A Graduate Introduction to Numerical Methods

Robert M. Corless and I are pleased to announce the publication of a new graduate textbook in applied mathematics, entitled A Graduate Introduction to Numerical Methods, From the Viewpoint of Backward Error Analysis. The book is currently available in stores.


The book has made the Notable Computing Books and Articles of 2013 list of the ACM Computing Reviews in the "Mathematics of Computing" section. Computing Reviews' Best of 2013 list consists of book and article nominations from their reviewers, Computing Reviews category editors, the editors in chief of journals they cover, and others in the computing community.

The book has also been featured in a positive review by Nick Higham, one of the leader in the field of numerical analysis and applied mathematics.
Other comments by leading figures include:
"I really like the focus on backward error analysis and condition. This is novel in a textbook and a practical approach that will bring welcome attention." Lawrence F. Shampine
"I love that book." John Butcher

To access the Matlab and Maple codes used in this book, consult the code repository.

Here are some features of the book:

  • Publisher: Springer. 868 p. 199 illus., 6 illus. in color. ISBN 978-1-4614-8452-3.
  • It is available as ebook.
  • The book is available for pre-order at many places, including Springer ($99 USD), Amazon.com ($79.17 USD) and Amazon.ca ($81.63 CAD). Overall, you can find the cheapest copy by using the metasearch engine bookfinder.com. We also encourage people to get a copy for $25 only using Springer's My Copy service.
  • Contents: Computer Arithmetic & Fundamental Concepts of Computation.- Polynomials and Series.- Rootfinding and Function Evaluation.- Solving Ax = b.- Solving Ax = x.- Structured Linear Systems.- Iterative Methods.- Polynomial and Rational Interpolation.- The Discrete Fourier Transform.- Numerical Integration.- Numerical Differentiation and Finite Differences.- Numerical Solution of ODEs.- Numerical Methods for ODEs.- Numerical Solutions of Boundary Value Problems.- Numerical Solution of Delay DEs.- Numerical Solution of PDEs.
  • About the book:
    • Provides consistent development of formulae using barycentric interpolation
    • Independence of chapters allowing for greater teaching flexibility
    • Integration with Matlab and Maple, many algorithms presented in pseudocode
    This book provides an extensive introduction to numerical computing from the viewpoint of backward error analysis. The intended audience includes students and researchers in science, engineering and mathematics. The approach taken is somewhat informal owing to the wide variety of backgrounds of the readers, but the central ideas of backward error and sensitivity (conditioning) are systematically emphasized. The book is divided into four parts: Part I provides the background preliminaries including floating-point arithmetic, polynomials and computer evaluation of functions; Part II covers numerical linear algebra; Part III covers interpolation, the FFT and quadrature; and Part IV covers numerical solutions of differential equations including initial-value problems, boundary-value problems, delay differential equations and a brief chapter on partial differential equations. The book contains detailed illustrations, chapter summaries and a variety of exercises as well as some Matlab codes provided online as supplementary material.
  • Download a preliminary sample of the book!

Cite as (APA format):
Corless, R.M. & Fillion, N. (2013). A Graduate Introduction to Numerical Methods, From the Viewpoint of Backward Error Analysis, Springer.

BibTeX Entry:
title={A Graduate Introduction to Numerical Methods, From the Viewpoint of Backward Error Analysis},
author={Corless, Robert~M. and Fillion, Nicolas},

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  Office hours

For the Winter 2016 semester, I will not hold regular office hours since it is my research semester. I will be available for meeting upon requests by email.

I will be away for the following weeks for conferences:

  • Week of April 11
  • May 11-16
  • Week of May 23
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