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Preface

Published online by Cambridge University Press:  05 June 2012

Wei-Chau Xie
Affiliation:
University of Waterloo, Ontario
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Summary

Background

Differential equations have wide applications in various engineering and science disciplines. In general, modeling of the variation of a physical quantity, such as temperature, pressure, displacement, velocity, stress, strain, current, voltage, or concentration of a pollutant, with the change of time or location, or both would result in differential equations. Similarly, studying the variation of some physical quantities on other physical quantities would also lead to differential equations. In fact, many engineering subjects, such as mechanical vibration or structural dynamics, heat transfer, or theory of electric circuits, are founded on the theory of differential equations. It is practically important for engineers to be able to model physical problems using mathematical equations, and then solve these equations so that the behavior of the systems concerned can be studied.

I have been teaching differential equations to engineering students for the past two decades. Most, if not all, of the textbooks are written by mathematicians with little engineering background. Based on my experience and feedback from students, the following lists some of the gaps frequently seen in current textbooks:

  1. • A major focus is put on explaining mathematical concepts

  2. For engineers, the purpose of learning the theory of differential equations is to be able to solve practical problems where differential equations are used. For engineering students, it is more important to know the applications and techniques for solving application problems than to delve into the nuances of mathematical concepts and theorems. Knowing the appropriate applications can motivate them to study the mathematical concepts and techniques. However, it is much more challenging to model an application problem using physical principles and then solve the resulting differential equations than it is tomerely carry out mathematical exercises.

Type
Chapter
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Publisher: Cambridge University Press
Print publication year: 2010

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  • Preface
  • Wei-Chau Xie, University of Waterloo, Ontario
  • Book: Differential Equations for Engineers
  • Online publication: 05 June 2012
  • Chapter DOI: https://doi.org/10.1017/CBO9780511761683.001
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  • Preface
  • Wei-Chau Xie, University of Waterloo, Ontario
  • Book: Differential Equations for Engineers
  • Online publication: 05 June 2012
  • Chapter DOI: https://doi.org/10.1017/CBO9780511761683.001
Available formats
×

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.

  • Preface
  • Wei-Chau Xie, University of Waterloo, Ontario
  • Book: Differential Equations for Engineers
  • Online publication: 05 June 2012
  • Chapter DOI: https://doi.org/10.1017/CBO9780511761683.001
Available formats
×