Daniel Flath

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Sturm’s theorems

Learning objectives

  • Deduce properties of sine and cosine using only the fact that they are solutions of the differential equation y^{\prime\prime} + y = 0
  • Find qualitative information about solutions of the differential equation  y^{\prime\prime} + q(x)y=0

In class

  • Definitions of sine and cosine
  • Prove Sturm’s theorems in a series of exercises, key

On your own

  • Qualitative analysis of Van der Pol’s equation

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