## Contact and Symplectic Topology

## Ada Lovelace

## Folios 157-158: AAL to ADM

**[157r] ** East Horsely Park

Ripley

Surrey

Dear M^{r} De Morgan

In consequence of

y^{r} kind reply to my

former note, Lord L

think I had better

send you the paper,

(which has been put

into type, tho' not

published).

## Folios 154-155: AAL to ADM

## Folios 46-47: AAL to ADM

[something written vertically here --- belongs at end of letter so transcribed there]

Ockham Monday. 4^{th} Sep^{r}

Dear M^{r} De Morgan

## Folio 175: ADM to AAL

**[175r] ** [in De Morgan's hand] This complete differential of \(\varphi\), as

it is called namely

\(\frac{d\varphi}{dx}.dx+\frac{d\varphi}{dy}.dy+\frac{d\varphi}{dz}.dz\)

is a perfectly distinct thing from

\(\frac{d\varphi}{dx}+\frac{d\varphi}{dy}+\frac{d\varphi}{dz}\)

and also from \(\frac{d^3\varphi}{dx\,dy\,dz}\)

Read again page 86 when \(x\) is changed

to of 87

page 198--199 & the

references

## Folios 168-170: ADM to AAL

**[168v] ** [In De Morgan's hand] When an equation involves only two

variables, it is easy enough to write all

differential equations so as to contain nothing

but differential coefficients; thus

\( y=\log x\frac{dy}{dx}=\frac{1}{x}\)

## Folio 45: ADM to AAL

**[45] **[in ADM's hand]

\(\int_a^{a'}f\,ds\)

\(\int_a^{a'}\varphi s.ds\) \(\varphi s\) meaning \(f\)

\(\int f\,ds\)

\(\int\frac{dv}{dt}.ds\)

\(\int\frac{dv.ds}{dt}\)

Negative & Impossible Qu. \(\int dv.frac{ds}{dt}\)

Operation \(\int dv.v\)

Relation \(\int v\,dv\) [diagram in original]

\( v^2=2\int_a^{a'}f\,ds+C\) \(dy/dx\)

\( V^2=0+C\)

\( v^2-V^2=2\int_a^{a'}f\,ds\)

## Folios 50-52: AAL to ADM

S^{t} James' Sq^{re}

Saturday Morning

Dear M^{r} De Morgan. I

hope you have not by

this time come to the

conclusion that I have

drowned the Differential

Calculus at least (if not

myself with it also) in

the Seine or the Channel.