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Practical Applied Mathematics: Modelling, Analysis, Approximation

Sam Howison
Cambridge Univesity Press
Publication Date: 
Number of Pages: 
Cambridge Texts in Applied Mathematics
[Reviewed by
Maeve McCarthy
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This book is written with more prerequisites than many other introductions to modeling or applied mathematics. Most US students taking such classes will have had calculus and linear algebra. They may even have had a probability and statistics class or a course on partial differential equations. It is unlikely that they will have had a fluid dynamics course — although there will be a few at universities with strong engineering programs.

The expectation of knowledge about basic fluid mechanics is both this book's strength and its weakness. On the positive side, the author can use this material to introduce many interesting and sophisticated examples. Howison treats a wide variety of key topics including (but not limited to) dimensional analysis, nondimensionalization, linear and non-linear PDEs, distribution theory and asymptotic analysis. Applications range from traditional examples, such as beams and traffic modeling, to less traditional examples such as incubating eggs.

Unfortunately, students who have not had a semester of fluid mechanics will be somewhat lost as early as Chapter 1. Overall, I like this book and would love to use it. But it really is more suitable for a second course in applied mathematics rather than the introductory modelling course offered at institutions like mine.

Maeve McCarthy is Associate Professor of Mathematics at Murray State University in Kentucky.


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.