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Center for Nonlinear Studies |
CNLS Ulam Scholar Carl Bender to present a two-part lecture series entitled "How to sum a series." Bender, the co-author of the well-known book "Advanced Mathematical Methods for Scientists and Engineers," is the 2006/2007 Ulam Scholar at the Center for Nonlinear Studies and is a world expert in mathematical physics. His lectures are noted for exceptional clarity with the proper share of education and humor present throughout. The lectures will be given at 1:30 in the CNLS Conference Room on Tuesday January 30 and Thursday February 1. Bender remarks that the lectures will provide lesser-known techniques and tricks that should be very useful in practical applications such as numerical simulation.
Perturbation theory almost always gives a divergent series representation of the answer to a problem. Therefore, it is important to know how to find the sum of such a series. I will show that it makes sense to talk about the sum of a divergent series and I will explain methods of summation such as Pade approximants, Euler, Borel, Zeta, and generic summation methods. Illustrative examples will be presented.