- #1

azdang

- 84

- 0

## Homework Statement

Consider the map F: C

^{0}([a,b],R

^{n}) --> R, F([tex]\phi[/tex])=[tex]\int\phi(t)\phi(t)[/tex]dt (This is the integral from a to b). Write F as a composition of three maps, each of which is linear or bilinear. Then use the chain rule and generalized product rule to compute DF([tex]\phi[/tex]).

## Homework Equations

## The Attempt at a Solution

The only maps I could think of would be something like this:

[tex]\phi[/tex]: [a,b] --> R

^{n}

A: C

^{0}([a,b],R

^{n}) --> C

^{0}([a,b],R

^{n})

And then maybe I would need a map for [tex]\phi[/tex][tex]\phi[/tex]? But I'm not sure what that would be or if that's even correct. I'm not even sure that I am on the right track at all with the maps. Does anyone have any ideas?

Is it possible that F is one of the three maps? So that the composition becomes F of A of phi?