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' … an entertainingly written book. The effective use of a large number of case studies, shows how mathematics can be used to help address serious real-world problems. this is demonstrated to such an extent that even the most sceptical engineer would have to concede that mathematics can be useful!' Mathematics Today
'Many exercises are the end of each chapter … it is shown in an interesting manner how mathematics can explain processes in nature and techniques … very useful for mathematicians and engineers.' ZAMM
' … a scenic but hands-on route through the classical topics of math modeling via PDEs … this book is an excellent example of the type of text needed for topics in modeling, analysis, and approximations, particularly in new areas that have spread in the forefront of applied math over the last few decades, such as imagining, stochastic modeling, optimization, and biological modeling.' SIAM
'Many exercises are the end of each chapter … it is shown in an interesting manner how mathematics can explain processes in nature and techniques … very useful for mathematicians and engineers.' ZAMM
' … a scenic but hands-on route through the classical topics of math modeling via PDEs … this book is an excellent example of the type of text needed for topics in modeling, analysis, and approximations, particularly in new areas that have spread in the forefront of applied math over the last few decades, such as imagining, stochastic modeling, optimization, and biological modeling.' SIAM
Product Description
Drawing from a wide variety of mathematical subjects, this book aims to show how mathematics is realised in practice in the everyday world. Dozens of applications are used to show that applied mathematics is much more than a series of academic calculations. Mathematical topics covered include distributions, ordinary and partial differential equations, and asymptotic methods as well as basics of modelling. The range of applications is similarly varied, from the modelling of hair to piano tuning, egg incubation and traffic flow. The style is informal but not superficial. In addition, the text is supplemented by a large number of exercises and sideline discussions, assisting the reader's grasp of the material. Used either in the classroom by upper-undergraduate students, or as extra reading for any applied mathematician, this book illustrates how the reader's knowledge can be used to describe the world around them.
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This short introductory chapter is about mathematical modelling. Read the first page
Front Cover | Copyright | Table of Contents | Excerpt | Index | Back Cover
This short introductory chapter is about mathematical modelling. Read the first page
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Front Cover | Copyright | Table of Contents | Excerpt | Index | Back Cover
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2 reviews
12 of 13 people found the following review helpful
Advanced, interesting, not always easy to follow...
2 Oct 2007
Format:Hardcover
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.
1 of 7 people found the following review helpful
nifty
14 April 2008
Format:Hardcover|Amazon Verified Purchase
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.
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