[Scaling (Cambridge Texts in Applied Mathematics)] [Author: Barenblatt, Grigory Isaakovich] [November, 2003]

Cambridge Texts in Applied Mathematics #34

by Grigory Isaakovich Barenblatt

Starting from dimensional analysis and physical similarity, G. Barenblatt describes the art of discovering scaling laws. He demonstrates the concepts of intermediate asymptotics and the renormalization group as natural consequences of self-similarity and shows how and when these tools can tackle the task at hand, and when they cannot. Based on courses taught to undergraduate and graduate students, the book can also be used independently by biologists, chemists, astronomers, engineers and geoscientists.

Hardcover

First published November 13, 2003

Reviews

[George · Rating 5 out of 5]

This is a very interesting subject. When I encountered dimensional analysis at school and in undergradute physics, it seemed like black magic. How can you get such important results so easily, surely there must be a price to pay for such powers? Do these tricks always work?

This book finally answered my longstanding questions. It shows you when dimensional analysis works, and tried to show why it works. More importantly, it shows you when it does not work. In short, it tells the full story, rather than just the 'best case' examples that my teachers showed me.

In addition, it goes one level deeper, and explains intermediate asymptotics. This is a technique that you might use when basic dimensional analysis is insufficient.

The book is sometimes too light on details. It appears to be a condensed version of Barenblatt's "Scaling, Self-Similarity and Intermediate Asymptotics" and the reader might want to get that also if they need more detail. Also, the very old book by Bridgman (Dimensional Analysis) might be worth reading if you only want to read about dimensional analysis.

But as an introduction to the topic, this short book is a excellent read.