Mathematica Cookbook

Chapter 13. Science and Engineering

Mmm—but it’s poetry in motion And when she turned her eyes to me As deep as any ocean As sweet as any harmony Mmm—but she blinded me with science And failed me in geometry

When she’s dancing next to me “Blinding me with science—science!” “Science!”

I can hear machinery “Blinding me with science—science!” “Science!”

—Thomas Dolby, “She Blinded Me With Science”

13.0 Introduction

Scientists and engineers make up a large part of the Mathematica user base, and it is hard to think of any scientific or engineering practitioner, no matter how specialized, who could not benefit from Mathematica. I am neither a scientist nor an engineer by profession, but just fiddling around with Mathematica has given me insights into scientific and engineering ideas that otherwise would have taken many years of study.

The goals of this chapter are threefold. First, I want to illustrate techniques for organizing solutions to problems. Many science and engineering problems require numerous variables, and organization becomes paramount. There is not one correct way to organize complex solutions, but I provide two different approaches in 13.6 Solving Basic Rigid Bodies Problems and 13.11 Modeling Truss Structures Using the Finite Element Method. The second goal is to take some of the theoretical recipes covered in earlier chapters and apply them to real-world problems. I often see posts on Mathematica’s primary mailing list questioning the usefulness of function or pattern-based ...