Industrial Mathematics: Case Studies in the Diffusion of Heat and Matter (Australian Mathematical Society Lecture Series)
Cambridge University Press, 12/13/2001
EAN 9780521807173, ISBN10: 0521807174
Hardcover, 216 pages, 22.9 x 15.2 x 1.6 cm
Language: English
The focus in this text is on mathematical modelling stimulated by contemporary industrial problems involving heat conduction and mass diffusion. These include continuous metal casting, laser drilling, spontaneous combustion of industrial waste, water filtration and crop irrigation. The industrial problems prove to be an excellent setting for the introduction and reinforcement of modelling skills, equation solving techniques, qualitative understanding of partial differential equations and their dynamical properties. Mathematical topics include setting up partial differential equations and boundary conditions, dimensional analysis, scaling, perturbation expansions, boundary value problems, Fourier series, symmetry reductions, Stefan problems and bifurcations. For students of mathematics, engineering, or any other related discipline, this will be a great introduction to modelling the real world.
1. Preliminaries
2. Case study
continuous casting
3. Case study
water filtration
4. Case study
laser drilling
5. Case study
factory fires
6. Case study
irrigation
7. Conclusions.
' ... an excellent text ... written and typeset so nicely, that it is a real pleasure to read it. This textbook is highly recommended for all students of mathematics, science and engineering, and will certainly benefit anyone who wishes to understand better how mathematical techniques are 'projected' onto the real-world problems. You will definitely understand much more about mathematical modeling and may even start loving it after having read this very nice book.' Zentralblatt fur Mathematik und ihre Grenzgebiete Mathematics Abstracts 'I can wholeheartedly recommend it for a second year modelling course.' The Mathematical Gazette