Cap. 1: Real numbers; functions.
Cap. 4: Vector space.
Cap. 2: Matrices and determinant.
Cap. 3: Linear systems.
Cap. 5: Limit of a sequence.
Cap. 6: Limit of a function; continuous function.
Cap. 7: Important theorem for continuous functions; Bolzano-Weierstrass theorem.
Cap. 9: Derivation; rules for derivatives; geometrical meaning of derivative.
Cap. 10: Study of functions
Cap. 11: Functions of many variables.
Cap. 12: Definite Integral.
Cap. 13: Indefinite Integral. Integration rules.

MARCELLINI P.,SBORDONE C., ELEMENTI DI CALCOLO [ED. LIGUORI ]
Classroom notes with exercises

USE OF EXCEL SOFTWARE: FORMATTING OF WORKSHEETS AND USE OF FUNCTIONS FOR REPRESENTATION AND DATA ANALYSIS. TABLES AND GRAPHICS. GRAPHICS OF LINEAR, QUADRATIC, CUBICS, TRIGONOMETRIC, EXPONENTIAL, LOGARITHMIC FUNCTIONS. LOGARITHMIC PLOT. NUMERICAL INTEGRAL. GRAPHIC METHODS FOR THE SOLUTION OF OPTICAL PROBLEMS: FERMAT PRINCIPLE (REFLECTION AND REFRACTION), PLANAR AND SPHERICAL MIRRORS , THIN LENSES, WAVE SUM. SPATIAL AND TEMPORAL REPRESENTATION OF THE WAVES.

The didactic materials is prepared by the teachers and loaded the web site the course.
Web Site:
https://app.scienze.uniroma3.it/courses/1/details/2018/didactic_activities/1748

USE OF EXCEL SOFTWARE: FORMATTING OF WORKSHEETS AND USE OF FUNCTIONS FOR REPRESENTATION AND DATA ANALYSIS. TABLES AND GRAPHICS. GRAPHICS OF NETWORKS, PARABLES, CUBICS, TRIGONOMETRIC, EXPONENTIAL, LOGARITHMIC, AND GRAPHICS OF VARIOUS FUNCTIONS. LOGARITHMIC GRAPHS. NUMERICAL INTEGRAL. GRAPHIC METHODS FOR THE SOLUTION OF OPTICAL PROBLEMS: FERMAT PRINCIPLE (REFLECTION AND REFRACTION), FLAT MIRRORS AND SEFRICI, THIN LENSES, WAVE SUM. SPATIAL AND TEMPORAL REPRESENTATION OF THE WAVES.

EDUCATIONAL MATERIAL PROVIDED BY THE TEACHER THROUGH THE COURSE WEBSITE

Electromagnetic wave properties: wave propagation speed; plane wave, spherical wave, sinusoidal harmonic waves; frequency and wavelength of harmonic waves; amplitude of the electric and magnetic field in electromagnetic waves; energy carried by an e.m. and wave intensity. Definition of wavefront and optical ray. Classification of electromagnetic waves.
Conditions of validity and limits of the approximation of geometric optical optics.
Fermat's principle; concept of optical path; Snell's laws of reflection and refraction; total reflection. Dispersion of light in the prism; prismatic deviation angle; minimum deviation angle; thin prisms; dispersive power and Abbe's number of a medium; prisms with direct vision and achromatic prisms; prismatic power.
The formation of images in the approximation of geometric optics. Centered optical systems and their description as an ordered succession of diopters in refraction and / or reflection. Stigmatic and astigmatic optical systems. Light and power of an optical system.
Spherical mirrors and planes: law of conjugation, transversal enlargement; graphic construction of the image
Centered dioptric systems: Gauss approximation; the spherical diopter, the plane diopter, the thin and thick lenses, thin lens systems. Focal points and focal planes, Principal Points and Principal Planes, Nodal Points; the effective focal length, the focal length of the posterior vertex, the focal length of the anterior vertex; nominal power, equivalent power, Gulstrand formula, power of the posterior and anterior vertex; law of conjugation of Gauss and Newton, transversal magnification, longitudinal magnification; graphical construction of the image. Images of flat cylindrical lenses and prisms.
Chromatic aberration in optical systems.

