MATH221 · Chapter 5 · Annotated SlidesThe Elementary Theory of Initial-Value Problems
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The Elementary Theory of Initial-Value Problems

Initial-value problems y′ = f(t, y), y(a) = α: Lipschitz conditions, existence and uniqueness, and well-posed problems.

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  1. 1 5.1
  2. 2 The Elementary Theory of Initial-Value Problems
  3. 3 Slide 3
  4. 4 Slide 4
  5. 5 Slide 5
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5.1

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The Elementary Theory of Initial-Value Problems

Slide 2: The Elementary Theory of Initial-Value Problems

Notes

  1. f satisfies a Lipschitz condition in y if |f(t, y₁) − f(t, y₂)| ≤ L|y₁ − y₂|; then the IVP has a unique solution and is well-posed.

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Slide 5

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