Analysis Math Seminar:
4:10pm; Neill Hall 5W
Polynomial approximation for functions on the real line is an old and well-studied area of mathematics. It has attracted the attention of men like Weierstrass, Jacobi and Taylor and has been permanently attached to names like Legendre, Hermite and Chebyshev. Many of the results are beautiful but have little practical significance in the age of high performance computing. One name, Chebyshev has recieved renewed attention as a important tool in approximation theory. In this talk we intend to give a roadmap to Chebyshev polynomials that is both elegant and practical. We will illustrate the fundamental relationship between Laurent series, Fourier series and Chebyshev polynomials. The ideas and theorems are accessible to anyone with a basic understanding of complex analysis and Fourier series.