J. S. Walker: “Fondamenti di Fisica”
dispense del corso
Jurgen R. Meyer Arendt “Introduction to Classical and Modern
OPTICS” : Cap. 1 5

1 Atomic theory and atomic structure. Atoms, molecules, moles; atomic weight and molecular weight. Rutherford atom, Bohr atom, 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. Metallic bond. Intermolecular forces.
3 Nomenclature and Chemical Reactions. Oxides, hydroxides, acids, salts, ions. Balancing of chemical reactions.
4 States of aggregation. Gaseous state and gas laws. Solid state: ionic, molecular, metallic, covalent solids. Liquids and amorphous. State changes and state diagrams.
5 Solutions. Concentration of solutions. Colligative properties. Electrolyte solutions.
6 Thermodynamics and chemical equilibrium. Matter, energy, heat. First and second principle. Enthalpy, entropy, free energy. Balance constant. Equilibria in the gaseous and heterogeneous phase. Van’t Hoff equation.
7 Equilibria in solution. Acids and bases, pH, dissociation constants, polyprotic acids, hydrolysis, buffers. Precipitation equilibria: solubility and solubility product.
8 Electrochemistry. Electric batteries, electrodes, Nernst equation.
9 Chemical kinetics. Speed ​​of chemical reactions.
10 Basics of Organic Chemistry. Functional groups, nomenclature, molecular structure and isomerism.

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

1. ATOMIC THEORY: ATOMS, MOLECULES, MOLES; STRUCTURE OF THE ATOM; PERIODIC SYSTEM.
2. MOLECULES: CHEMICAL BOND, MOLECULAR STRUCTURE, INTERMOLECULAR FORCES
3. CHEMICAL NOMENCLATURE: OXIDES, HYDROXIDES, ACIDS, SALTS.
4. CHEMICAL REACTIONS AND THEIR BALANCING; OXIDREDUCTIONS.
5. STATES OF AGGREGATION: GASEOUS, LIQUID, SOLID; CHANGES OF STATE AND STATE DIAGRAMS.
6. SOLUTIONS: CONCENTRATION, COLLIGATIVE PROPERTIES, SOLUTIONS OF ELECTROLYTES.
7. THERMODYNAMICS: FIRST AND SECOND PRINCIPLE; ENTHALPY, ENTROPY, FREE ENERGY.
8. CHEMICAL KINETICS: REACTION SPEED AND FACTORS THAT INFLUENCE IT.
9. CHEMICAL EQUILIBRIUM: CONSTANT OF EQUILIBRIUM; BASE ACID AND SOLUBILITY BALANCES.
10. ELECTROCHEMISTRY: BATTERIES AND ELECTROLYSIS CELLS.
11. OUTLINE OF ORGANIC AND BIOCHEMISTRY.

“Elementi di Chimica” L.Palmisano, M. Schiavello. Editrice Edises

The theoretical lessons will focus on the following topics:

Tools and measures. Measurement units - Trigonometry angles and definitions - Sizes and errors - Systematic error and random error - Instrument error - Standard deviation and standard error - Error propagation - Representing data: significant figures, comparison of measurements, tables and graphs, histograms

Descriptive statistics. Indices of central tendency: average, median and mode - Percentiles - Indices of variability: variance and standard deviation - Limit distributions

Correlation between variables. Linear regression, least squares method - Linearization of a function - Verification of the acceptability of a fit: Chi square test and determination coefficient - Pearson r coefficient, Spearman correlation coefficient for ranks

Probability. Definition and fundamental properties - Probability distributions (binomial, Poisson and uniform distribution - Gaussian and error integral, justification of sum in quadrature and standard deviation of the mean, standard normal distribution) - Average and variance of a random variable - Confidence intervals - Standard deviation as acceptability percentage - Applications and verifications: correlation index and chi-square test - Student's t test for comparison between measurements

Inferential statistics. Hypothesis test and significance - The null hypothesis and the alternative hypothesis - Types of studies and sampling - Sample distributions - Criterion of significance and critical values - Errors and decisions of a statistical test - Sign test - Chi square test as test of significance - z-test and t-test - Distribution F - Analysis of variance (ANOVA) with one and two ways

