Part A Differential Equations

  1. what is an ODE?
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  2. A function f(x, y) continuous on a rectangle R satisfies a Lipschitz condition with constant
    L if
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  3. Theorem 1.1. (Picard’s existence theorem):
    • y' = f(x, y) with y(a) = b has a solution in the rectangle R := {(x, y) : |x − a| ≤ h, |y − b| ≤ k} provided:
    • P(i): (a) f is continuous in R, with bound M (so |f(x, y)| ≤ M) and (b) Mh ≤ k.
    • P(ii): f satisfies a Lipschitz condition in R.
    • Furthermore, this solution is unique.
  4. what is Gronwall's inequality
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  5. what is the CMT
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  6. what is P(iii) (condition for a global soln.)
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  7. what is Picard's existence theorem
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Card Set
Part A Differential Equations
part a differential equations