How Many Of You Had To Teach Yourself The Math?

Seriousry.

Math was pure tedium when I was in high school. I programmed my computer to do my math homework for me. As a result, I didn't learn much. I'm paying the price now. In fact, the first few times I've tried getting started in electronics as a hobby over the last 10-15 years, it was the math that kicked my ass and made me give up. The first example in AoE (1 foot wide power cable powering NYC) makes me feel like a class A dunce.

Well dammit, I think I've wasted enough time. I've got a couple of books from a local used book store that specifically deal with algebra/trig/calculus and such that applies to electronics. Going through the first chapter, so far I've surprised myself in how much I

*did* learn, and still remember, but surely I've got a long uphill struggle ahead.

I'm sure that I'm quite the black sheep in all this (the geek that hates math), but is there any hope? Have any of you learned the math from basic algebra up?

Thoughts?

Suggestions?

Insults?

thx

-phaeton

Reply to
phaeton
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When I went to college we had a lecturer for all math courses - except trig. I asked why and was told that one year they had to do without a lecturer and the results went up! Too bad they never tried it for the other courses.

It's a matter of finding the right books. I have a fondness for "Mechanics via the Calculus" by P.W. Norris and Mathematics for the Million by Lancelot Hogben but that's me. Try your library - and Amazon.

Reply to
Homer J Simpson

I too sucked in HS. I was into computers though and then got into computer graphics. I couldn't understand any of it. I didn't know what cos or sin ment or even what = really ment. This was about when I was 16-18 or so. There was a local library sale and I picked up some books on algebra, trig, and geometry for a few bucks. After having them for a few months and trying to learn 3D programming I then realized I would make myself work through the books. I really wanted to know what a matrix was and what a dot product was and such. Then for the next few months I worked through the books. I forced myself to understand and figure out what was going on. I didn't know how to multiply fractions.

They had something like, say

3 9 27

- x - = --

4 5 20

I had no idea what that ment and how they got it but I realized very quickly what htey were doing is multiplying the top to get the new top and multiplying the bottom to get the new bottom.

For addition it was harder. I'd read what they were saying but just didn't really understand it. I had to sit down and look at what they started and what they ended up with and try to figure out how to do that and then test what I thought they did.

Eventually I picked it up quite quickly and it wasn't hard at all. Its very simple stuff but you just have to work at it. I then moved on to college and got a degree in applied math. It really is amazing stuff and very fun to do once you realize it's not hard but just requires some attention.

Make sure though that you start from the basics if you don't have a good foundation. If your foundation is weak everything you build on top of it will be weak too. i.e., it won't do you much good to jump into calculus if you don't know "precalculus"(which is pretty much just a sum of everything before). Being very strong in algebra should make it much easier as everything is based off that. Calculus is very simple ideas that are taken to the "extreme". The fundamental concept in calculus is limits. Limits are very simple to understand if you put in a little effort. Once you understand that then you can easily understand derivatives and integration. This about all you really need to know to do well in electronics. Its not even necessary but sheds some more light on the more basic concepts(i.e., functions).

Two things to note though is that sometimes the problem with understanding something is the context and time. Either it has to be put in the right words for you to understand or sometimes it just takes time for it to sink in. Don't be afraid to read something 10-20 times to get it. When working through math books you might have to spend 10x longer on a chapter than reading a work of fiction. Once you get get the foundation built you will get better at it and it won't take as long. The majority of mathematics is really learning a language and how to use it. You already know most of the concepts such as limits, integration, derivatives, functions and such. Its just a matter of understanding and refining them in an intellectual way and being able to have a language where you can communicate those ideas with others.

If you are serious about mathematics then it will pay off. It will open up many doors for you. You will even see mathematics in things that you might never have though they had anything to do with it. Math is everywhere. Math isn't just numbers but its training your brain to think about things in an intellectual way.

Again though, you have to realize that its not hard because its hard but simply that it takes time... it does get easier though. In fact, your brain might give up after you having to force feed it some concepts and then just shut down where nothing makes sense. But give it a little free time then try it again. Your brain will realize that you mean buisiness and then will try to make it easier.

Its all up to you though. If you really want it then you can have it. Don't expect it to be easy though, atleast first. There are many resources on the internet too that can help you. You can goto sci.math and post questions(no matter how basic) if you get stuck, but don't ask for help until you have tried many times to understand. The reason for this is many times you will get the result without doing anything. Your subconscious will work on the problem and eventually solve it. Many times I had no clue about how to do something and spend many hours on it only to wake up the next day with the answer(which is very rewarding). If you always ask for help then you will only end up using that as a crutch and never really learn to figure things out for yourself. (and this is probably the hardest part of math) It will get easier though.

Have fun and good luck, Jon

Reply to
Jon Slaughter

I worked as an electronics technician all my life and later with computers, routers and networks. The only time I ever had to use math is in test taking for higher level work. You need math to take the tests, not for working with electronics. Now if you are into engineering and circuit design that may be another thing. I think they just used math as a screening tool. Now they use degrees to screen people. You can be a complete idiot but as long as you have a degree you get the job.

