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1 - Harmonic Oscillator

Published online by Cambridge University Press:  02 April 2020

Joel Franklin
Joel Franklin
Affiliation:
Reed College, Oregon
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Summary

A review of the problem of motion for masses attached to springs.That's the physics of the chapter, a familiar problem from high school and introductory college classes, meant to orient and refresh the reader.The mathematical lesson is about series solutions (the method of Frobenius) for ordinary differential equations (ODEs), and the definition of trigonometric special functions in terms of the ODEs that they solve.This is the chapter that reviews complex numbers and the basic properties of ODEs and their solutions (superposition, continuity, separation of variables).

Keywords

Series solutionFrobenius methodTaylor expansionComplex numbersexponentiallogarithmsolving ODEs
Type
Chapter
Information
Mathematical Methods for Oscillations and Waves , pp. 1 - 30
Publisher: Cambridge University Press
Print publication year: 2020

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  • Harmonic Oscillator
  • Joel Franklin, Reed College, Oregon
  • Book: Mathematical Methods for Oscillations and Waves
  • Online publication: 02 April 2020
  • Chapter DOI: https://doi.org/10.1017/9781108769228.003
Available formats
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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 Dropbox.

  • Harmonic Oscillator
  • Joel Franklin, Reed College, Oregon
  • Book: Mathematical Methods for Oscillations and Waves
  • Online publication: 02 April 2020
  • Chapter DOI: https://doi.org/10.1017/9781108769228.003
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.

  • Harmonic Oscillator
  • Joel Franklin, Reed College, Oregon
  • Book: Mathematical Methods for Oscillations and Waves
  • Online publication: 02 April 2020
  • Chapter DOI: https://doi.org/10.1017/9781108769228.003
Available formats
×