For reasons that are explained in the preface to Foundation Mathematics for the Physical Sciences (FMPS), the text of the third edition of Mathematical Methods for Physics and Engineering (MMPE) (Cambridge: Cambridge University Press, 2006) by Riley, Hobson and Bence, after a number of additions and omissions, has been republished as two somewhat overlapping texts. Essential Mathematical Methods for the Physical Sciences contains most of the more advanced material, and specifically develops mathematical methods that can be applied throughout the physical sciences; FMPS is an augmented version of the more introductory material, principally concerned with mathematical tools rather than methods. The full text of MMPE, including all of the more specialised and advanced topics, is still available under its original title.

As in the third edition of MMPE, the penultimate subsection of each chapter of FMPS consists of a significant number of problems, nearly all of which are based on topics drawn from several sections of that chapter. Also as in the third edition, hints or outline answers are given in the final subsection, but only to the odd-numbered problems, leaving all even-numbered problems free to be set as unaided homework.