated term by term.

NERDY THINGS
Various approximations of $\sqr 2$; machin's formula for $\pi$; the infinite product of Wallis; the formula of De Moivre Stirling; the area under the Gaussian with the formula of Wallis; Euler's summation formula; a model of the distribution of wealth; a continuous but nowhere differentiable function.

B. Palumbo - M.C. Signorino, Funzioni algebriche e trascendenti, ed. Accademica, 2015.

Marcellini-Sbordone, Analisi Matematica 1.

De Marco-Mariconda, Analisi Matematica 1.

REAL NUMBERS AND OTHER INTRODUCTORY SUBJECTS
The rationals; $\sqrt 2$ is irrational. The real numbers contain the rationals and have the sup property. A distance on the reals; functions and sequences; limits of sequences. Monotone sequences always admit a limit; series with positive terms; the comparison test, the condensation test, the root and ratio test. Cauchy sequences; series with non-positive terms; absolute convergence and convergence. The Leibnitz convergence theorem. power series and convergence radius. Definition of sine, cosine, exponential and logarithm through their series; important limits.

REAL FUNCTIONS
Definition of the limit of a function; continuous functions; power series are continuous; uniform continuity; a continuous function in a closed and bounded interval is uniformly continuous. The intermediate value theorem; the theorem of Weierstrass. The derivative; differentiability implies continuity; the derivative in the point of maximum is zero. The chain rule and the derivative of the inverse. The theorems of Rolle and Lagrange. Convex functions; the slope of their chords is increasing; if they are differentiable, the derivative is increasing. Inequalities among the means and Young's inequality. Two versions of L'Hopital's theorem. Taylor's formula with the remainder in the forms of Lagrange and of Peano. Convergence of Taylor series: counterexamples and examples. The rjavascript:void(0);elationship between convergence of sequences and of functions.

INTEGRATION
Riemann's integral; integration by parts and by substitution; fundamental theory of calculus. The complex numbers; the complex plane and Euler's representation. Integration of rational functions. Taylor's formula with integral remainder. Improper integrals; absolute integrability. Uniform convergence for sequences and series of functions. Limits of Riemann integral under uniform convergence. Power series can be integrated and differentiated term by term.

NERDY THINGS
Various approximations of $\sqr 2$; machin's formula for $\pi$; the infinite product of Wallis; the formula of De Moivre Stirling; the area under the Gaussian with the formula of Wallis; Euler's summation formula; a model of the distribution of wealth; a continuous but nowhere differentiable function.

B. Palumbo - M.C. Signorino, Funzioni algebriche e trascendenti, ed. Accademica, 2015.

Marcellini-Sbordone, Analisi Matematica 1.

De Marco-Mariconda, Analisi Matematica 1.

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

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

- Linear algebra: linear equations, matrices, Gauss-Jordan reduction, rank of a matrix, solutions of systems of linear equations, sum and product of matrices, invertible matrices and their construction, Rouchè-Capelli theorem.
- Square matrices and determinants: definition of determinant, properties of determinants, determinants and invertible matrices.
- Vector spaces: the example of geometric vectors, definition and examples of vector spaces, linearly independent vectors, independence, finitely generated vector space, basis, change of basis
- Scalar products: definition, euclidean spaces, examples of scalar products, perpendicularity, orthogonal basis, orthonormal basis and orthogonal matrices.
- Cartesian cordinates: coordinates on an affine euclidean space, fundamental metric properties, basic affine and euclidean geometry in dimension n.
- Plane and Space Geometry: isometries of the euclidean plane - points, straight lines, circles in the plane, angle between two straight lines, metric formulae for plane geometry, straight lines and planes in a space, equations of straight lines, planes, spheres, circles.
- Linear maps: Kernel and Image of a linear map, associated matrix after fixing the basis, linear operators, eigenvalues and eigenvectors of a linear operator, characteristic polynomial, search for eigenvalues and eigenvectors
- Quadratic equations: conics in the cartesian plane, conics and symmetric matrices, classification up to isometries, canonical form of a conic, metrical properties, quadrics in the space, type and canonical form.