The topics of the laboratory exercises will be chosen from the following list

1) Use of precision instruments (decimal and twentieth caliber, spherometer) for the measurement of quantities. Statistical treatment of the error.
2) Verification of the law of light reflection from a plane mirror.
3) Verification of the law of refraction in a plexiglass plate.
4) Verification of Kepler's law on the reduction of light intensity as a function of distance.
5) Verification of the Lambert-Beer law on the attenuation of luminous intensity on passing through an opaque medium.
6) Determination of the focal distance and dioptric power of a thin lens through an optical measurement.
7) Determination of the focal distance and dioptric power of a lens system with the Bessel method.
8) Determination of the focal distance and dioptric power of an ophthalmic lens by measuring with a spherometer and with a dioptrometer and characterization of an astigmatic lens
9) Verification of Gullstrand's law and search for the main planes of an optical system consisting of two thin lenses.
10) Dispersion of light through a prism: verification of Cauchy's law and determination of the number of Abbe
11) Estimate of the magnification of an optical system: the magnifying lens
12) Use of Student's t test to compare experimental data and the chi-square test to assess how well a theoretical trend reproduces the behavior of experimental data; construction of a histogram and its limit function.

- Lecture notes distributed by the teacher during the course

- S. Walker, Fondamenti di Fisica (Pearson, 2010)

- R. Meyer-Arendt, Introduction to classical and modern optics (Prentice Hall, 1995)

- R. Taylor, Introduzione all’analisi dell’errore (Zanichelli, 2010)

- M. Bland, Statistica medica (Maggioli Editore, 2014)

- M. M. Triola e M. F. Triola, Fondamenti di Statistica (Pearson, 2013)

- J. Welkowitz, B. Cohen e R. Ewen, Statistica per le scienze del comportamento (Apogeo)

The theoretical lessons will focus on the following topics:

Tools and measures. Measurement units - Trigonometry angles and definitions - Sizes and errors - Systematic error and random error - Instrument error - Standard deviation and standard error - Error propagation - Representing data: significant figures, comparison of measurements, tables and graphs, histograms

Descriptive statistics. Indices of central tendency: average, median and mode - Percentiles - Indices of variability: variance and standard deviation - Limit distributions

Correlation between variables. Linear regression, least squares method - Linearization of a function - Verification of the acceptability of a fit: Chi square test and determination coefficient - Pearson r coefficient, Spearman correlation coefficient for ranks

Probability. Definition and fundamental properties - Probability distributions (binomial, Poisson and uniform distribution - Gaussian and error integral, justification of sum in quadrature and standard deviation of the mean, standard normal distribution) - Average and variance of a random variable - Confidence intervals - Standard deviation as acceptability percentage - Applications and verifications: correlation index and chi-square test - Student's t test for comparison between measurements

Inferential statistics. Hypothesis test and significance - The null hypothesis and the alternative hypothesis - Types of studies and sampling - Sample distributions - Criterion of significance and critical values - Errors and decisions of a statistical test - Sign test - Chi square test as test of significance - z-test and t-test - Distribution F - Analysis of variance (ANOVA) with one and two ways

The topics of the laboratory exercises will be chosen from the following list

1) Use of precision instruments (decimal and twentieth caliber, spherometer) for the measurement of quantities. Statistical treatment of the error.
2) Verification of the law of light reflection from a plane mirror.
3) Verification of the law of refraction in a plexiglass plate.
4) Verification of Kepler's law on the reduction of light intensity as a function of distance.
5) Verification of the Lambert-Beer law on the attenuation of luminous intensity on passing through an opaque medium.
6) Determination of the focal distance and dioptric power of a thin lens through an optical measurement.
7) Determination of the focal distance and dioptric power of a lens system with the Bessel method.
8) Determination of the focal distance and dioptric power of an ophthalmic lens by measuring with a spherometer and with a dioptrometer and characterization of an astigmatic lens
9) Verification of Gullstrand's law and search for the main planes of an optical system consisting of two thin lenses.
10) Dispersion of light through a prism: verification of Cauchy's law and determination of the number of Abbe
11) Estimate of the magnification of an optical system: the magnifying lens
12) Use of Student's t test to compare experimental data and the chi-square test to assess how well a theoretical trend reproduces the behavior of experimental data; construction of a histogram and its limit function.

