I am trying to solve a vector calculus problem, find r(t) given:

a(t) = < 4t, sin t, cos(2t) > ,  v(0) = <1,0,0>  , r(0) = <0, 1, 0 >

My approach below seems kind of complicated for such a straightforward problem.  I am trying to do this without copying pasting previous results. Also there might be a recursion issue when i defined v in terms of v(t).

Question on the ditto operator, labels, and unapply, using three examples.

Example 1:

The ditto operator produces no output. Why is that? I presumed that the ditto operator is equivalent to copying pasting the last output.

Example 2:

Here the label approach seems to work, but in example three, both the ditto and label approach fails.

Example 3:

Someone earlier said that I should use unapply.

Why isn't    " v := x->% " equivalent to "v:=unapply(%,x)"

And why does the label approach fail in the vector calculus example.

I am trying to avoid having to copy paste an entire line of output.

The context of the problem , I am given an acceleration vector and want to find the position vector.

a:= <4t, sin t, cos 2t) with v(0) = <1,0,0> and r(0) = <0,1,0>

My problem is with an intermediate step, finding the velocity vector.

There is no output.

Another attempt. This time using a label

This time i do get an output, but v(1) should be (2 + c1) e_x + (-cos(1) + c2) e_y + (1/2 sin(2) + c3)e_z

The only way for it to work is to copy paste manually the output from line (21) as shown here

I am not sure why p is assigned to 1 when I do a logic problem.

The letter p should stay as p and not be assigned to one. I suspect it has something to do with a statement that is always true. This is annoying because sometimes I have expressions with p in a formula later on, and I didn't realize p has been assigned to 1. And I can't use p in a logical formula either since it's already been assigned to 1.

I am trying to solve an equation using surd and I get a strange result.

solve(surd(x^4,8)=-2)
    4, -4, 4 I, -4 I

These solutions are clearly wrong.

The equation (x^4)^(1/8) = -2 has no solution.

This problem is equivalent to asking the computer to solve sqrt(x) = -2

which has no solution in R or C.

However if I type

solve((x^4)^(1/8) = -2) , then I get no answer, which is what I expected.

Why does surd behave in this unexpected way.

Also another thing I am wondering, why doesn't Maple simplify (x^4)^(1/8) to x^(1/2).

I tried the simplify command it didn't work.