Top critical review
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Let down by deplorably slapdash maths
on 24 August 2016
I wanted to like this book - it is engagingly written and in places explains things really well. Unfortunately, in other places it makes a complete mess of things, particularly where the mathematics is concerned. There is a vital difference between a judicious choice of the level of mathematical rigour that is appropriate to context and audience, and sweeping key analytical issues under the carpet. This author gets it wrong: he cops out and engages in magical hand waving whenever the going gets tough; the passages on the differences between differentials, variations, partial derivatives, and virtual displacement read more like medieval zoology. It is books like this one that deprive physics undergrads from properly understanding the fundamental concepts of analysis, and perhaps making them feel that they are to blame for their persistent befuddlement. Incidentally, readers of this book are advised to look elsewhere for the correct definition of "functional" --- it does not bother me so much that he gets the terminology wrong, but that it betrays a compete lack of understanding of what is going on mathematically.