@Carl Love 

Thank you very much, it's exactly what I wanted, and thank you very much for your correction.

@rlopez 

I have found the inert tool too, it's good, but fully not expanded, just a Nabla symbols, I will check that more.

the unprojected vertor is a interesting tool, I will take that.

I'm now try use subs combine the Divergence() to get some more, but I think this full of tricky, and not have general meanings. 

Mr RJL,Thank you very much!

@ecterrab

Thank you very much for this tips.

I will check the help for these. 

tensor is a useful tools in continuum media mechanics , like nonlinear elasticity, howerver, all the demo in Physics is almost in vector for statics or for general relativity , and the Physics tensor is specially in time-space metric, so how these powerful tools's application to advanced elasticity is not obvious in these tools and metric, also not so much demo on these, I have tried some, but it's a little difficulty for me, could the team for Physics package or tensor give some time to demo the application to elasticity , continuum media problems.

@sazroberson 

your trick about use set is very useful

and the 

T := 1/`Δx` * Sum( b[i,n] * (f[n]-f[i]), n='{0,1,2,3,4,5,6}\{i}');

eval(eval(T,1),i=2)

this too work right, and the later not work.

and you use Sum, this not to sum instantly, I can understand

but could you give me more eval(T,1),  I found it do nothing to the \{i}, this is very important

but why the  eval(T,i=2) not work, neither the  eval(eval(T),i=2)

always  we use eval(exp, eq),   you use eval(T,1) is very tricky, could you be kind to give more explain on this. 

Thank you very much

there is some little typing problem

T := (Sum(b[i, n]*(f[n]-f[i]), n = ('`minus`')(${(0 .. 6)}, {i})))/`Δx`

should be

T := (Sum(b[i, n]*(f[n]-f[i]), n = ('`minus`')({`$`(0 .. 6)}, {i})))/`Δx`

and the later will work

eval(eval(T,1),`0..6≠i`={$0..6)\{i})

should be

eval(eval(T,1),`0..6≠i`={$0..6}\{i})

but the result not work

could you give more tips on this

@Carl Love 

I want to calculate, not perfect typing

I indeed know somthing about index now,

the third form is something natrual now

Thank you

in fact I want do take a taylor expansion of a summation expression

taylor 

@Carl Love 

i:=0;

then

fun1:=sum(a[i[m]]*diff(f(x+m*dx),x), m= 1..4);

will not right, only a[0], not a[0[1]]

but if i:=1

fun1:=sum(a[i[m]]*diff(f(x+m*dx),x), m= 1..4);

this is ok

and with not assign i

fun1:=sum(a[i[m]]*diff(f(x+m*dx),x), m= 1..4);

is ok too

could you give more details why should be iterate on m, but not i variable

@Carl Love 

I always struggle from the subscript from maple's scheme, could you do give some more practice how to use this indexed subscript, what many people( I think) is just want to use the subscript to summation or product , not for indexed.

@Carl Love 

yes make no sense, but I want to said is how to use double index variables to do some things.

like if I want to do some operation natural.

sum(a[i[m]]*diff(f[m](x),x), i= 1..4);

this is ok, but not so natural for double index. especially in display, and I must take very careful to use.

Thank you very much.