Mathematical Modelling Techniques

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Courier Corporation, 1 gen 1994 - 269 pagine

"Engaging, elegantly written." — Applied Mathematical Modelling
Mathematical modelling is a highly useful methodology designed to enable mathematicians, physicists and other scientists to formulate equations from a given nonmathematical situation. In this elegantly written volume, a distinguished theoretical chemist and engineer sets down helpful rules not only for setting up models but also for solving the mathematical problems they pose and for evaluating models.
The author begins with a discussion of the term "model," followed by clearly presented examples of the different types of models (finite, statistical, stochastic, etc.). He then goes on to discuss the formulation of a model and how to manipulate it into its most responsive form. Along the way Dr. Aris develops a delightful list of useful maxims for would-be modellers. In the final chapter he deals not only with the empirical validation of models but also with the comparison of models among themselves, as well as with the extension of a model beyond its original "domain of validity."
Filled with numerous examples, this book includes three appendices offering further examples treated in more detail. These concern longitudinal diffusion in a packed bed, the coated tube chromatograph with Taylor diffusion and the stirred tank reactor. Six journal articles, a useful list of references and subject and name indexes complete this indispensable, well-written guide.
"A most useful, readable-and stimulating-book, to be read both for pleasure and for enlightenment." — Bulletin of the Institute of Mathematics and Its Applications

 

Sommario

What is a model?
12 Relations between models with respect to origins
5
13 Relations between models with respect to purpose and conditions
16
14 How should a model he judged?
20
The different types of model
25
22 Finite models
27
23 Fuzzy subsets
30
24 Statistical models
32
How should a model be evaluated?
102
52 Extensions of models
110
53 Observable quantities
116
54 Comparison of models and prototypes and of models among themselves
117
Longitudinal diffusion in a packed bed
120
The coated tube chromatograph and Taylor diffusion
129
The stirred tank reactor
143
References
156

26 Stochastic models
34
How to formulate a model
37
32 Constitutive relations
42
33 Discrete and continuous models
45
How should a model he manipulated into its most responsive form?
52
42 Natural languages and notations
56
43 Rendering the variables and parameters dimensionless
58
44 Reducing the number of equations and simplifying them
67
45 Getting partial insights into the form of the solution
75
Subject index
174
Name index
178
a conversation on some aspects of mathematical modelling
184
THE JAIL OF SHAPE
194
THE MERE NOTION OF A MODEL
210
Ut Simulacrum Poesis
222
MANNERS MAKYTH MODELLERS
240
HOW TO GET THE MOST OUT OF AN EQUATION WITHOUT REALLY TRYING
250
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