Overview

Perturbation methods are old and powerful. Solutions are provided as formulas rather than numbers or pictures, so the skill of the person (or machine!) reading the formula is essential. This unique book presents several classical methods to solve perturbation problems using backward error analysis. This lessens the likelihood of blunders because the method for testing the validity of the answers is uniform. It also demands that the modeler consider the effects of other changes to the data or model equations. For this the concept of a condition number from numerical analysis is used. Perturbation Methods Using Backward Error includes includes a discussion of the impact on science of the idea of perturbation, includes a chapter on the relatively novel renormalization group method, uses computer algebra (via Maple) to ease the computing of symbolic answers, and provides solutions to all exercises.

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9781611978865

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Robert M. Corless is emeritus distinguished university professor at Western University, a member of the Rotman Institute of Philosophy, former scientific director of The Ontario Research Center for Computer Algebra, and an adjunct professor at the Cheriton School of Computer Science, the University of Waterloo. He is the editor-in-chief of Maple Transactions. In 2019 he was awarded the Ford-Halmos Prize, along with the late Jonathan Borwein, for expository excellence for the paper Gamma and Factorial in the Monthly. Nicolas Fillion is an associate professor of philosophy at Simon Fraser University. His main research contributions are in the philosophy of science and applied mathematics, but his research and teaching include the history of logic, mathematics, and science, formal logic, decision and game theory, critical thinking, philosophy of language, ancient Greek philosophy, and epistemology broadly construed. In 2019 he was awarded the Cormack Award for Excellence in Teaching.

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