Practical Applied Mathematics
Modelling, Analysis, Approximation

This book illustrates how the reader's knowledge of applied mathematics can be used to describe the world around them.

Sam Howison (Author)

9780521603690, Cambridge University Press

Paperback, published 24 March 2005

340 pages, 20 b/w illus. 123 exercises
24.6 x 17.5 x 2.3 cm, 0.59 kg

' … 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

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.

Subject Areas: Applied mathematics [PBW]