Mathematica: array of functions

[Anna Kaladze]

Hi intelligent people,

Forgive me for a silly question, but I am really new to Mathematica and thus I need your help for my own research (I am done constructing NIntegrate values for some "non-integrable" functions, involving multiple steps, and I am kinda stuck at the last step. Here is the example which will help me if I know how to crack it).
OK, Here are the series of simple inputs-outputs in the command window:

f:={1+t^2,1/t,5-t}

f

{1+t2,1/t,5-t}

j=Table[x,{x,0,2,1}]

{0,1,2}

All I need to do, is to create a new list, where the first function in f list (i.e. 1+t^2) would take as an argument the first value in j vector (0), the 2nd function in f (i.e. 1/t) would take as an argument the 2nd element in j vector (2), and so on and then display the resulting values in an array. I tried to use some Table commands, and basic looping, could not go far ... The answer is apparently this:

{0,1,3}

But the question is how to get to there...

Many thanks,

Anna.

 

[CompuChip]

I suppose the quickest way to do it is construct a list of expressions and values first:

xy = Transpose[{j, f[t]}]

gives {{0, 1 + t^2}, {1, 1/t}, {2, 5 - t}}

Then you can replace the t's in the second list by the values in the first list, using an anonymous function with two arguments:

Function[{x, y}, y /. t -> x] @@@ xy

Note that you need the @@@ to properly pass the arguments (you can see what happens if you do

g @@@ xy

But I was wondering, if f is a function, why don't you define it as such?

f[t_]:={1+t^2,1/t,5-t}
J = Range[0, 2, 1];

Then you can also do something like

Table[f[j[[i]]][[i]], {i, 1, Length[j]}]

 

[Anna Kaladze]

Dera CompuChip,
Thanks a lot for your answers, they are really great!
Can you please help me to find out where I can read about "[[]]" command/operators to understand your 2nd method better? Wolfram online gives basic info about tables, etc. only. I am a little confused what "f[j[]][]" does, and more so about the very last [] part. Your method works fine, just would like to understand it better (the 1st one made perfect sense).
Thanks again for your time.
Anna.

 

[Bill Simpson]

[[]] is described here http://reference.wolfram.com/mathematica/ref/Part.html

 

[CompuChip]

list[] takes the i'th element from a list, for example, if

list = {2, 4, 6, 8}

then list[[1]] = 2, list[[2]] = 4, list[[3]] = 6 and list[[4]] = 8; list[[5]] will give an error.

So basically what I am doing is taking the i'th x-value from j and applying f to that.

f[j[[i]]]

Now f produces a list again. Since we are interested in the i'th (for the same value of i) output, we need to use the [[ ]] operator again. So

f[j[[i]]][[i]]

I hate defining variables when it is not necessary, but just for educational purposes, you could write it like this:

i = 3; (* for example, let's look at the third element *)
x = j[[i]]; (* or x = Part[j, i] or x = Take[j, {i}] *)
yArray = f[x];
y = yArray[[i]]; (* this is the value you want *)