Time for action - putting together mathematical functions

1. 1. Let us try to calculate the range of the function:

(3.3)

octave:12> x = 0.5;
octave:13> f = exp(-5*sqrt(x))*sin(2*pi*x)
f = 3.5689e-018

1. 2. In a more useful vector form:

octave:14> x = [0:0.1:1];
octave:15> f = exp(-5*sqrt(x)).*sin(2*pi*x)
f =
Columns 1 through 7:
0.00000 0.12093 0.10165 0.01650 0.02488 0.00000 -0.01222
Columns 8 through 11:
-0.01450 -0.01086 -0.00512 -0.00000

What just happened?

It should be clear what Commands 12 and 13 do. In Command 15, we must use the element-wise .* operator. Had we not done so, Octave would try to perform a matrix multiplication between the vectors given by exp(-5*sqrt(x)) and sin(2*pi*x), which is not defined, and not what we want either.

We could also have used the element-wise operator in Command 13 when x is a scalar; that is, Command 14 is a generalized version that works for both scalars and vector and matrix arrays.

Note

Whenever possible, always make generalized versions of...