Customer Reviews

Practical Applied Mathematics: Modelling, Analysis, Approximation (Cambridge Texts in Applied Mathematics)

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Oliver Heaviside of operational calculus (i.e. Laplace transform) fame once said "Even Cambridge mathematicians deserve justice." However, the author of this Cambridge Press book is actually from Oxford, and so I did not bump up my rating of 3 stars. However, this rating may also be unjust. There are many very interesting examples from a wide range of subject areas, but unless you are studying that subject area, I think it will be hard for most to follow along. I would absolutely rate this book 5 stars if there was a substantial "hints" section in the back or a little more exposition in the text that would enable those with a less broad background to follow along more easily. When the author says in the preface he assumes you have a background in vector calculus, partial differential equations, fluid mechanics, linear algebra, etc., pay attention, he means it. The book is good for advanced students who want to get a taste of areas often not covered in undergraduate engineering coursework (e.g. Charpit's method for solving first order nonlinear PDEs, Buckingham-Pi theorem of dimensional analysis, "generalized" functions, asymptotics, perturbation theory, etc.). I think the order of presentation is questionable at times. As one example, in problem 2 of section 2.5, after giving the formula for the capacitance of a parallel plate capacitor, the author asks us to estimate the electrical capacitance of an elephant by dimensional analysis. I like this as an unusual example, but I am not sure how the parallel plate capacitor formula helps. After another paragraph about how much charge a human body can store (still part of problem 2.5), he gives an outline of the derivation of a capacitance of an isolated sphere, which I know can be used to give an upper bound (if the sphere encloses the elephant) for both the above examples, but the author never points this out, leaving it just hanging there. He then continues on with an RC circuit example (while still in problem 2.5!!). Because the spherical capacitance formula comes well after the elephant question, and looks like it is leading into the next part of the question (which rambles on endlessly), I am torn between applauding the author for including an interesting example that makes one think about how to calculate a useful estimate when the elephant shape is too complex to handle exactly and complaining that he can give a few more hints so that someone not that familiar with electrostatics can follow the problem more easily.

so the math is for, like, juniors (US/ugrad) who have had a smattering of mechanics/E&M/etc. it's lots of tiny tricks (ahem i mean techniques) and neat-o examples. i thouroughly enjoy it. each section is some cool useful technique applied to a fairly original problem like eggs or bombs or underwater cables.