  This article discusses several erroneous claims which appear in textbooks on
numerical methods and computational physics. These are not typos or mistakes an
individual author has made, but widespread misconceptions. In an attempt to
stop these issues from further propagating, we discuss them here, along with
some background comments. In each case, we also provide a correction, which is
aimed at summarizing material that is known to experts but is frequently
mishandled in the introductory literature. To make the mistakes and corrections
easy to understand, we bring up specific examples drawn from elementary physics
and math. We also take this opportunity to provide pointers to the specialist
literature for readers who wish to delve into a given topic in more detail.
