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2 - Mathematical calculations

Published online by Cambridge University Press:  05 June 2012

I. R. Walker
I. R. Walker
Affiliation:
University of Cambridge
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Summary

Introduction

In books on mathematical methods in physics, there is a very frequent tendency to ignore the subject of errors, and what can be done to prevent them. In conversations on this topic, two common points of view are: (1) error prevention is an ability that is acquired through practice (i.e. it is not something that is taught explicitly), and (2) one just has to be careful. While both viewpoints contain elements of truth, it is also true that techniques exist for preventing and detecting errors. Furthermore, these can be passed on explicitly like other skills (i.e. they do not have to be learned through hard experience.) Such techniques are the subject of the present chapter. These are mostly concerned with the prevention of errors in symbolic (i.e. algebraic) calculations, rather than numerical ones, unless otherwise indicated.

Sources and kinds of error

Conceptual problems

The first and most subtle types of error in analysis in general arise from conceptual problems: understanding the essential physics of a problem and expressing it in mathematical form.

Transcription errors

A second very common type, frequently encountered when calculations are done by hand, is transcription errors. These occur when formulae and numbers are copied from one line in the calculation to the next, often taking place when the handwriting is untidy and cramped. They also arise very frequently if more than one mathematical operation is attempted per line in the calculation.

Type
Chapter
Information
Reliability in Scientific Research
Improving the Dependability of Measurements, Calculations, Equipment, and Software
 , pp. 36 - 57
Publisher: Cambridge University Press
Print publication year: 2011

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  • Mathematical calculations
  • I. R. Walker, University of Cambridge
  • Book: Reliability in Scientific Research
  • Online publication: 05 June 2012
  • Chapter DOI: https://doi.org/10.1017/CBO9780511780608.003
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  • Mathematical calculations
  • I. R. Walker, University of Cambridge
  • Book: Reliability in Scientific Research
  • Online publication: 05 June 2012
  • Chapter DOI: https://doi.org/10.1017/CBO9780511780608.003
Available formats
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Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • Mathematical calculations
  • I. R. Walker, University of Cambridge
  • Book: Reliability in Scientific Research
  • Online publication: 05 June 2012
  • Chapter DOI: https://doi.org/10.1017/CBO9780511780608.003
Available formats
×