Matrices and Vectors' by F. Flamini and A. Verra (Carocci Editore).

Further information on other useful texts for consultation and performance of exercises will be provided at the beginning of the course.

Some handouts will be distributed.

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 the teacher's website (http://host.uniroma3.it/laboratori/escher/ESP_I.html)
they can consult the following texts:

(a) Gaetano Cannelli, Metodologie sperimentali in Fisica - Introduzione al metodo scientifico, Terza Edizione 2018, EdiSES, Napoli (ISBN 978 88 7959 679 4)
(c) Diego Giuliani, Maria Michela Dickson, Analisi statistica con Excel, Maggioli Editore (ISBN: 978 88 3878 990 8)

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 the teacher's website (http://host.uniroma3.it/laboratori/escher/ESP_I.html)
they can consult the following texts:

(a) Gaetano Cannelli, Metodologie sperimentali in Fisica - Introduzione al metodo scientifico, Terza Edizione 2018, EdiSES, Napoli (ISBN 978 88 7959 679 4)
(c) Diego Giuliani, Maria Michela Dickson, Analisi statistica con Excel, Maggioli Editore (ISBN: 978 88 3878 990 8)

lassroom 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 the teacher's website (http://host.uniroma3.it/laboratori/escher/ESP_I.html)
they can consult the following texts:

(a) Gaetano Cannelli, Metodologie sperimentali in Fisica - Introduzione al metodo scientifico, Terza Edizione 2018, EdiSES, Napoli (ISBN 978 88 7959 679 4)
(c) Diego Giuliani, Maria Michela Dickson, Analisi statistica con Excel, Maggioli Editore (ISBN: 978 88 3878 990 8)

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

Material point kinematics: position, velocity, scalar and vector acceleration of a material point. 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 point systems: 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, quantity of motion and their relationship. The moment of 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.
Universal law of gravitation, potential energy and applications. Inertial mass and gravitational mass. Kepler's laws and their explanation using Newton laws.

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 quantity of motion 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; arbitrariness of the translation and uniqueness of the rotation. Quantity of motion, angular momentum and kinetic energy of a rigid body. Moment of inertia, Steiner's theorem.
Relationship between angular moment and angular velocity of a rigid body, main axes of inertia. Analysis of the motion in systems with a fixed axis rotation, with a rotation axis moving parallel to itself, with a fixed point; gyroscope, trowel and gyroscopic compass.

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

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

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

Relativity: Galileo’s relativity and Einstein's relativity: the axioms of special relativity and their consequences, time dilation, length contraction; Lorentz's transformations and speed composition. Mass, energy, impulse and equation of motion in special relativity.

The recommended textbook is:
C. Mencuccini e V. Silvestrini:
Fisica: Meccanica e Termodinamica
Editor Zanichelli

In addition, for a better understanding of how to apply Physics to specific situations, students should use also one of the two following textbooks:

D. Halliday, R. Resnick, J. Walker:
Fisica I
Casa Editrice Ambrosiana

or

R.A. Serway, J.W. Jewett Jr:
Fisica per Scienze ed Ingegneria vol. 1
Editor EdISES

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

Material point kinematics: position, velocity, scalar and vector acceleration of a material point. 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 point systems: 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, quantity of motion and their relationship. The moment of 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.
Universal law of gravitation, potential energy and applications. Inertial mass and gravitational mass. Kepler's laws and their explanation using Newton laws.

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 quantity of motion 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; arbitrariness of the translation and uniqueness of the rotation. Quantity of motion, angular momentum and kinetic energy of a rigid body. Moment of inertia, Steiner's theorem.
Relationship between angular moment and angular velocity of a rigid body, main axes of inertia. Analysis of the motion in systems with a fixed axis rotation, with a rotation axis moving parallel to itself, with a fixed point; gyroscope, trowel and gyroscopic compass.

