[sdiy] SDIY MATH GOALS--need real help!

[Magnus Danielson]

Dan Snazelle skrev:
> ok
> 
> what about if it has little triangles? (are these delta? what school of math is this? algebra?)

I hope you are aware of the way functions is annotated, that a function 
f(x) is an annotation to say that the output of the function f depends 
on the input variable x. More variables can be used such as f(x,y,z), 
which could represent "it is a function of the position in space" or 
just a function of three variables just conveniently labeled x, y and z.

The little triangle is the greek Delta sign (big delta) which is used to 
signify some difference. For example:

/| x(n) = x(n+1)-x(n)

It is still normal algebra, just a handy notation to describe a 
difference (which often is just called "a delta"). For clarity I will 
write delta below, but it means the same thing.

If define a delta of a functions f(x) output with some delta x variable
like this (notice that delta x is a different variable to that of x, 
think of it as a delta along the x axis):

delta y = f(x+ delta x) - f(x)

and divides it by delta y you get an expression of the slope over the 
delta x distance as a function of where on x you are. If you now let the 
delta x go towards very very very small... just taking the plunge 
towards zero... but not quite get there... we say that we let delta x 
goes towards the limit value of 0 (at this time) you get the funky formula

                       f(x+delta x) - f(x)
f'(x) =      lim      -------------------
         delta x -> 0        delta x

As you can see it removes the DC component of f(x) at the value of x, 
but scales the slope so it is the slope at x and not tainted by nearby 
values. This is called derivation and this is what the funky d notation 
also says... and the ' in the f(x) tells you that the function f(x) you 
had now has been transformed into another function, f'(x), which has the 
slope or derivate of f(x).

          d f(x)
f'(x) =  ------
           d x

describes the same thing...

This is the step from algebra over to calculus.

> also...i keep reading about transform functions...is that calculus?

Not necessarilly, to be strict anything you do in algebra is transforms 
too, but the transforms you hear about such as Fourier Transform, 
Laplace Transform etc. is generic linear transforms that builds upon 
calculus and is so important methods that they got a name of their own.

> i am also seeing a few other weird symbols pop up.
> thanks so much

Not all of them will be needed initially.

> spending my saturday night reading "mastering technical mathematics"

How about Saturday Night Live Mathematics?

Cheers,
Magnus