Help me

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1. How do I add a value to c_1 (page 1), for example the value of 1, in the third position and how would it be done to place it at the end?

You can't do that because c_1 is a range, not a vector!

2. c_1 Is not considered a vector? What is it?

Its a range. A range is sort of an implicit loop. You should use ranges for three purposes only:
- index a vector or matrix

- in program (for loop)

- for plotting to have more control than quickplot provides

BTW, I consider it a design error that in Prime ranges and vector look exactly alike when displayed

To read more about ranges vs. vectors you may check the articles of Stuart Bruff which I attached here:

https://community.ptc.com/t5/PTC-Mathcad/How-to-Calculate-Gain-and-Phase/m-p/475811/highlight/true#M172174

Being rather old they still apply, though.

EDIT: Just noted that the pdf in the thread above is corrupt. This forum really is ... very special 😞

I attach the file here.

3. From the function f_s (i, c_1) (page 1), what is the sequence that the program follows? If I check the values ​​of ε_t the program first evaluates the values ​​of i together with the first value of c_1, before move to the next value of c_1, however the general function f_s (i, c_1) first exhausts the values ​​of c_1 before moving to the next value of i. The general sequence is what designates the order of evaluation or varies depending on whether it is a function or only the evaluation of variables?

When you define a function, what you use are so called formal parameters (formal arguments). The name of those arguments does not matter at all. So your function is the very same as
, no difference. So the c_1 and i you used when defining the function have absolutely nothing to do with the variables of same name you defined right above (you probably can abandon that variable definition, unless you need them later for something else).

Evaluation of the function only takes place when you later call it, providing actual arguments

For d, etc. the evaluation is using the values which where valid when you defined the function. If you changed them afterwards, this has no effect on the function outcome.

4. Like question one, I would like to add a value to the response of a function for example to ΦMn (c_1) (page 3)

No, thats a different question 😉 In question 1 you wanted to add a value to a range, which is not possible. But now you are asking for changing the output of a function. If you want to change the output of a function, you have to change the function definition. You may do this using if..else statements. E.g. "if c_1>h .... else ...."

Keep in mind that in your sheet c_1 is a range. if you call ΦMn (c_1) the result is something which looks like a vector, but isn't (its not a range,too). You can use it only for plotting (or to display the values). If you try to access the third element by typing ΦMn (c_1)[4 it will fail. If you try to assign the outcome to a variable via x:=ΦMn (c_1) it will fail. You remember: Use ranges in three situations only!

5. I would like to have, for example, the values ​​from 102 to 202 of the vector f_s (i, c_1), in another side the values ​​from 203 to 303 ...

Sorry, I don't understand that question. And  f_s (i, c_1) is not a vector!

A word of caution: The "stack" command Terry was talking about only applies to vectors, NOT ranges!