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sort of an odd situation

Discussion in 'General Electronics Discussion' started by moop the reckoner, Oct 25, 2011.

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  1. moop the reckoner

    moop the reckoner

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    Oct 25, 2011
    So I taught myself to program right? Ruby, python, C++, learning asm slowly now.... recently I've garnered an interest in amateur radio, specifically the RF and protocol stuff, but integrally, this new interest requires lots of calculus.

    apparently I know alot of the calculus required for beginning in this new hobby but.... I SUCK AT ALGEBRA! I barely passed my prereqs which ended at an introduction to imaginary numbers. Now ordinarily I would just think that was cool as **** and continue drawing parallels and realizing that conceptually.... programming is calculus.... but i think i need to learn more basic maths.

    I know I stopped at imaginary numbers... what else do i need for cornerstones, foundations and rebar?
     
  2. BobK

    BobK

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    Jan 5, 2010
    It is unlikely that you actaully need to do calculus, i.e. solve differential equations in order to be an electronic or radio hobbyist. Yes, if you where to try to invent the Chebyshev filter and calculate it's poles and zeros, you would need to solve differential equations in complex space. But all of this has already been done for you. All you really need is the tables that others have calculated for you.

    Bob
     
  3. moop the reckoner

    moop the reckoner

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    Oct 25, 2011
    i dont think you understood that I'm asking for information that is the underpinning of this science, I dont where to start and instead of stumbling around in the dark I'd rather ask for guidance

    clarification: help with algebera, not calculus.
     
    Last edited: Oct 25, 2011
  4. BobK

    BobK

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    Jan 5, 2010
    I would reccomend "The Art of Electonics" by Horowitz and Hill. It gives you the basic theory you need to understand how electronic circuits work without drowning you in math, but also without avoiding it where it is necessary.

    Bob
     
  5. moop the reckoner

    moop the reckoner

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    Oct 25, 2011
    *walks to math forum to ask "wat comes after imaginary numbers when they teach you math in school"*


    not avoiding math...
     
  6. BobK

    BobK

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    Jan 5, 2010
    Calculus, linear differential equations, linear algebra, vector calculus. Maxwell's equations, which are the foundations of electricty and magnetism, are expressed in vector calculus, if you want to really get to basics.

    Bob
     
  7. daddles

    daddles

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    Jun 10, 2011
    The place where most people really learn their basic algebra is in the freshman calculus course in college. This is because the usual problems given require a reasonable amount of algebraic manipulation, so you get lots of practice at it. Such a course should be easy to find at any local junior college, so that's probably the most efficient way to get the practice you need. The course I'm thinking of is the traditional year and a half of elementary calculus that is taught to technical students (well, things may be different today, but that's what everyone went through when I was a student).

    If you're teaching yourself, it's harder because, frankly, it's hard to discipline yourself to slow down and master each section by doing the problems. Most of the practical math used in science and engineering is relatively straightforward conceptually, by which I mean the key ideas are relatively easy to explain. But the devil is in the details and if you know the ideas but can't do the requisite manipulations to use the material as a tool, you can't claim understanding. The knowledge of how to use the stuff as a tool comes, again, from doing lots of problems.

    You can use the excellent videos at the Khan Academy to help yourself understand the key topics. The topic listing there can help you understand some of the things that might be holes in your knowledge. But then you need to supplement that understanding with lots of problems to develop the facility. If you have the money for it, you could hire yourself a tutor. If not, there are lots of websites with suitable information. An excellent one for explaining various problems is Dr. Math.

    If you're teaching yourself, I'd recommend finding a college algebra text and making sure you know the material in it. If you're in the US, you can go to google books and find something that's free to download. For example, I found the book "College algebra: with applications" by Wilczynski and published in 1916. That looks like a pretty good book, although realize it has substantially more material than is typically covered in a freshman algebra class. If you're not ready for college algebra, you can find a suitable high school text and work through that material first.
     
  8. Laplace

    Laplace

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    Apr 4, 2010
    You can do some very sophisticated electronic systems analysis using the Laplace transform. It is the Laplace transform and the inverse Laplace transform that let you switch back and forth between the complex frequency domain and the time domain representations of a signal. Already it sounds complicated, but once you know the technique it is quite simple.

    Circuits are easily modeled in the complex frequency domain, or s-domain. Resistance in the time domain is still resistance in the frequency domain, inductors become the product of the complex frequency variable 's' and the inductance, capacitors become the reciprocal of the product of the complex frequency variable 's' and the capacitance (R=R, L=sL, C=1/sC). This lets you bypass solving circuit behavior using differential equations, instead use just simple algebra in the s-domain.

    If you are trying to model your circuit behavior in the steady-state frequency domain (the usual case, a Bode plot) just substitute s=jω and solve the model using the familiar complex algebra. However, if you need to find the time domain performance of a circuit, then you need to put the complex frequency model through an inverse Laplace transform. For this you will need some fairly complicated integral calculus, or a table of Laplace transforms.

    I use "Laplace Transform Tables and Theorems" by Paul A. McCollum/Buck F. Brown, 1965, Holt Rinehart and Winston, Inc. Alternatively, a decent table can be downloaded from the internet, for example, see http://www.dartmouth.edu/~sullivan/22files/

    Simple & complex algebra is all you really need to know - if you have a table of Laplace transforms. Also, having a computer algebra system such as Mathcad eliminates calculation drudge work.
     
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