Part A Differential Equations

what is an ODE?
A function f(x, y) continuous on a rectangle R satisfies a Lipschitz condition with constant
L if
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.
what is Gronwall's inequality
what is the CMT
what is P(iii) (condition for a global soln.)
what is Picard's existence theorem

Author

Nat1234

334937

Card Set

Part A Differential Equations

Description

part a differential equations

Updated

2017-10-20T08:47:13Z

Show Answers