Acquire the basics for using the features and mathematical methods necessary for the description of physical phenomena in optics. Acquire skills to understand and describe in rigorous form the classical and modern optics phenomena.
teacher profile teaching materials
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 II" [C.T.II]
Greg Gbur ``Mathematical Methods for Optical Physics and Engineering" [Gbur]
Programme
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.
Core Documentation
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]
Type of delivery of the course
Blackboard lectures and exercises. Most of the course consists in blackboard excersises, aimed at clarifying and making familiar with the topics.Type of evaluation
Middle course written exam, written exam. The oral exam is optional, under request of the student. The program is divided in two parts.The written exam can last two hours: one hour for the first part of the program, one hour for the second part of the program. teacher profile teaching materials
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 II"
Greg Gbur, "Mathematical Methods for Optical Physics and Engineering"
Programme
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.
Core Documentation
Claudio Canuto, Anita Tabacco, "Analisi Matematica I"Claudio Canuto, Anita Tabacco, "Analisi Matematica II"
Greg Gbur, "Mathematical Methods for Optical Physics and Engineering"
Reference Bibliography
Claudio Canuto, Anita Tabacco, "Analisi Matematica I" Claudio Canuto, Anita Tabacco, "Analisi Matematica II" Greg Gbur, "Mathematical Methods for Optical Physics and Engineering"Type of delivery of the course
In order to achieve the expected goals, lessons will take place through taught classes on the board which will also provide a suitable number of exercises to allow the student to apply what they have learned to problems that can be easily found in physics.Attendance
Course attendance is optional; the study of the recommended texts is sufficient to achieve the goal of the course.Type of evaluation
Learning is checked firstly through written exams. The written tests are aimed at verifying the level of effective understanding of the concepts and the students' ability to apply them in recurrent physics problems in Optics. The exam is passed if, in addition to reporting the sufficiency in the written assignments, the student will be able to pass an oral test based on questions extracted from the course program.