Professors F. Offi and F. Fontana lecture notes

- S. Walker, Fondamenti di Fisica (Pearson, 2010)

- R. Meyer-Arendt, Introduction to classical and modern optics (Prentice Hall, 1995)

- R. Taylor, Introduzione all’analisi dell’errore (Zanichelli, 2010)

- M. Bland, Statistica medica (Maggioli Editore, 2014)

- M. M. Triola e M. F. Triola, Fondamenti di Statistica (Pearson, 2013)

- J. Welkowitz, B. Cohen e R. Ewen, Statistica per le scienze del comportamento (Apogeo)

Introduction to the optics of vision: historical backgrounds, conventions and symbols, geometric optics in relation to the applications of vision optics.
Anatomical structure of the eye and nods on the physiology of the visual system.
Schematic models of eye optics. Schematic eyes and Emsley's reduced eye. Calculation tutorials.
Axes of the eye and size of the retinal image.
The condition of emmetropy, definition of remote point.
Astigmatism and classification of eye astigmatism.
Compensation with ophthalmic lenses and contact lenses.
Accommodation, definition of near point, the condition of presbyopia.
Eye aberrations and retinal image quality.
From retinal image to visual information processing: hints of vision psychophysics, visual acuity and criteria in the construction of optometric boards, sensitivity to contrast, field of vision, color perception, anomalies of sense Color.

F. ZERI, A. ROSSETTI, A. FOSSETTI, A.CALOSSI (2012): Ottica Visulae, Società editrice Universo, Roma
A. ROSSETTI, P. GHELLER (2003): Manuale di Optometria e contattologia, Edizioni Zanichelli
L. Lupelli (2014): Optometria A-Z, dizionario di SCienze, tecnica e Clinica della Visione, Edizioni Medicl Books

Part I - Outlines of Organic Chemistry
Hydrocarbons and derivatives - Alkanes, Alkenes, Alkynes, Aromatic Compounds - Alcohols, Phenols, Thiols, Ethers - Aldehydes, Ketones, Carboxylic Acids, Esters, Anhydrides - Amines and Amides - Heterocyclic compounds - Stereoisomerism
Part II - General biochemistry
Water and its properties - Water properties - Hydrogen bond - Basic acid equilibria, pH and pK
Biomolecules - Amino acids, Carbohydrates, Lipids, Nucleotides, Vitamins - Peptides and Proteins
Nucleic acids - DNA, RNA - Transcription and Translation
Metabolism - Catabolism and anabolism - Energy metabolism - Ocular metabolism - Ocular fluids - Carbohydrate metabolism
The process of vision - ion channels - rhodopsins and opsins - transduction of the light impulse into a nerve impulse - chromatic vision - proteins of the lens

Gabriele D’Andrea
Biochimica Essenziale
Edizioni EdiSES

David R. Whikehart
Biochemistry of the Eye
Elsevier
Available in the Library (Biblioteca di Area Scientifica)

1. Electrostatics: introduction to electrical phenomena, charge and Coulomb's law, charge distributions and Gauss's law, electric field.

2. Magnetism: electrical currents, magnetic phenomena, Ampère's and Biot-Savart's law.

3. Electromagnetism: induction, Faraday-Lens law, displacement current. Maxwell's equations, and electromagnetic waves.

4. Wave optics: polarisation, interference, diffraction.

5. Applications: wavefront sensors, Optical Coherence Tomography, light pulses.

Three laboratory sessions are part of this course, each made of two sessions. The subjects of the sessions are part of the syllabus.

parts 1-4: J.S. Walker, Fondamenti di fisica (5A ed., Pearson)

parts 1-4: H.D. Young, R.A. Friedman, Principi di fisica, vol. 2 (Pearson)

part 5: Lecture notes, available at https://app.scienze.uniroma3.it/courses/1/details/2018/didactic_activities/1561

Complex numbers:
Algebraic operations; Cartesian, trigonometric and exponential forms; Powers and roots; Equations.

