🚀 go-pugleaf

22nd July 1992

In article <14hl22INNcfa@nigel.msen.com>,
emv@msen.com (Edward Vielmetti) writes:
>I did the first unit of the course OK w the help of the
>"function plotting" piece of my hp 95 pocket calculator.
>Couldn't manage to get it to draw the parametic equations,
>tho.

How about some hand drawn plots on graph paper?

I have often found that, once I get sat down to it, possibly during
an evening or on a weekend afternoon, plotting graphs by hand, working
out the points as I go along, can be quite interesting and rewarding
in terms of insight.

That was behind my thinking in providing the sets of tables, so that
all of the information needed is there within the unit.


>
>i guess i'm missing part of the point.  are these then polynomials
>that approximate sin and cos within some part of their range?
>in which case you might bring in some talk of taylor expansions?
>
>(time for alt.uu.maths?)
>
>--Ed

As far as I know, and I too am learning, Chebyshev Polynomials are
not used to approximate sin and cos within some part of their range.

The idea is that you can approximate functions that you know numerically
by computing a Chebyshev Series, which is akin to a Fourier Series
in concept, except that the Chebyshev Series is for ordinary functions
rather than repetative ones in the way that Fourier Series are used.

For example, you might try computing something such as

y = 0.1 * T3(x) + 0.2 * T2(x) + T1(x) + 0.3 * T0(x)

I have not selected the coefficients to have any significance at all,
merely to have a graph that has a general upward trend within it.

You could try several different examples, including negative coefficients.

Thank you for your interest in the course.