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If a group\'s goal is the complete destruction of free people
then extermination is the only choice and shouldn\'t be delayed.
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Reply to
Claude

Engineering design absolutely needs math, make no mistake. Yes, as an eng tech, I can confirm that one can do 95% of the job without math. Learning how to diagnose and troubleshoot is a matter of experience and creative/critical thinking. But, working out the fine details is in the math.

That's why engineers need technicians! ;)

nb

Reply to
notbob

I'm afraid that is math. Math doesn't have much to do with numbers but with concepts and ideas... with figuring things out and trying to understand them. Some people get distracted by the numbers but really they are just used because its the easiest way to express math and its something everyone has a fundamental concept of. i.e., without critical and creative thinking you don't have math.

But, working out the fine details is

yep. Thats the truth. I have a friend that has a degree in EE that can't make an LED blink. He makes 50k a year and I probably know more about electronics then he does. I doubt he could build a simple regulated power supply even if he a schematic.

He once tried to build an 8w guitar amp from a kit he ordered and it didn't work. I had to fix it for him and that was before I knew much about anything in EE(I knew the basics of what a resistor, cap, inductor and such did from physics but never really did to much with amplifiers or tubes or anthign lik ethat). I was supprised though that he got as far as he did with it. Its just you would/should expect more from someone like that. The said fact is that he was probably avg.

Anyways, thats life...

Reply to
Jon Slaughter

So Jon, do you think you can work on your spelling now? :-)

Reply to
Lord Garth

Nope, sorry. I tried. Just a huge waste of time for me. I'd rather do something useful instead.

Reply to
Jon Slaughter

I'm currently studying for a degree in Mechatronic Engineering. So far I've had to use little of the maths that I've learnt with circuit design. Where its been real handy is with dynamics and analysis. I guess, from my experience and what other people have said, if you already know the answer to a physical problem then you probably won't need math. However math is always handy when trying to transform natural phenomonae into discrete and quantifiable relationships.

Reply to
Chris Lloyd

Well- you can always go back to basics. Start with a line, then chop it up into evenly spaced hash marks. Now number the marks. Bingo, number line. Play around with lengths, add and subtract. Observe how multiplication and division behave.

Too elementary? Replace numbers with letters that can represent many numbers. Write things down and observe how they behave; acceptable and unacceptable rules; move things around. Viola, algebra. Now you are open to linear and nonlinear (polynomial) equations.

Add another dimension. Don't necessarily graph things on a whole coordinate system, but fiddle around with Euclidian geometry, of lines and segments, assemblies such as triangles, and the wide world of geometry involving circles. Incorporate algebraic representations of the various line segments and angles. Circles and right triangles beget trigonometry.

Now place things on a Cartesian coordinate plane and, using your rules of geometry, determine a whole new set of relations; distance, equations of lines, polar coordinates; if you want to get adventerous, you can even delve into loci of curves such as parabolas, elipses, etc., and their algebraic solutions.

The last big, important part of math starts with the limit. What happens when you make a variable very big, very small, or very close to another value? What if that variable is part of a ratio? Discover derivative and integral calculus. You can also go about it from the less abstract standpoint of position, velocity and acceleration, as Newton himself did. Establish vector math, vector calculus; expand into three dimensions and discover the cross product; for more examples from reality, perform electromagnetic experiments and derive Maxwell's equations from first principles.

And that's just a miniscule fraction of all the math that has been derived to date, let alone a further miniscule portion of all the math that is ultimtely possible!

Ohhh, the world is an exciting place, and so much of it defined in fully abstracted, fully logical mathematical terms. The only problem is that you probably don't have nearly the impulse to go and do all that; I know I don't. Hell, even Euler didn't go and derive that much, and he produced so much work that it was still being printed currently in journals a half century after he died!

I certainly don't have the drive to do all this, but I can see the value in doing so. I tend to skip over reading equations and doing problems (they are *problems*...what's that tell you? ;) unless I have to, so I've learned the most from classes on the subjects.

Math is a language, as much as any other; it describes things just a bit more abstract than spoken language, but it's also immensely precise. As with any other language, it will take time and effort to speak it.

Tim

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Reply to
Tim Williams

[snip]

I worked with a guy that has an MSEE. He was trying to make a +/-15vdc power supply from a single +15vdc. This is what he came up with: (view in courier)

+15 >------+--------> +15v | | [1uF] | | GND >------+--------> 0 | | [1uF] | | +--------> -15V

...jerry

Reply to
Jerry R

I took Calculus in college and got a passing grade of "D". The only thing I remember is the derivative of X^2 is 2X, but I'm not sure what that means. I think it has something to do with the slope of the line at some point on a curve, but I forget.

So, what significance does 2X have in terms of X^2?

-Bill

Reply to
Bill Bowden

I tried to take 3rd year college math (grad, div and curl etc). Couldn't do it. But my teacher told me he tried to put an auto battery charger kit together and burned all the copper off the board! I guess we all have our skills.

