The essential skills of modeling — abstraction, analysis, simulation, and validation — are central in engineering, natural sciences, social sciences, medicine, and many other fields. Some students learn these skills implicitly, but in most schools they are not taught explicitly, and students get little practice. That's the problem this book is meant to address.

At Olin College, we use this book in a class called Modeling and Simulation, which all students take in their first semester. My colleagues, John Geddes and Mark Somerville, and I developed this class and taught it for the first time in 2009.

It is based on our belief that modeling should be taught explicitly, early, and throughout the curriculum. It is also based on our conviction that computation is an essential part of this process.

If students are limited to the mathematical analysis they can do by hand, they are restricted to a small number of simple physical systems, like a projectile moving in a vacuum or a block on a frictionless plane.

And they will only work with bad models; that is, models that are too simple for their intended purpose. In nearly every mechanical system, air resistance and friction are essential features; if we ignore them, our predictions will be wrong and our designs won't work.

In most freshman physics classes, students don't make modeling decisions; sometimes they are not even aware of the decisions that have been made for them. Our goal is to teach the entire modeling process and give students a chance to practice it.

This book teaches the entire modeling process and give students a chance to practice it. It is used in a class called Modeling and Simulation at Olin College, which all students take in their first semester.