Disclaimer – I was sent a review copy of this book, upon request.
(Image taken from here).
A detailed review of a book like this is almost impossible, given both the range of topics, as well as the number of authors involved. However, I can attempt to give an overview of the feel and breadth of the book.
As can be seen from the table of contents, this is a book of absolutely vast scope, and such scope has both advantages and disadvantages. Its advantages are simply that it covers so many topics, that almost every aspect of applied mathematics that you could think of is included, from numerical techniques, to cell biology, from the theory of solitons to cosmology, from how to write a book for the general public to science in the media, from complex analysis to graph theory, and so many more areas besides. As such it is an amazing reference to give very useful leads to go into the world of research in applied mathematics. It is not a book to give direct and detailed answers, but really it takes one to the right questions to ask and the right techniques to look up.
Perhaps as a disadvantage, or maybe just a feature of such a style of book, it is not a contiguous lesson where one can start at the beginning and learn applied mathematics as you go through it. On reading through each section you will find it is more a taster of a given topic. In a rather encyclopaedic style, it will tell you the common techniques used, the possible problems, the most interesting questions in the field and it does indeed go into the mathematics, but not necessarily in a way that will solve your question. That isn’t necessarily a detraction of how good this book is, but merely a statement of what it is not. Anybody working in a reasonably diverse range of areas of applied mathematics should find this text helpful, simply as a roadmap of the field as a whole. You would not use a map to discover a land, but it could give you an idea of the interesting places to go and will lead to a much richer journey when you get there.
Though the book is written by some hundred authors, the style doesn’t feel artificially discontinuous, and you become used to jumping linguistically, if not stylistically from section to section.
While I would not necessarily recommend this book as an aid if you are trying to pass an applied mathematics exam at undergraduate level, it will give you a greater overview than I can imagine any such course could hope to provide. This is a book for the fascinated student and the working applied mathematician who wants a quick reference to a thousand+ techniques spreading right across the field. In addition, aesthetically, it is a beautiful book to have and I will be happy to continue browsing this book for many years to come, as it is clear that on every read a new area will be discovered which may spark a new line of interest and investigation.