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"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
- Sales Rank: #770836 in Books
- Published on: 1995-01-27
- Released on: 1995-01-27
- Original language: English
- Number of items: 1
- Dimensions: 9.24" h x .63" w x 6.52" l, .93 pounds
- Binding: Paperback
- 286 pages
Most helpful customer reviews
16 of 20 people found the following review helpful.
are we reading the same book ?!?
By Greg Ruo
I read the previous two reviews and purchased this book... and now I am quite disappointed. Frankly, I wonder if these reviews are made by real users, or...
First of all, this book is a mere reprint of a 1978 edition. The fonts are typewriter-style of three decades ago, so symbols are awkward and difficult to read. Many drawing and sketches are handwritten.
The first two chapters it talks in general about what is a model. These chapters are mainly philosophical, pretty boring in my opinion.
The third chapter "How to formulate a model" should contain what I was looking for. However, it describe in very general terms how you can put down a model. The description is in my opinion too general, discussing trivial well known principles. There is not a clear, well-stated method of approach. I expected a discussion based on examples of real life problems, firstly simple ones then going to more complex ones. Instead the author make a foggy presentation on how to deal with a problem, jumping to another one, without a clear line of thought.
The treatment is incredibly jumpy: the third equation of this chapter is already involving integrals, page 38 starts with "How to formulate a model", page 41 there is an example involving triple integrals on a volume...
If you are interested in a modern book that guides you or your students to the art of putting down a mathematical model of a system you want to describe, I do not think this book is for you and I do not suggest you to purchase it.
Honestly, I have no idea how this book can be useful at all these days.
MR
35 of 40 people found the following review helpful.
Mathematical Modelling Genius
By Mr Steven L. McGahey
One thousand word limit to this review, eh? Well, I could do it in one word: Fantastic.
This book approaches mathematical modelling from a conceptual level, with Rutherford explaining how to make numbers dance through equations any which way you want them. His depth of knowledge as a Chemical Engineer, combined with his fantastic mathematical skills means that he has knows what needs to be done in various situations and how best to do it.
The attribute that makes this, and all of Rutherfords work stand out from the rest of the pack, is his undeniable presence when writing. Rhetoric, personal insights and may the dry-and-dusty-academic world forgive him, humour (!) can be found throughout this book, making its reading quite pleasurable.
Finally, a number of thoughtful articles of his have been bound into the back of this edition, providing useful "food for thought" for those people for whom modelling is a way of life. If you are considering any of the finer points of mathematical modelling (I was doing a PhD on the subject), this book is a must-have (not just a must-read). You'll come back to it time and time again for the articles, long after you've digested the rest of the book.
3 of 3 people found the following review helpful.
Very interesting and thought provoking, but not as your first book in modelling
By Secluded Path
This is an extremely rich book which deals with the basics and philosophy of mathematical modelling. Despite it's age, the book has a lot to give to those who already have experience in the field of mathematical modelling and who certainly will see through the oddities of the book and appreciate its many subtleties. The book is affordable and is well written, albeit in a form that seems "ancient". The author was not only an outstanding scientist but also a gifted writer and a highly educated person. His prose might therefore feel strange for people not used to read philosophical or more verbose "social science"-type texts. I enjoyed the book indeed, but I would not recommend it as your first approach to mathematical modelling. For that purpose you might choose Edward A. Bender's book instead.
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