Fundamentals of Numerical Analysis and Symbolic Computation: Theory and applications of orthogonal polynomials

Lecturer: Prof. Diego Dominici

Lecture no.: 326.003

ECTS: 3.00, hours: 2.0

Time: Tuesdays, 1:45 pm to 3:15 pm

Place: seminar room BA 9912; exceptions: March 20, 2018: S2 044 and April 24, 2018: S2 046

Abstract:

Orthogonal polynomials have a long history, whose origins can be traced back to Legendre's work on planetary motion. They have important applications to physics, probability and statistics, computer science, and virtually every branch of mathematics.

In this course we will cover the fundamental theory of orthogonal polynomials, including structure relations, properties of the zeros, Gauss quadrature, characterization theorems, and asymptotic behavior.

Topics to be considered (depending on the interest of the audience) would include: semiclassical polynomials, Toda systems, quantum mechanical models, numerical analysis, stochastic processes, continued fractions, and q-series.