Quantifiers. Numbers: natural, integer, rational, real. Axioms of real numbers; density of Q in R. Irrationality of 2.
Cartesian coordinates in the plane. Distance between points on the line, in the plane. Equation of a circle. Absolute value as distance from the origin of a point on the real line.

Linear algebra (in 2 and 3 dimensions): points and vectors; slope of a segment; sum and difference of vectors, product by a scalar, parallelism conditions; scalar product, orthogonality conditions; vector product, equivalence of the geometric and coordinate formulation for both products.

Introduction to the functions of a variable, relationships between quantities. Graph of a function. Algebra of graphs.
Examples and definition of limit: to infinity, and then to a point. Operations with limits, Squeeze theorem. Limits of quotients of polynomials. Asymptotes. Some important limits.

Continuous functions; continuity at a point and an interval. Theorems on continuous functions: existence of the maximum and minimum, intermediate values. Discontinuity.

Exponential and logarithm functions.

Derivatives: geometric meaning, definition. Operations with derivatives: sum, product, quotient, multiplication by a constant. Derivation techniques, derivatives of the main functions. Derivation of composite functions and the inverse of a function. Equation of the tangent line at a point on the graph. Stationary points.
Fermat's theorem. Rolle and the mean value or Lagrange theorems. Monotonicity and sign of the first derivative. Linear approximation, or first-order Taylor formula. Second derivatives, concavities, inflections. Graph sketching. Related changes, growth rates.
Introduction to integrals: indefinite and definite integrals, their meaning. The problem of calculating the area of a region in the plane. The mean value theorem. The fundamental theorem of integral calculus. Integration for parts and replacement.
Introduction to Differential Equations: growth models, logistic equation. Separation of variables method; Cauchy problems. Exponential growth and decay.
Harmonic oscillator, its solution, modeling discussion of the solution.

James Stewart, Calcolo. Funzioni di una variabile. Apogeo Education - Maggioli Editore (più i capitoli del secondo volume, sull’algebra lineare e sulle equazioni differenziali, che verranno forniti in pdf)
Dario Benedetto, Mirko Degli Esposti, Carlotta Maffei Matematica per le scienze della vita, Terza edizione, Casa Editrice Ambrosiana. Zanichelli, 2015
Giorgio Israel, La Matematica e la realtà. Capire il mondo con i numeri. Carocci, 2015.

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

See the web page of the course of prof. De Seta

See the webpage prof. De Seta above

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

1. Measurement units, physical quantities and vectors
2. Newton's laws of motion
3. Work and energy
4. Linear momentum
5. Rotational motion
6. Fluid mechanics
7. Periodical motions
8. Waves
9. Thermal properties of matter
10. Laws of thermodynamics
11. Introduction to statistics

James S. Walker: Fondamenti di Fisica
H.D. Young, R. A. Freedman and A. L. Ford: Principi di Fisica

.One-dimensional kinematics (chap. 2)
Vectors in Physics (chap. 3)
Two-dimensional kinematics (chap. 4)
The laws of motion (chap. 5)
Application of Newton's laws (chap. 6)
Work and kinetic energy (chap. 7)
Potential energy and conservation of energy (chap. 8)
Momentum and collisions in one dimension (chap. 9, except collisions in two dimensions)
Rotational motions and moment of momentum (chap. 10, par. 6.5)
Oscillations around equilibrium (chap.13)
Gravitation (chap.12)
Fluids (chap.15)
Temperature and heat (chap.16)
Phases and phase change (chap.17, except par. 17.3)
Thermodynamics (chap.18)
Waves and sound (chap. 14, except par. 14.9)

JAMES S. WALKER “FONDAMENTI DI FISICA” [PEARSON-ADDISON-WESLEY]

Scientific method. The Atom. Chemical bond. Ionic bond. Covalent bond (VB). VSEPR. Hybridization. Dative bond. Resonance. Nomenclature and chemical structures.
Mole, weight composition, minimal and molecular formula.
States of aggregation of the matter. The gas. Gas laws. Ideal and real gas. Liquids and Solids.
Chemical reactions. Stoichiometry. Redox reactions. Acid-Base reactions.
The solutions: concentration and vapor tension. Colligative properties.
Basics of chemical kinetics
Thermodynamics I and II Principle. III Principle. Gibbs Free Energy and spontaneity of a chemical reaction. Chemical equilibrium.
Acids and Bases. Equilibria and pH calculation. Saline hydrolysis and tampons.
laboratory exercises
Basics of Electrochemistry
Basics of Organic Chemistry

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

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

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

- Lecture notes distributed by the teacher during the course

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

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

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

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, as made available by the teacher

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
DU SILVERTHORN, FISIOLOGIA;
Stanfield, Fisiologia, Edises.
C. L. Stanfield, 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.

