Sam HowisonCambridge University Press, 3/24/2005EAN 9780521603690, ISBN10: 0521603692Paperback, 340 pages, 24.6 x 17.5 x 2.3 cmLanguage: EnglishDrawing 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.Part I. Modelling Techniques1. The basics of modelling2. Units, dimensions and dimensional analysis3. Non-dimensionalisation4. Case studieshair modelling and cable laying5. Case studythe thermistor (1)6. Case studyelectrostatic painting (1)Part II. Mathematical Techniques7. Partial differential equations8. Case studytraffic modelling9. Distributions10. Theory of distributions11. Case studythe pantographPart III. Asymptotic techniques12. Asymptotic expansions13. Regular perturbation expansions14. Case studyelectrostatic painting (2)15. Case studypiano tuning16. Boundary layers17. Case studythe thermistor (2)18. 'Lubrication theory' analysis19. Case studycontinuous casting of steel20. Lubrication theory for fluids21. Case studyeggs22. Methods for oscillators23. Ray theory and other 'exponential' approaches.' ... 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
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