TARANTINO CECILIA
(syllabus)
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.
(reference books)
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]
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Università Roma Tre