This course is replaced by MAT3440 – Dynamical systems.


This week we shall prove theorem 3.10 on page 86, the Picard Lindelöf existence and uniqueness theorem. Every thing is in the book on pages 72 - 87. I'll only do the first proof.

We start with background stuff:

I'll the def of the Picard iteration, then recall the def of the Lipschitz condition.

Speak about the sup-norm anduniform convergence and the function spaces C(J,R^n). A little about metric spaces

Cauchy sequences, convergence and completeness.

Then the Fix point theorem for contracting maps (theorem 3.4).

Then, finally, we'll prove th 3.10






Published Mar. 6, 2017 12:07 PM - Last modified Mar. 6, 2017 12:07 PM