Areas of Applied Mathematics since they can be viewed as implicitly defining the highest derivative as a function of y and its lower derivatives. Clairaut's. been described elsewhere, including in The Princeton. Companion to Mathematics. In one sense, most applied mathematicians have for decades aggressively. Contents. Preface ix. Contributors xiii. Part I Introduction to Applied. Mathematics. I What Is Applied Mathematics? 1. I The Language of Applied Mathematics.
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Home; The Princeton Companion to Applied Mathematics. AddThis Sharing Buttons. Share to Table of Contents [PDF] · Preface [PDF] · Contributors [PDF]. eBook (PDF): Publication Date: September ; Copyright year: ; ISBN Modeled on the popular Princeton Companion to Mathematics, this volume is an disciplines seeking a user-friendly reference book on applied mathematics. This is the most authoritative and accessible single-volume reference book on applied mathematics. Featuring numerous entries by leading experts and.
It is certainly a desktop book, that you would not conveniently take on your lap. Moreover, it is not like a dictionary where you look up something briefly, but you probably want to sit down and read through an entry completely. What I do appreciate are the ample graphical illustrations and that references are restricted to the essentials for further reading and these are placed at the end of the entry, and not scattered through the text.
In the text we do find pointers to other entries in the book, but also that is kept to a moderate level. It is obvious that some topics will show up at several places.
Think of linear algebra, differential equations, or numerical techniques, that will repeatedly need discussion in different contexts. So for these topics you do not have a single structured entry.
You will have to look it up in the elaborate index and compose your own survey by jumping back and forth. As I said before, you do not read this book cover to cover, and yet many definitions and concepts are given in parts I and II that are used in the more advanced entries.
There is not always a cross reference, and if you are a beginning student, it might require many jumps to the index, diversions to other entries, swiping back and forth, that can make it difficult to keep track.
That would not be different with an e-version, but it would reduce the unwieldy manipulation needed for flapping thick layers of pages. If you are a more experienced scientist, you will have easy access to a comprehensive survey of some topic you might be less familiar with.
As the editors state it themselves, they do not claim to be exhaustive, and it will not be difficult to find your favorite topic that is not or not in sufficient detail discussed here.
For example support vector machines and neural nets are mentioned relatively briefly, machine learning is not explicitly discussed, and there is big activity in nano-science that one might consider not well represented, etc.
But one could come up with many other topics as well. Some topics are deliberately left out. These are mentioned in the introduction: like wavelets, statistics, cryptography, For these the reader is referred to the Mathematics Companion one more reason to have both volumes. Do not consider this a shortcoming.
It is an unavoidable feature of such a project, since a limited time and space forces the editors to make a choice. So, all in all, do not interpret my critique too hard. In fact, I quite like the concept and the book, which is the result of a lot of hard work by many. It must be possible though to work out a hyperlinked version with the same kind of ideas.
It would be possible to make that more dynamic and keep it more easily up-to-date. That however, would require much higher investment of editors, authors and maintenance.
For the moment, this is probably the best alternative available. Reviewer: Adhemar Bultheel Book details This is an extensive, though not exhaustive, survey of applied mathematics.
It has a mixture of short definitions and concepts, and longer survey entries.
It has been a major project that eventually resulted in this amazing product. It is surely a valuable resource for exposing young mathematicians to possible areas of applied mathematics for research and further study. Without a doubt PCAM is an important contribution to the mathematical literature.
Graham, MathSciNet "[A]n excellent reference that successfully compiles into a readable and engaging form the broad range of topics that an applied mathematician might encounter in their career. As a reader, I find myself flipping through the pages and becoming engaged in new and interesting ideas from the world of applied math.
Farmer, Reference Reviews "Astonishing. As a reference, it is superb. This book took years to produce, and that effort shows in the excellent final product.
Better still, it does so in a remarkably clear and friendly voice. An instant classic.
This book will be a landmark for decades ahead.