Practical Applied Mathematics: Modelling, Analysis, Approximation (Cambridge Texts in Applied Mathematics)
Cambridge University Press, 3/24/2005
EAN 9780521603690, ISBN10: 0521603692
Paperback, 340 pages, 24.6 x 17.5 x 2.3 cm
Language: English
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.
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.
' ... 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