Sets and elementary mathematics: logical symbols and basics of logics, notion of set and difficulties with simple set theory, axiomatic theory of sets, natural numbers, relative numbers, rational and real numbers, extrema and infinites, Functions: function as an association, injections, surjections, bijections, invertibility, composition, graphs, monotonicity and strict monotonicity, elementary functions, linear and parabolic f., power f., trigonometry.
Limits: neighbourhood, definition of limit, theorem of unicity, persistence of the sign, comparison, operations on limits, limits of the kind L/0, limits of composite functions, Neper's constant e as a limit, exponential and logarithm function, infinite and infinitesimal order.
Derivatives: intuitive notion as a variation rate and rigorous definition, geometric interpretation, derivation rules, notable cases, theorem about the continuity of derivable f., monotonicity and sign of the derivative, relative minima and maxima, convexity and concavity, de l'Hôpital rule
Study of function: tracing the graph given the expression of the function.
Integrals: antiderivative of a function, indefinite integral, integration rules, integrals by substitution and by parts, contiguous sets, rectangoloid of a non-negative function, Riemann's integral, definite integral and its properties, theorem of the average, Torricelli-Barrow's theorem, fundamental theorem of integral calculus, integrability criteria, absolute integrability.
Linear systems: definitions, study of the coefficient matrix, Cramer and Gauss-Jordan techniques for the solutions.

C. Sbordone e M. Sbordone: Matematica per le Scienze della Vita, EDISES

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.
Moodle, Teams

Use of excel software: formatting of worksheets and use of functions for representation and data analysis. Tables and Graphics. Graphics of linear, quadratic, cubics, trigonometrics, 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.
Moodle, Teams

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.

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: ATOMS, MOLECULES, MOLES; ATOMIC STRUCTURE; PERIODIC SYSTEM.
2. MOLECULES: CHEMICAL BOND, MOLECULAR STRUCTURE, INTERMOLECULAR FORCES
3. CHEMICAL NOMENCLATURE: OXIDES, HYDROXIDES, ACIDS, SALTS.
4. CHEMICAL REACTIONS AND THEIR BALANCING; REDOX REACTIONS
5. STATE OF AGGREGATION: GASEOUS, LIQUID, SOLID; PHASE TRANSISTIONS AND PHASE DIAGRAMS.
6. SOLUTIONS: CONCENTRATION, COLLIGATIVE PROPERTIES, ELECTROLYTE SOLUTIONS
7. THERMODYNAMICS: FIRST AND SECOND PRINCIPLE; ENTHALPY, ENTHROPY, FREE ENERGY.
8. CHEMICAL KINETICS: SPEED OF REACTION AND FACTORS THAT INFLUENCE IT.
9. CHEMICAL EQUILIBRIUM: EQUILIBRIUM CONSTANT; ACID-BASE AND SOLUBILITY EQUILIBRIA.
10. ELECTROCHEMISTRY: BATTERIES AND ELECTROLYSIS CELLS.
11. NOTIONS OF ORGANIC CHEMISTRY.

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

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

- D. Halliday, R. Resnick, S. Walker, Fondamenti di Fisica (Casa Editrice Ambrosiana, 2015)

- 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)

- S. A. Glantz, Statistica per Discipline Biomediche (McGraw-Hill, 2007)

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)

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

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

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]

homeostasis, fedback, structure/function relationship,
Cell physiology, cell membranes, osmosis, excitability of cells, cell metabolism. ,
Nervous system: - action potential, refractariety, synapses, reflexes, neurotransmitters and receptors
Muscles, contraction. Smooth and skeletal muscle working mechanisms
Breathing: Breathing physiology, excanges of gas
Kidney: philtration, absorbption, electrolitic homeostasis.
Heart functions, contractility mechanisms
Sensor Physiology: - Ihow nervous signals are decoded, sense organs. Olfactory, taste, hearing systems.
Visual system: retina functions and mecanismganglion cell functions and mechanisms of action, color vision, vision pathways and brain areas involved in.

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.

1. AFTER CARE: Protocol; Comfort management.
2. CONTACT LENS MANAGEMENT DURING PANDEMIC INFECTION
3. SOFT CONTACT LENSES: Soft toric lenses; Silicone rubber lenses.
4. RIGID AND HYBRID CONTACT LENSES: Toric and asymmetrical corneal rigid lenses. Scleral rigid lenses. Hybrid lenses.
5. CONTACT LENSES IN THE LABORATORY: Parameters checking and quality inspection of rigid and soft contact lenses; Notes on modification of rigid contact lenses parameters.
6. THE SPECIALIST INSTRUMENTAL EXAMINATION OF THE EYE SURFACE: Corneal esthesiometry; Corneal pachymetry; Specular microscopy; In vivo confocal microscopy; Anterior segment tomography.
7. COMPLICATIONS INDUCED BY CONTACT LENSES WEAR: Classification; Quantification.
8. HIGH ORDER ABERRATIONS CONTROL: Induced by corneal ectasias, by refractive surgery and by keratoplasty.
9. ADVANCED APPLICATIONS: Continuous wear; Correction of presbyopia; Tinted contact lenses; Infancy; orthokeratology; Control of myopic progression: contact lenses vs to other procedures; Therapeutic use; Wear of contact lenses in conditions of environmental stress.
10. PROBLEM SOLVING: Clinical contact lens cases.

EFRON N. (Ed.) CONTACT LENS PRACTICE. THIRD EDITION, [ELSEVIER, 1998].
ANON. A GUIDE TO OVERNIGHT ORTHOKERATOLOGY, [BOSTON MATERIALS, 2010].