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

[Magnus Danielson]

David G. Dixon skrev:
> Dan,
> 
> If it's got "d something" over "d something" in it, its differential
> calculus (the d's on top and the somethings on the bottom can also have
> exponents).  If it has a big S-shaped thingy to the left of everything
> (often with little numbers or symbols above and below it), with a "d
> something" at the far right, its integral calculus.  If its got "e" or "exp"
> or "ln" or "log", then its an exponential or logarithmic function.  If it's
> got "sin" or "cos" or "tan" or "cot" or "sec" or "csc", with or without an
> "arc" in front or an "h" behind, then its trigonometry.  If everything is a
> function of "s" then it's a Laplace transform.  Alternatively, if everything
> is a function of "jw" (where the "w" is really an undercase omega), then
> it's a Fourier transform, which is really a Laplace transform where s = jw.
> If it's got lots of "j"s all over the place, then its complex math.
> Otherwise, it's just algebra!  (See how easy it all is?!?  ;->)

Hehe... the Laplace transform and its variations (Z-transform, Fourier 
transform and Discrete Fourier Transform) is a very powerful tool. It 
allows converting complex linear diffrential equations into much simpler 
things and allows analysis of them. Some of that can be a bit 
hairpulling still, but it will be much more usefull in the end.

Many people having math skills may still fail to recognice that the 
Fourier transform is a proper subcase of the Laplace transform (they 
claim that the integration limits are not matching, which they can be 
made to be) and another approach is to say that Laplace is a side-case 
to the Fourier transform. Ah well.

For filters, it is convenient to learn about the concept of poles and 
zeros. It is usefull to learn about amplitude responce and phase 
responce (both being responce of frequency on the jomega-axis) and also 
concepts of phase-delay and group-delay. When getting used to those 
concepts some analysis can be made on a conceptual level and guide you 
in the right direction.

While these are the more complex aspects, they are important tools, and 
sometimes you don't really need to know the inner workings of these 
tools to make good use of them, you just need to learn the overall plot 
they give you. Studing them closer and closer to be able to learn them 
better is recommended as there might be important side-cases you need to 
learn about, limitations which may prohibit you or enable you depending 
on how you do things and is actually trying to achieve.

As for algebra, you don't need very advanced algebra skills most of the 
time. You can get away with pretty basic stuff using some tables for the 
more complex conversions such as those that the Fourier transform does 
for you. You need to be able to insert values into a formula to 
calculate a value, you need to be able to modify a formula to take the 
shape that the value you want is alone on one side of the equal sign and 
the rest of it is on the other side. You also needs to know how to 
"insert" a formula into another, to replace some variable by that 
formula. You will need to know how to reduce unnecessary complexity in 
formulas. It is usefull to be able to take basic formulas and build 
algebraic expressions from them. There is a whole list of small formula 
conversion tricks, all very basic, which can safely be applied. Then 
again some of them needs some care, as they cannot always be used. Just 
like a hammer may not be the best tool to hit a drum, or you need to 
know how to use it properly, as with a screw-driver hitting the trum, 
tapping with the handle on the drum is far better than hacking with the 
screwhead side into the drumskin...

Math can be fun, when you master it. Also, the more you learn, the less 
you need to actually remember, as you can figure things out backways if 
you want to and need to. It becomes easier to convert methods from other 
fields, which is a method in itself... working with analogies. One 
should however always recall that we use much simplified models for 
electronics compared to the complex physical phenomenes we have going 
on. The macroscopic models are that, models on the large scale of 
things. To fully understand it you would need to know details of what 
particles is where in a design, know details of physics still in deep 
research and resolve the complex equations... which is impossible. But 
models gives us simplifications which makes us be able to understand 
most of it... until the limits of the model prohibits us, such as it 
being a linear and noise-free model for instance.

Cheers,
Magnus