INTRODUCTION: THE WORLD AT THE NANOSCALE. SPECTROSCOPY: ABSORPTION AND EMISSION. SPECTRAL DISTRIBUTIONS. BLACK BODY RADIATION AND THE PLANCK EQUATION. THE PHOTOELECTRIC EFFECT: PHENOMENOLOGY AND THE INTERPRETATION OF EINSTEIN. ATOMIC MODELS. BOHR'S POSTULATES. ELECTRONIC TRANSITIONS. DE BROGLIE’S HYPOTHESIS, STATIONARY WAVES. INTRODUCTION TO THE WAVE FUNCTION. DETERMINISTIC AND PROBABILITY DESCRIPTION OF THE MOTION. HEISENBERG'S INDETERMINATION PRINCIPLE. THE PARTICLE CONFINED IN A SEGMENT. ONE DIMENSIONAL SCHRÖDINGER EQUATION. STATIONARY STATES. THE PARTICLE CONFINED IN A SEGMENT REVISITED. ONE-DIMENSIONAL POTENTIALS. WAVE FUNCTION OF MANY PARTICLES. FERMIONS AND BOSONS (MENTION). FERMI DISTRIBUTION (MENTION). PAULI’S EXCLUSION PRINCIPLE. SCHRÖDINGER'S EQ. FOR A CENTRAL POTENTIAL. THE QUANTUM NUMBERS. THE SPIN. DIPOLE SELECTION RULES. THE AUFBAU PRINCIPLE. THE HUND’S PRINCIPLE. THE PERIODIC TABLE. AFFINITY AND ELECTRONEGATIVITY. IONIC BOND AND COVALENT BOND. THE MOLECULAR ORBITALS. ROTATIONAL AND VIBRATIONAL ENERGIES OF BIATOMIC MOLECULES. HYBRIDIZATION AND POLYATOMIC MOLECULES. RHODOPSIN AND THE MECHANISM OF VISION. INTRODUCTION TO THE CRYSTALLINE STRUCTURE OF SOLIDS. BINDING ENERGY IN SOLIDS. THE ENERGY BANDS. CONDUCTORS, INSULATORS AND SEMICONDUCTORS. LINEAR OPTICS. ABSORPTION AND EMISSION: LUMINESCENCE: FLUORESCENCE AND PHOSPHORESCENCE. THE COLOR: RADIATION-MATTER INTERACTION. PRINCIPLE OF LASER OPERATION. HE-NE, AR + ION AND SEMICONDUCTOR LASER.

INTRODUCTION: THE WORLD AT THE NANOSCALE. SPECTROSCOPY: ABSORPTION AND EMISSION. SPECTRAL DISTRIBUTIONS. BLACK BODY RADIATION AND THE PLANCK EQUATION. THE PHOTOELECTRIC EFFECT: PHENOMENOLOGY AND THE INTERPRETATION OF EINSTEIN. ATOMIC MODELS. BOHR'S POSTULATES. ELECTRONIC TRANSITIONS. DE BROGLIE’S HYPOTHESIS, STATIONARY WAVES. INTRODUCTION TO THE WAVE FUNCTION. DETERMINISTIC AND PROBABILITY DESCRIPTION OF THE MOTION. HEISENBERG'S INDETERMINATION PRINCIPLE. THE PARTICLE CONFINED IN A SEGMENT. ONE DIMENSIONAL SCHRÖDINGER EQUATION. STATIONARY STATES. THE PARTICLE CONFINED IN A SEGMENT REVISITED. ONE-DIMENSIONAL POTENTIALS. WAVE FUNCTION OF MANY PARTICLES. FERMIONS AND BOSONS (MENTION). FERMI DISTRIBUTION (MENTION). PAULI’S EXCLUSION PRINCIPLE. SCHRÖDINGER'S EQ. FOR A CENTRAL POTENTIAL. THE QUANTUM NUMBERS. THE SPIN. DIPOLE SELECTION RULES. THE AUFBAU PRINCIPLE. THE HUND’S PRINCIPLE. THE PERIODIC TABLE. AFFINITY AND ELECTRONEGATIVITY. IONIC BOND AND COVALENT BOND. THE MOLECULAR ORBITALS. ROTATIONAL AND VIBRATIONAL ENERGIES OF BIATOMIC MOLECULES. HYBRIDIZATION AND POLYATOMIC MOLECULES. INTRODUCTION TO THE CRYSTALLINE STRUCTURE OF SOLIDS. BINDING ENERGY IN SOLIDS. THE ENERGY BANDS. CONDUCTORS, INSULATORS AND SEMICONDUCTORS. LINEAR OPTICS. ABSORPTION AND EMISSION: LUMINESCENCE: FLUORESCENCE AND PHOSPHORESCENCE. THE COLOR: RADIATION-MATTER INTERACTION. PRINCIPLE OF LASER OPERATION. HE-NE, AR + ION AND SEMICONDUCTOR LASER.