Taylor expansion:
Taylor formula; Taylor expansion of the elementary functions; Operations on the Taylor expansion.

Numerical series:
Numerical sequences; numerical series; positive term series; alternate sign term series; algebraic operations on series.

Fourier series:
Trigonometric polynomials; Fourier series and coefficients; Exponential form of the Fourier series; Derivation of the Fourier series; Convergence of the Fourier series; Periodic functions with period T0.

Fourier Transform:
Dirac delta function; Introduction to the Fraunhofer diffraction; Definition of the Fourier transform and antitransform; Examples of Fourier transforms; Mathematical properties of the Fourier transform; Physical properties of the Fourier transform; Multidimension transforms; Spatial filter.

Zernike Polynomials

Ordinary differential equations:
General definitions; First order equations; Second order linear differential equations with constant coefficients.

Claudio Canuto, Anita Tabacco ``Analisi Matematica I" [C.T.I]
Claudio Canuto, Anita Tabacco ``Analisi Matematica II" [C.T.II]
Greg Gbur ``Mathematical Methods for Optical Physics and Engineering" [Gbur]

1- Complex numbers; Taylor developments and applications.
2- Numerical series: References on sequences; Numerical series; Series with positive terms; Series with terms of alternate sign; Algebraic operations on the series.
3- Fourier series: Trigonometric polynomials; Fourier coefficients and series; Exponential form of the Fourier series; Fourier series and derivation;
Convergence of the Fourier series; Periodic functions of period T 0.
4- Fourier transform: Introduction to Fraunhofer diffraction; Definition of Fourier transforms and anti-transforms; Examples of Fourier transforms; Mathematical properties of the Fourier transform; Physical properties of the Fourier transforms; Self-functions of the Fourier operator; Fourier transform in multidimensional spaces; Spatial filter.
5- Zernike polynomials
6- Ordinary differential equations: General definitions; First order equations; Examples; Scalar equations of the first
order; The Cauchy problem for the equations of the first order, Linear equations of the second order with constant coefficients.

Claudio Canuto, Anita Tabacco, "Analisi Matematica I"

Claudio Canuto, Anita Tabacco, "Analisi Matematica II"

Greg Gbur, "Mathematical Methods for Optical Physics and Engineering"

INTRODUCTION: THE WORLD AT THE NANOSCALE. SPECTROSCOPY. EMISSION AND ABSORPTION SPECTRA. SPECTRAL INTENSITY DISTRIBUTION. THE BLACK-BODY RADIATION AND THE PLANCK’S SOLUTION. THE PHOTOELECTRIC EFFECT: PHENOMENOLOGY AND EINSTEIN’S INTERPRETATION. ATOM MODELS. BOHR’S POSTULATES. ELECTRONIC TRANSITIONS. THE DE BROGLIE WAVELENGTH, STATIONARY WAVES. INTRODUCTION TO THE WAVE FUNCTION. THE DETERMINISTIC AND PROBABILISTIC DESCRIPTION OF MOTION. HEISENBERG’S UNCERTAINITY PRINCIPLE. A PARTICLE CONFINED IN A SEGMENT. THE SCHRÖDINGER EQUATION IN 1D. STATIONARY STATES. A PARTICLE CONFINED IN A SEGMENT REVISED. UNIDIMENSIONAL ENERGY POTENTIALS. MANY-PARTICLES WAVE FUNCTIONS. FERMIONS AND BOSONS. PAULI’S EXCLUSION PRINCIPLE. THE SCHRÖDINGER EQUATION FOR A CENTRAL POTENTIAL. QUANTUM NUMBERS. THE SPIN. DIPOLE SELECTION RULES. THE AUFBAU PRINCIPLE. HUND`S PRINCIPLE. THE PERIODIC TABLE. ELECTRON AFFINITY AND ELETTRONEGATIVITY. IONIC AND COVALENT BONDS. MOLECULAR ORBITALS. ROTATIONAL AND VIBRATIONAL ENERGY IN DIATOMIC MOLECULES. HYBRIDIZATION AND POLYATOMIC MOLECULES. INTRODUCTION TO THE CRYSTAL STRUCTURE IN SOLIDS. BINDING ENERGY IN SOLIDS. CLASSICAL THEORY OF CONDUCTIVITY. THE FERMI DISTRIBUTION. ENERGY BANDS. CONDUCTORS, INSULATORS, AND SEMICONDUCTIRS. DOPED SEMICONDUCTORS. BASICS OF LASER.

