@Scot Gould 

Thanks

Yes, the dot notation can be also used for ordinairy calculus too as it seems , but is especially meant for vector calculus
Looks on the prime notation y'  with the dots.
With this code below you could see the prime notation 
Its converting the diff notation(maple input) into prime notation. (2D input)
But you could use also the prime notation directly in 2D Input too.

Note: if i do want to see a ODE written in Maple input in 2D input can convert it also in the worksheet.  

But it seems that parsing the " goes wrong if you enter a second order ODE directly notated with primes..no i must use two times the single prime. 
But the prime notation is default on in Typesetting Rules .. '   and double '' and more to 4 . 
Also the dot notation can be set in the Typesetting Rules .. keystroke  ? ..no need for palette anymore then.

So your example can be done also with the prime notation for a time t ( or x in Typesetting Rules)

Code for converting diff notation to prime notation

restart; # by Preben Alsholm
interface(typesetting=extended);
### 
P:=proc(ode)
  local idiff,t;
  idiff:= convert(indets(ode,specfunc(diff)),D);
  t:=op~(idiff);
  if numelems(t)<>1 then error "Only one independent variable allowed. Got %1", t end if; 
  t:=op(t);
  Typesetting:-Settings(usedot=false,prime=t,typesetprime=true);
  ode
end proc:
###
ode1:= diff(y(t),t$2)+a*diff(y(t),t)+y(t)= b*diff(z(t),t);
P(ode1);
ode2:= diff(y(t),t$2)+a*diff(y(s),s)+y(t)= b*diff(z(t),t)
P(ode2); # error by design - jd foutmelding 

@acer 

Thanks !
I am trying to add a custom palette, but it is yet not clear in Maple how to do this

@dharr 
Thanks!

It was only the(") what i  overlooked then.

@vv 

Thanks

Straightforward this without use of the VectorCalculus package

@acer 

Thanks

There is a vectorfield and the Gradient is graphed in this plot as a rootvector : is this correct ?
 

@rlopez 

Thanks

I am curious how this plot looks like : is there a example of this gradient vectorplot ?

@acer 

Thanks!

Great, now i can stay in the VectorCalculus package
 

@radaar 

Thanks

Never thought on this package 

I prefer the VectorCalculus package, because it is in the vector notation with the unitvectors

The with(Student[MultivariateCalculus]); version has interesting tutors
  

@Carl Love 

Thanks

The CD is from 1998 , yes for Maple V-4 and  want to learn more from vectorcalculus for using in partial differential equations

This error seems to be more difficult to solve

CH7B.mw
   

@Preben Alsholm 

Thanks

Got it now also working and i replaced " by % together with the (t)
Saved also from .mws (old) to .mw (new)
It are old worksheets and nowadays Maple has probably more to offer for easier visualising this topic ?
DYNAMIC DE plots 

The author has made a procedure for this 

@dharr 

Thanks

Don't get the worksheet  working yet unfortunately.

@Thomas Richard 

Thanks

I will look at it, what all new is and LinearAlgebraMigration is a help too

@Carl Love 
Thanks

I think  its a hopeless task , because matrix is written in capital letters in the old worksheets
So, i must restore this manual . .eh no with copy gifs ( much text ) 

Don't see another way 

@Mac Dude 

Thanks

There is no .mpl  extension as such in Maple V
I am afraid that this old sheets are not to restore for the current version of Maple

@Joe Riel 

Thanks

I made a mistake : It is the theory worksheet Dynamod.mws (now mw) you openened, but the answer worksheets are no complete anymore
I am not sure if the all theory worksheets are complete and also if all anwers worksheets are complete?
I think both two groups are missing text , pictures 

When i open them in Maple V-4 its all correct content

Uitw-03.mws