Cambridge Texts in Applied Mathematics - 國立臺灣大學

1 Cambridge Texts in Applied MathematicsAll the titles listed below can be obtained from good booksellers or fromCambridge University Press. For a complete series listing FlowH. Ockendon and OckendonA First Course in the Numerical Analysis of Differential EquationsArieh IserlesMathematical Models in the Applied FowlerThinking About Ordinary Differential EquationsRobert E. O'MalleyA Modern Introduction to the Mathematical Theory of Water JohnsonRarefied Gas DynamicsCarlo CercignaniSymmetry Methods for Differential EquationsPeter E. HydonHigh Speed ChapmanWave MotionJ.

2 Billingham and KingAn Introduction to DavidsonLinear Elastic WavesJohn G. HarrisVorticity and Incompressible Majda and BertozziInfinite-dimensional Dynamical RobinsonIntroduction to Symmetry AnalysisBrian J. CantwellB acklund and Darboux TransformationsC. Rogers and SchiefFinite Volume Methods for Hyperbolic LevequeIntroduction to Hydrodynamic DrazinTheory of Vortex BarenblattComplex Variables: Introduction and Applications (Second edition)Mark J. Ablowitz and Athanassios S. FokasA First Course in Combinatorial OptimizationJon Lee Cambridge University University Press0521603692 - Practical Applied Mathematics : Modelling, Analysis, ApproximationSam HowisonFrontmatterMore informationPractical Applied MathematicsModelling, Analysis, ApproximationSAM HOWISONM athematical Institute, Oxford UniversityDirector of The Oxford Centre for Industrial andApplied Mathematics Cambridge University University Press0521603692 - Practical Applied Mathematics .

3 Modelling, Analysis, ApproximationSam HowisonFrontmatterMore informationcambridge university pressCambridge, New York, Melbourne, Madrid, Cape Town, Singapore, S ao Paulocambridge university pressThe Edinburgh Building, Cambridge CB2 2RU, on this title: Cambridge University Press 2005 This book is in copyright. Subject to statutory exceptionand to the provisions of relevant collective licensing agreements,no reproduction of any part may take place withoutthe written permission of Cambridge University published 2005 Printed in the United Kingdom at the University Press.

4 CambridgeA catalogue record for this book is available from the British LibraryLibrary of Congress Cataloguing in Publication dataISBN-13 978-0-521-84274-3 hardbackISBN-10 0-521-84274-3 hardbackISBN-13 978-0-521-60369-2 paperbackISBN-10 0-521-60369-2 paperbackCambridge University Press has no responsibility for the persistence or accuracy of URLs for externalor third-party internet websites referred to in this book, and does not guarantee thatany content on such websites is, or will remain, accurate or appropriate. Cambridge University University Press0521603692 - Practical Applied Mathematics : Modelling, Analysis, ApproximationSam HowisonFrontmatterMore informationContentsPrefacePagexiPart I Modelling techniques1 The basics of do we mean by a model?

5 Of modelling: physical laws and constitutive Units, dimensions and dimensional and fields and and further and dimensional Navier Stokes equations and Reynolds s and further Case studies: hair modelling and cable Euler Bernoulli model for a cable and and further Cambridge University University Press0521603692 - Practical Applied Mathematics : Modelling, Analysis, ApproximationSam HowisonFrontmatterMore informationviContents5 Case study: the thermistor (1) and current flow in thermistor in a and further Case study: electrostatic and further II Analytical techniques7 Partial differential quasilinear partial differential equations: : Poisson nonlinear equations: Charpitt s linear equations in two Case study: traffic models for traffic jams and other discontinuous sophisticated and further The delta function and other point force on a stretched string.

6 Definition of the delta and Heaviside s and further Cambridge University University Press0521603692 - Practical Applied Mathematics : Modelling, Analysis, ApproximationSam HowisonFrontmatterMore informationContentsvii10 Theory of Test The action of a test Definition of a Further properties of The derivative of a Extensions of the theory of Sources and further Exercises14811 Case study: the What is a pantograph? The Impulsive attachment for an undamped Solution near a Solution for a whole Sources and further Exercises167 Part III Asymptotic techniques12 Asymptotic Order Convergence and Sources and further Exercises18013 Regular perturbation Example: stability of a spacecraft in Linear Example: the Small perturbations of a Caveat Exercises19514 Case study: electrostatic painting (2) Small parameters in the electropaint Exercises20215 Case study: piano The notes of a piano.

7 The tonal system of Western music205 Cambridge University University Press0521603692 - Practical Applied Mathematics : Modelling, Analysis, ApproximationSam HowisonFrontmatterMore Tuning an ideal A real Sources and further Exercises21116 Boundary Functions with boundary layers; Examples from ordinary differential Case study: cable Examples for partial differential Exercises23017 Case study: the thermistor (2) Strongly temperature-dependent Exercises23818 Lubrication theory analysis in long thin Lubrication theory approximations: slender Heat flow in a bar of variable Heat flow in a long thin domain with Advection diffusion in a long thin Exercises24919 Case study: continuous casting of Continuous casting of Exercises26020 Lubrication theory for Thin fluid layers.

8 Classical lubrication Thin viscous fluid sheets on solid Thin fluid sheets and Further Exercises27521 Case study: turning of eggs during Incubating Exercises29022 Multiple scales and other methods for nonlinear The Poincar e Linstedt The method of multiple scales294 Cambridge University University Press0521603692 - Practical Applied Mathematics : Modelling, Analysis, ApproximationSam HowisonFrontmatterMore Relaxation Exercises29923 Ray theory and the WKB Classical WKB Geometric optics and ray theory: why do we say light travels in straight lines?

9 Kelvin s ship Exercises314 References318 Index321 Cambridge University University Press0521603692 - Practical Applied Mathematics : Modelling, Analysis, ApproximationSam HowisonFrontmatterMore informationPrefaceThis book was born out of my fascination with Applied mathematicsas a place where the physical world meets the mathematical structuresand techniques that are the cornerstones of most Applied mathematicscourses. I am interested largely in human-sized theatres of interaction,leaving cosmology and particle physics to others. Much of my researchhas been motivated by interactions with industry or by contact withscientists in other disciplines.

10 One immediate lesson from these contactsis that it is a great asset to an interactive Applied mathematician to beopen to ideas from any direction at all. Almost any physical situation hassome mathematical interest, but the kind of Mathematics may vary fromcase to case. We need a strong generalist streak to go with our areas oftechnical thing we need is some expertise in numerical methods. Tobe honest, this is not my strong point. That is one reason why the bookdoes not contain much about these methods. (Another is that if it hadthen it would have been half as long again and would have taken fivemore years to write.)