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Why use the Fourier Transform? Spectrogram (in class demonstration)

2 of 7

D'Alembert's solution for a Gaussian

3 of 7

Characteristics in nozzle (see MAE 101B)

4 of 7

Nice overview of method of characteristics (video)

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KEEP/QUIT/START

  • Handwriting on the whole large enough
  • Could still talk more slowly
  • Intimidating (especially questions)
  • Two major issues:
    • Skipping steps in derivation
    • Would like more worked examples
  • Both non-trivial because of timing. Will try to address in the remaining time

6 of 7

Lecture 25 (May 27, 2015)

  • Find similarity solution. Reduce PDE to ODE, but on an infinite domain and not Fourier Transform
  • Begin method of characteristics
  • Obtain fundamental solution with Heaviside initial condition: similarity solution

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7 of 7

Summary

  • Similarity solutions exist when there is no other length scale. PDE reduces to ODE
  • Method of characteristics leads to solution of first-order quasilinear equations and to solution of the wave equation
  • For Friday: read sections 12.1–2
  • For next Wednesday: HW VI

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