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

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

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

Relativity: Galileo’s relativity and Einstein's relativity: the axioms of special relativity and their consequences, time dilation, length contraction; Lorentz's transformations and speed composition. Mass, energy, impulse and equation of motion in special relativity.

The recommended textbook is:
C. Mencuccini e V. Silvestrini:
Fisica: Meccanica e Termodinamica
Casa Editrice Ambrosiana

In addition, for a better understanding of how to apply Physics to specific situations, student should use also one of the two following textbooks:

D. Halliday, R. Resnick, J. Walker:
Fisica I
Casa Editrice Ambrosiana

or

R.A. Serway, J.W. Jewett Jr:
Fisica per Scienze ed Ingegneria vol. 1 - Quarta Edizione
Casa Editrice EdISES

1. ATOMIC THEORY AND ATOMIC STRUCTURE. Atoms, molecules, moles; atomic and molecular weight. Atomic models: Rutheford, Bohr. Quantum theory, quantum numbers and energy levels. Polyelectronic atoms; periodic system.
2. CHEMICAL BONDS. Ionic bond. Covalent bond: and bonds. Polyatomic molecules: molecular structure. Hybridization and resonance. Molecular orbital. Metallic bond. Intermolecular forces.
3. NOMENCLATURE AND CHEMICAL REACTIONS. Oxides, hydroxides, acids, salts, ions. Balancing chemical reactions: redox reactions.
4. STATES OF AGGREGATION. Gas state, ideal gas law. Solid state: ionic, covalent, molecular and metallic solids. Conductors, semiconductors, insulators. Liquid and amorphous states. Phase transitions and phase diagrams.
5. SOLUTIONS. Concentration, colligative properties; electrolyte solutions.
6. THERMODYNAMICS. Matter, energy, heat, first and second principles; enthalpy, entropy, free energy.
7. CHEMICAL EQUILIBRIUM. Equilibrium constant and free energy. Gas-phase and heterogeneous equilibria. Le Chatelier’s principle. Van’t Hoff equation.
8. EQUILIBRIA IN SOLUTION. Acid-base equilibria: acids and bases, pH, dissociation constant, polyprotic acids, hydrolysis, buffers. Acid-base titrations and pH indicators. Solubility equilibria: solubility product, common ion effect.
9. ELECTROCHEMISTRY. Batteries, electrode potentials, Nernst’s equation. Electrolysis.
10. CHEMICAL KINETICS. Reaction speed, speed constant. Influence of the temperature on the reaction speed: Arrhenius equation. Catalysts.
Numerical exercises on all the listed subjects.

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

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

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

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, 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, available online
G. Gentile, Introduzione ai sistemi dinamici. 2. Meccanica lagrangiana e hamiltoniana, available online

ELECRTICAL 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 digital oscilloscope
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. The gnuplot package

Elementary optics
Basic geometrical options. 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

ELECrTICAL 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 digital oscilloscope
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. The gnuplot package

Elementary optics
Basic geometrical options. 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

The learning process designed for this subject is based mainly on the following activities: lectures by the teaching faculty and laboratory exercises.

Course Syllabus
Fundamental concepts in electronics applied to measurements. Introduction of theory of solid state electronics including semiconductor physics, diodes, BJT, MOSs. Fundamental of amplifiers and principles of feedback. Applications of operational amplifiers. Fundamental topics on digital electronics and application of logical gate.
The lectures are complemented by laboratory exercises (with compulsory attendance).
The purpose of the laboratory exercises is to give students hands-on experience to allow them to test electronic components who have studied during lectures. Students will be required to carry out the laboratory exercises and collect their data and present a written report. The report must be submitted within the following week for evaluation.

