How to use this book

Print editions¶

Bound print books are available for purchase in MATLAB and Julia editions at the SIAM Bookstore. That material is copyright © Society of Applied and Industrial Mathematics.

For everyone¶

First, set up your computing environment:

• Julia
• MATLAB
• Python

This book is littered with computer examples. Here is a Julia example:

println("Welcome to Julia! Do you know π to 100 digits? Because I do! Look:")
setprecision(328)
BigFloat(π)

Welcome to Julia! Do you know π to 100 digits? Because I do! Look:

The output above was not pasted in manually, but inserted by the code cell above it. If you hover over that code cell, you will see an icon in the upper right corner that allows you to copy that code to your clipboard. You will probably do this kind of thing a lot as you work though this book. Many exercises are primarily variations on the examples presented in the text.

One thing you do not have to copy is the code for the functions that are presented in the book as implementations of key algorithms. They will all be available once you install them, as described in the links above.^[1]

Here is a short overview of major features of the book.

Reporting issues¶

If you find an error or want to make a suggestion, please open an issue on GitHub.

Supporting the authors¶

This resource is provided free of charge. We hope it demonstrates how textbooks on the web can be useful in ways printed books can’t match. If you do find it useful, please consider making a small donation to show your support! (Students at the University of Delaware are excepted from this request, because we don’t like the idea of pressuring our own students to pay us.)

For instructors¶

If you find errors or want to suggest improvements, please open an issue.

My publisher, SIAM, is cautious about how this kind of text affects sales of the print book. If you are an instructor, please consider supporting us directly or buying a print copy in MATLAB or Julia so that we can show them this kind of resource can be financially viable.

The table of contents is the same as for the print editions, and most of the content is the same as well. A few of the MATLAB functions in later chapters have been updated from the original for better clarity. Exercises are largely the same, but there have been updates, changes, and additions to those in print, so always check the online version for exercise numbers and details.

Chapters 1–6 can be used as a single-semester introduction to numerical methods, and Chapters 7–13 can be used for a follow-up course. Many sections have downstream connections, but if you are looking for sections that can be skipped with minimal impact on other sections, we suggest the following:

• Section 3.4 on Householder QR factorization
• Section 4.7 on nonlinear least squares
• Section 5.3 on cubic splines
• Section 5.7 on adaptive integration
• Section 6.8 on zero-stability of ODE methods
• Section 7.5 on dimension reduction
• Section 8.7 on matrix-free linear algebra
• Section 8.8 on preconditioning
• Section 9.4 on orthogonal polynomials
• Section 9.7 on improper integrals
• Section 10.6 on the Galerkin method
• Section 12.4 on the wave equation