This series of lectures treats certain amusing and interesting aspects of rational function approximations, striving for variety and diversity rather than depth or thoroughness. Graduate students and faculty, knowledgeable in the elements of real and complex analysis, should gain insight into recent developments in the field.

Readership

Table of Contents

• Approximation to \(x^k\)
• Müntz rational functions
• Quadrature in \(H^p\)
• Quadrature in \(H^p\), concluded
• Rational approximation to \(e^x\)
• Using only real zeros and poles
• Approximation of Lip 1 Functions
• Proof of the Lip 1 conjecture
• \(e^x\) using only negative zeros and poles
• Open problems