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The purpose of this module is to explain units and dimensional analysis.

Table of contents

Preface

General

This module is part of a series of modules designed for teaching the physics component of GAME2302 Mathematical Applications for Game Development at Austin Community College in Austin, TX. (See GAME 2302-0100: Introduction for the first module in the course along with a description of the course,course resources, homework assignments, etc.)

The purpose of this module is to explain units and dimensional analysis.

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General background information

As a young engineering student many years ago, I was told that when evaluating mathematical expressions, I should always embed the units in theexpression, manipulate them algebraically, and confirm that the units that survive until the end of the evaluation are correct relative to the problemspecifications.

Three good reasons

There are at least three good reasons for following this procedure:

  • It shows what the units of the result are. A common mistake is to get the correct numerical result of a calculation but to write it with the wrong units.
  • It shows where unit conversions must be performed. If units that should have canceled do not cancel, we need to go back and perform the necessary conversions. Forexample, when a speed in miles per hour is being calculated and the result comes out with units of miles per second, we should convert seconds to hours.
  • It helps to locate mistakes. If a velocity (meters per second) is being calculated and the units come out as seconds per meter, we know to look for an error.

Formatting mathematical expressions

Multiple-line format

We might typically write a fraction as a horizontal line with the numerator above the line and the denominator below the line using superscripts to indicateexponents. The product of two fractions would typically be written in the same format with a multiplication indicator joining the two fractions.

Single-line format

Figure 1 shows multiplication and division of fractions in a single-line format similar to how we write expressions incomputer programs.

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Source:  OpenStax, Game 2302 - mathematical applications for game development. OpenStax CNX. Jan 09, 2016 Download for free at https://legacy.cnx.org/content/col11450/1.33
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