Essential Mathematical Methods for the Physical Sciences

Описание

Preface
Since Mathematical Methods for Physics and Engineering (Cambridge: Cambridge
University Press, 1998) by Riley, Hobson and Bence, hereafter denoted by MMPE, was
first published, the range of material it covers has increased with each subsequent edition
(2002 and 2006). Most of the additions have been in the form of introductory material covering polynomial equations, partial fractions, binomial expansions, coordinate geometry
and a variety of basic methods of proof, though the third edition of MMPE also extended
the range, but not the general level, of the areas to which the methods developed in the
book could be applied. Recent feedback suggests that still further adjustments would be
beneficial. In so far as content is concerned, the inclusion of some additional introductory
material such as powers, logarithms, the sinusoidal and exponential functions, inequalities
and the handling of physical dimensions, would make the starting level of the book better
match that of some of its readers.
To incorporate these changes, and others to increase the user-friendliness of the text,
into the current third edition of MMPE would inevitably produce a text that would be too
ponderous for many students, to say nothing of the problems the physical production and
transportation of such a large volume would entail. It is also the case that for students for
whom a course on mathematical methods is not their first engagement with mathematics
beyond high school level, all of the additional introductory material, as well as some
of that presented in the early chapters of the original MMPE, would be ground already
covered. For such students, typically those who have already taken two or three semesters
of calculus, and perhaps an introductory course in ordinary differential equations, much
of the first half of such an omnibus edition would be redundant.
For these reasons, we present under the current title, Essential Mathematical Methods
for the Physical Sciences, an alternative edition of MMPE, one that focuses on the core of a
putative extended third edition, omitting, except in summary form, all of the “mathematical
tools” at one end, and some of the more specialized topics that appear in the third edition
at the other. The emphasis is very much on developing the methods required by physical
scientists before they can apply their knowledge of mathematical concepts to significant
problems in their chosen fields.
For the record, we note that the more advanced topics in the third edition of MMPE
that have fallen victim to this approach are quantum operators, tensors, group and representation theory, and numerical methods. The chapters on special functions, and the
applications of complex variables have both been reduced to some extent, as have those
on probability and statistics.
At the other end of the spectrum, the excised introductory material has not been
altogether lost. Indeed, Appendix A of the present text consists entirely of summaries,
in the style described in the penultimate paragraph of this Preface, of the material that

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