TESTI: PAUL A. TIPLER : “CORSO DI FISICA” VOL. 3 ED. ZANICHELLI, TERZA EDIZIONE ITALIANA
PAUL A. TIPLER, GENE MOSCA: “CORSO DI FISICA” VOL. 3 ED. ZANICHELLI, QUARTA EDIZIONE ITALIANA
handouts distributed by the teacher

FISIOLOGIA CONCETTI PRINCIPALI - OMEOSTASI, FEEDBACK, RELAZIONI STRUTTURA/FUNZIONE, MODIFICAZIONI NEL CORSO DELLA VITA
FISIOLOGIA CELLULARE - PASSAGGIO DI SOSTANZE ATTRAVERSO LA MEMBRANA, OSMOSI, FENOMENI ELETTRICI DI MEMBRANA, METABOLISMO CELLULARE,VOLUME CELLULARE,
IL SISTEMA NERVOSO - ORGANIZZAZIONE, POTENZIALE D'AZIONE DI UNA CELLULA NERVOSA, PERIODI REFRATTARI, PROPAGAZIONE DEL MESSAGGIO NERVOSO, LE SINAPSI, ARCO RIFLESSO, NEUROTRASMETTITORI E RECETTORI)
FUNZIONI D'ORGANO • IL SISTEMA MUSCOLARE - MECCANICA DELLA CONTRAZIONE MUSCOLARE, MIOGRAFIA, SCOSSA SEMPLICE, TETANO MUSCOLARE, FUNZIONI DEL MUSCOLO LISCIO•
RESPIRAZIONE: FISIOLOGIA DELLA RESPIRAZIONE: VENTILAZIONE, SCAMBI GASSOSI
FUNZIONE RENALE: FILTRAZIONE, RIASSORBIMENTO, EQUILIBRIO IDRICO ED ELETTROLITICO,
IL SISTEMA CARDIO-CIRCOLATORIO - FUNZIONI DEL SANGUE, EMODINAMICA,
CUORE, CICLO CARDIACO, LA PRESSIONE SANGUIGNA E LA SUA REGOLAZIONE
LA FISIOLOGIA SENSORIALE - INFORMAZIONI SENSORIALI, RECETTORI SENSORIALI, LE VIE SENSORIALI E GLI STATI DI ELABORAZIONE, LA CODIFICA DEL SEGNALE NERVOSO, ORGANIZZAZIONE DEGLI ORGANI DI SENSO)• IL SISTEMA VISIVO - FORMAZIONE DELL'IMMAGINE RETINICA, CRISTALLINO E RIFRAZIONE, FOTOTRASDUZIONE, RISPOSTA DELLE CELLULE GANGLIARI, VIE OTTICHE, ADATTAMENTO ALLA LUCE E AL BUIO, LA VISIONE STEREOSCOPICA, LA VISIONE CROMATICA)

Taglietti, Fondamenti di Fisiologia generale e integrata, Edises
Stanfield, Fisiologia, Edises.
DU SILVERTHORN, FISIOLOGIA;

LIBRI CONSIGLIATI DISPONIBILI NELLA BIBLIOTECA D'AREA: RANDALL ET AL., FISIOLOGIA DEGLI ANIMALI; CASELLA E TAGLIETTI, FISIOLOGIA.
GUSSONI ET AL., FISIOLOGIA DEGLI ORGANI DI SENSO.

the professor meets students on Monday 10-13 by mail appointment.

Binocular Vision , Mitchell Scheiman-Bruce Wick; W.Kluwer Lippincott William&Wilkins