Mathematical Methods for Physics and Engineering - Matematica.NET

Preface to the second editionSince the publication of the first edition of this book, both through teaching thematerial it covers and as a result of receiving helpful comments from colleagues,we have become aware of the desirability of changes in a number of areas.The most important of these is that the mathematical preparation of currentsenior college and university entrants is now less thorough than it used to be.To match this, we decided to include a preliminary chapter covering areas suchas polynomial equations, trigonometric identities, coordinate geometry, partialfractions, binomial expansions, necessary and sufficient condition and proof byinduction and contradiction.Whilst the general level of what is included in this second edition has notbeen raised, some areas have been expanded to take in topics we now feel werenot adequately covered in the first. In particular, increased attention has beengiven to non-square sets of simultaneous linear equations and their associatedmatrices. We hope that this more extended treatment, together with the inclusionof singular value matrix decomposition, will make the material of more practicaluse to engineering students. In the same spirit, an elementary treatment of linearrecurrence relations has been included. The topic of normal modes has been givena small chapter of its own, though the links to matrices on the one hand, and torepresentation theory on the other, have not been lost.Elsewhere, the presentation of probability and statistics has been reorganised togive the two aspects more nearly equal weights. The early part of the probabilitychapter has been rewritten in order to present a more coherent developmentbased on Boolean algebra, the fundamental axioms of probability theory andthe properties of intersections and unions. Whilst this is somewhat more formalthan previously, we think that it has not reduced the accessibility of these topicsand hope that it has increased it. The scope of the chapter has been somewhatextended to include all physically important distributions and an introduction tocumulants.xxiii