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Klappentext This book shows how mathematics is more than a series of calculations. Mathematical topics include distributions! ordinary and partial differential equations! asymptotic methods and the basics of modelling. Applications range from piano tuning to egg incubation and traffic flow. The text is supplemented by large numbers of exercises and sideline discussions! assisting the readers 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 readers knowledge can be used to describe the world around them. ' ... 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 Zusammenfassung Used either 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. Topics include distributions! asymptotic methods and the basics of modelling. Applications range from piano tuning to egg incubation and traffic flow. Inhaltsverzeichnis Part I. Modelling Techniques: 1. The basics of modelling; 2. Units, dimensions and dimensional analysis; 3. Non-dimensionalisation; 4. Case studies: hair modelling and cable laying; 5. Case study: the thermistor (1); 6. Case study: electrostatic painting (1); Part II. Mathematical Techniques: 7. Partial differential equations; 8. Case study: traffic modelling; 9. Distributions; 10. Theory of distributions; 11. Case study: the pantograph; Part III. Asymptotic techniques: 12. Asymptotic expansions; 13. Regular perturbation expansions; 14. Case study: electrostatic painting (2); 15. Case study: piano tuning; 16. Boundary layers; 17. Case study: the thermistor (2); 18. 'Lubrication theory' analysis; 19. Case study: continuous casting of steel; 20. Lubrication theory for fluids; 21. Case study: eggs; 22. Methods for oscillators; 23. Ray theory and other 'exponential' approaches....