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
NOTES DISTRIBUTED BY THE TEACHER

- Introduction to the course: purpose and presentation of the program.
- Outlines of Physics of Matter and Optics.
- Diffraction (X-rays and neutrons), Phase transitions, Nucleation of crystals and Gibbs free energy.
- Formation and processing of silica glasses
- Mechanical properties of materials.
- Description of soft matter, polymers and Random Walk.
- Entropy, entropic forces and free energy.
- Viscoelastic response and mechanical properties of soft matter.
- Processing of "soft" glass.
- Forced harmonic oscillator. Response of an electron distribution to an oscillating electric field.
- Origin of the refractive index and its dependence on the wavelength.
- Optical properties of metals and non-metals. Color. Absorption, dispersion and reflection of light. Diffusion of light. Abbe number and its relationship with the refractive index. Polarizers.
- Shape memory materials.
- Optical fibers.
- Surface treatments of the lenses.
- In-depth study of new materials for the production of contact lenses

Suggested book:
- William D. Callister, Jr – Scienza e ingegneria dei materiali. Un introduzione. Edises
- Lecture notes

SYLLABUS 2024-25 (LECTURES)

1. CONTACT LENSES FITTING AFTERCARE: Protocol; Comfort management.
2. FURTHER SOFT CONTACT LENSES: Soft toric; Made of silicone rubber.
3. FURTHER RIGID AND HYBRID CONTACT LENSES: Rigid toric and asymmetrical corneal lenses. Rigid scleral Lens. Hybrid contact lenses
4. CONTACT LENSES IN THE LABORATORY: Quantitative/qualitative verification and inspection of rigid and soft contact lenses; In-office modification notes of rigid contact lenses parameters.
5. ADAVANCED INSTRUMENTAL EXAMINATION OF THE ANTERIOR SEGMENT OF EYE: Corneal aesthesiometry; Corneal pachymetry; Specular microscopy; In vivo confocal microscopy; Anterior tomography
6. OCULAR SURFACE COMPLICATIONS INDUCED BY CONTACT LENS WEAR: Classification; Quantification.
7. CONTROL OF HIGH-ORDER ABERRATIONS: Induced by corneal ectasias, refractive surgery and keratoplasty.
8. ADVANCED APPLICATIONS: Continuous wear; Correction of presbyopia; Tinted contact lenses; Contant lens fitting in infancy; Control of myopic progression: contact lenses compared with other procedures; Orthokeratology; Therapeutic wear; Use of contact lenses under environmental stress.
9. PROBLEM SOLVING: CLINICAL CASES

BOOKS
• LUPELLI L, FLETCHER R, ROSSI A “CONTATTOLOGIA. UNA GUIDA CLINICA” [MEDICAL BOOKS 1998]. ISBN 88-8034-027-1
• EFRON N (EDITOR) “CONTACT LENS PRACTICE” 4TH EDITION, (ELSEVIER, 2023) (ISBN: 9780702084287)
• BENNETT ES , ALLEE HENRY V “CLINICAL MANUAL OF CONTACT LENSES” 5TH EDITION (WOLTERS KLUWER 2020) (ISBN-13978-1496397799)
• LUPELLI L “OPTOMETRIA A-Z. DIZIONARIO DI SCIENZA, TECNICA E CLINICA DELLA VISIONE” (MEDICAL BOOKS, 2014) ISBN 88-8034-003-4; EAN 978-88-8034-002-7

MONOGRAFIE
• SORBARA L. CORREZIONE DEL CHERATOCONO CON LENTI GAS PERMEABILI.
• VAN DER WORP E. “A GUIDE TO SCLERAL LENS FITTING”, VERSION 2.0 [MONOGRAPH ONLINE]. FOREST GROVE, OR: PACIFIC UNIVERSITY; 2015. AVAILABLE FROM: HTTP://COMMONS.PACIFICU.EDU/MONO/10/.
• BARNETT M, D FADEL D, CLINICAL GUIDE FOR SCLERAL LENS SUCCESS. AVAILABLE FROM HTTPS://WWW.SCLERALSUCCESS.COM/


PDF FILES OF PRESENTATIONS AND ARTICLES FROM SCIENTIFIC JOURNALS (IN ITALIAN OR ENGLISH) WILL BE AVAILABLE ON THE TEAMS PLATFORM


PDF DELLE PRESENTAZIONI DEL DOCENTE E ARTICOLI DA RIVISTE SCIENTIFICHE DI AAVV (IN LINGUA ITALIANA O INGLESE) SARANNO DISPONIBILI SULLA PIATTAFORMA TEAMS

The course takes place in the first semester of the third year. Each lesson lasts 4 hours.
Introduction to the Study of Vision
Binocular vision reminders
The stereoscopic sense
Binocular Abnormalities
AC/A ratio and its alterations
Asthenopia
Amblyopia
Aniseiconia
Eccentric fixation
Abnormal retinal correspondence
Strabismus
The numbers of the visual system
Visual Analysis Mathematical Models
OEP – Morgan – Scheiman & Rouse - Scheiman Wick Integrated Analysis
Geriatric Optometry
The field of view
Fundus examination
Pediatric Optometry
NSUCO
DEM test
Mohindra and MEM Schiascopy
Advanced Optometry:
Relationship between the visual-vestibular system and postural tonic
Visual skills and space-time relationship
Vision and balance disorders
Principles of Visual Training
Use of lenses and prisms in visual training
The role of the optometrist in the diagnosis and treatment of the above
Each topic is presented in its theoretical aspects and with detailed explanation of the