List of laboratory demostrations
Applications of circuits with diodes
Solar cell
Exercises with operational amplifiers (Three laboratory demonstrations)
Exercises with BJT and MOS (Two laboratory demonstrations)
Applications of Logical gates

For exam preparation, students,
in addition to consulting the material available on the teacher's website (http://host.uniroma3.it/laboratori/escher/ESP_I.html)
they can consult the following texts:

(a) G. Schirripa Spagnolo, Elettronica Applicata, Edizioni Efesto, 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 learning process designed for this subject is based mainly on the following activities: lectures by the teaching faculty and laboratory exercises.

Course Syllabus
Fundamental concepts in electronics applied to measurements. Introduction of theory of solid state electronics including semiconductor physics, diodes, BJT, MOSs. Fundamental of amplifiers and principles of feedback. Applications of operational amplifiers. Fundamental topics on digital electronics and application of logical gate.
The lectures are complemented by laboratory exercises (with compulsory attendance).
The purpose of the laboratory exercises is to give students hands-on experience to allow them to test electronic components who have studied during lectures. Students will be required to carry out the laboratory exercises and collect their data and present a written report. The report must be submitted within the following week for evaluation.

List of laboratory demostrations
Applications of circuits with diodes
Solar cell
Exercises with operational amplifiers (Three laboratory demonstrations)
Exercises with BJT and MOS (Two laboratory demonstrations)
Applications of Logical gates

For exam preparation, students,
in addition to consulting the material available on the teacher's website (http://host.uniroma3.it/laboratori/escher/ESP_I.html)
they can consult the following texts:

(a) G. Schirripa Spagnolo, Elettronica Applicata, Edizioni Efesto, 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

Quantum mechanics: The crisis of classical physics. Waves and particles. State vectors and operators. Measurements and observables. The position operator. Translations and momentum. Time evolution and the schrodinger equation. Parity. One-dimensional problems. 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 - Seconda Edizione [Zanichelli, Bologna, 2014]
An english version of the book is also available:
Sakurai J.J., Modern Quantum Mechanics (Revised Edition) [Addison-Wesley, 1994]

Quantum mechanics: The crisis of classical physics. Waves and particles. State vectors and operators. Measurements and observables. The position operator. Translations and momentum. Time evolution and the schrodinger equation. Parity. One-dimensional problems. 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 - Seconda Edizione [Zanichelli, Bologna, 2014]
An english version of the book is also available:
Sakurai J.J., Modern Quantum Mechanics (Revised Edition) [Addison-Wesley, 1994]

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.
• Notes from the former course of Istituzioni di Fisica Nucleare e Subnucleare from Prof. Ceradini will be made available on the web page

Please register to the following web pages
moodle https://matematicafisica.el.uniroma3.it/course/view.php?id=51
sharepoint https://uniroma3.sharepoint.com/sites/ElementidiFisicaNucleareeSubnucleareAA201920
teams https://teams.microsoft.com/l/team/19%3a57c8fc1e646a489894614511aea22a8c%40thread.tacv2/conversations?groupId=b5330848-367f-43b5-ae3c-b75bc4257d05&tenantId=ffb4df68-f464-458c-a546-00fb3af66f6a

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.
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 hypothesis, Fermi theory,
Kurie plot, lifetime, Fermi and Gamow-Teller transitions. Weak interaction and Fermi constant.
Discovery of the neutrino.
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.
• A.Das and T.Ferbel, Introduction to Nuclear and Particle Physics, 2nd Edition, World
Scientific, 2003.
• B.Povh, K.Rith, G.Sholtz, F.Zetsche: Particelle e nuclei, Bollati Boringhieri, 1998.
• Appunti del corso di Istituzioni di Fisica Nucleare e Subnucleare,
http://webusers.fis.uniroma3.it/~ceradini/efns.html

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)


Web page with additional material about the lecture course

https://sites.google.com/a/personale.uniroma3.it/robertoraimondi/home/teaching/elementi

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).

Further information is available on
https://sites.google.com/a/personale.uniroma3.it/robertoraimondi/home/teaching/elementi

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)