Practical applied mathematics : modelling, analysis, approximation
著者
書誌事項
Practical applied mathematics : modelling, analysis, approximation
（Cambridge texts in applied mathematics）
Cambridge University Press, 2005
- : hbk
- : pbk
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注記
Includes bibliographical references and index
内容説明・目次
内容説明
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.
目次
- 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.
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