Thursday,
April 11, 4:30 p.m. PSA 203
Toby Driscoll
Dept Math Sciences, U Delaware
Numerical Computing with Functions
Abstract
Most of what we teach students in early calculus is the manipulation of algebraic expressions. While these manipulations unquestionably made calculus the valuable subject it is today, they are no longer the only legitimate way to apply calculus; in fact, in the area of differential equations, numerical manipulations are the dominant mode of solution. Experienced numerical analysts and approximation theorists understand the many connections between numerical values and the underlying function objects they represent, but this understanding does not always penetrate deeply into other areas and application domains. The Chebfun project represents a vision and implementation of what it means to compute numerically from a function-centered point of view. By exploiting advanced theory, fast algorithms, and modern programming techniques, key operations such as integration, differentiation, and rootfinding become as straightforward and as accurate as arithmetic on numbers, with no computational expertise required from the user in most cases. The resulting system combines symbolic feel with numeric speed.
