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

[Dan Snazelle]

thanks a ton for all that info on which things i need to be able to do,etc

great read



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> Date: Sun, 1 Mar 2009 02:31:36 +0100
> From: magnus at rubidium.dyndns.org
> To: dixon at interchange.ubc.ca
> CC: subjectivity at hotmail.com; synth-diy at dropmix.xs4all.nl
> Subject: Re: [sdiy] SDIY MATH GOALS--need real help!
>
> 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