This course is replaced by MAT3440 – Dynamical systems.

Status

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

Geir

 

 

 

 

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