Thinking About Equations: A Practical Guide for Developing Mathematical Intuition in the Physical Sciences and Engineering Review

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Thinking About Equations: A Practical Guide for Developing Mathematical Intuition in the Physical Sciences and Engineering Review"Thinking About Equations" is a collection of techniques and examples from across a broad range of science and engineering disciplines, organized according to the underlying themes, with insightful demonstrations of how they may be applied to realistic situations.
In his autobiography, Physicist Richard Feynman attributes his success at solving problems, in part, to the "Different Box of Tools" he acquired in his early studies. This text now offers any reader a versatile set of tools to dissect, analyze, and solve problems across a broad range of fields. It also includes general strategies for analyzing problems and identifying interrelations and common motifs, whereby one may gain a deeper understanding of the material.
The book addresses broad themes common to a variety of disciplines. For example, several chapters illustrate the use of diagrams, graphs, and symmetries to quickly and efficiently pare down the feasible solutions of a problem, and characterize the final result. These techniques have a natural application for numerical problems, and the text illustrates this using Fourier Series as an example.
Another chapter highlights the utility of special and limiting cases. For example, proving that an equation is correct can be a difficult task in general, while demonstrating an equation is incorrect requires only one counterexample. This technique can be used to quickly eliminate "dead ends" and "wrong turns" in the search for correct solutions.
Movies often portray scientists and engineers as memorizing inconsequential data out to the sixth decimal place. The truth is often the opposite--they are more interested in relationships and interdependencies, and the chapter on scaling and dimensional analysis will help the reader to appreciate the power of such relations.
This text can serve as a valuable reference for undergraduate and graduate students in science and engineering, as well as anyone interested in understanding a technical subject at a deeper level.Thinking About Equations: A Practical Guide for Developing Mathematical Intuition in the Physical Sciences and Engineering Overview

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