Reply to
Homer J Simpson

IIRC, the slope of the X^2 curve is 2X at all points.

Reply to
Homer J Simpson

Only one suggestion: Keep going!! Higher mathematics is exquisitely beautiful, elegant, and powerful.

Hang in there. Everything gets easier, eventually. During high school, I didn't enjoy the math courses, usually, to say the least. And some of it seemed VERY difficult, to me. But, somehow, when I started studying Calculus, and Physics, in my first semester of Electrical Engineering, even huge algebraic equations suddenly seemed almost trivially easy. I remember being amazed, especially since I had once gotten a "D" in Algebra 1, in high school.

SOME stuff just has to be learned the hard way, or needs time to "soak in" right. During my first university semester, it once took me eight hours to fully-understand a single page in my Calculus textbook. If that's what it takes, do it. It will be WELL worth it.

I believe that, essentially, everyone has to "teach themself" the math (and everything else). I learned at least 80% of my course-work on my own, and maybe 20% from the lecturers (but maybe only because I usually went to the lecture before I studied the material, myself. Otherwise it might have been 99%/1%.).

Anyway....

After you learn Calculus, one of the really-big "payoffs" is that you can then learn about Differential Equations. THAT'S when the REAL fun begins. (And no, I'm not being sarcastic.)

Then, you can/should also learn about Fourier Series, and Fourier and Laplace Transforms, and signals and systems theory, and then probabilistic signals and systems. (You'll be able to find the Transfer Function to characterize a system by simply injecting a little pink noise into the system. [That can be very handy to use for industrial processes, for example.]) Digital Logic, or Symbolic Logic, is also good stuff to learn, and is quite easy.

And you can learn about the discrete-time version of differential equations, called Difference Equations, and the z-Transform.

With Laplace Transforms and z-Transforms, you can transform differential and difference equations into (gasp!) algebraic equations.

And knowing about Difference Equations will also make it very easy to do things with Differential Equations on a digital system, e.g. a computer.

Maybe you can also study Linear Algebra and learn about sets of simultaneous equations, for multi-variable systems, which you can then make into one vector/matrix algebraic equation. Then you can also learn things involving vector/matrix differential and difference equations.

I've left a lot out. But that kind of stuff would give you a pretty good foundation. After that, if you have learned well, "the sky's the limit".

Good luck! Keep at it!

- Tom Gootee

"He who lives in a glass house should not invite he who is without sin."

Reply to
tomg

Yes, that's right.

Mark

Reply to
redbelly

The joy of differentials !

The advent of Mahtcad radically changed ( increased ) my use of more involved maths in engineering. A very powerful tool indeed.

Graham

Reply to
Eeyore

More generally the slope of X^Y is Y*X^(Y-1) for any integer value of Y (including negative).

Examples :

1/x -> -1/x^2 x -> 1 x^2 -> 2x x^3 -> 3x^2

etc ...

vic

Reply to
vic

At college, some students complained to one lecturer that they weren't getting Laplace Transforms which put them at a disadvantage. He then gave us a 50 minute rapid lecture on them which took me from zero to 90% - best lecture I ever heard. It confirmed the old rule that if you can't teach it in 50 minutes you'll never teach it at all.

Reply to
Homer J Simpson

But that's not really quite so helpful. Start out by thinking in terms of that point (3,9) for Y=X^2. Imagine you are slightly further away, say at X=3.1. Y would then be 9.61. What would the slope be between these two points? Well, it is (9.61-9) / (3.1-3) or .61/.1 which is 6.1. That's not much different from the 6 computed above. So what if you used X=3.05 to get just a little closer? Well, that would be Y=9.3025. So what would the slope be between these two points of (3,9) and (3.05,9.3025)? Well (9.3025-9)/(3.05-3) = .3025/.05 or

6.05. Note that it is closer. It turns out that as we slide that second point closer and closer, the resulting calculation will show a slope closer and closer to 6, too.

Generalizing, we have Y1=X1^2 and Y2=X2^2 for the two points and the slope between them is (Y2-Y1)/(X2-X1). But let's just call the short distance between X1 and X2 as delta-X or more simply, just dX. Then we can modify things a little so that we call X2=X1+dX. Then we have Y1=X1^2 and Y2=(X1+dX)^2=X1^2+2*X1*dX+dX^2. We can then re-express the slope as (X1^2+2*X1*dX+dX^2-X1^2)/(X2-X1). But this is also just (2*X1*dX+dX^2)/dX or dX*(2*X1+dX)/dX, which amounts to 2*X1+dX.

Returning to the above calculations, we can now see that when I set X2=3.05, it was 0.05 away from X1=3. Thus, dX=0.05 in this case. The above equation suggests that I will calculate the slope as 2*3+0.05, which would be 6.05, just as I did compute above. Nice. Now what happens if we let dX go very, very close. Setting dX=0 (that is very close, yes?), we compute 2*3+0 or 6. Just right.

Anyway, this is quite general. So the expression 2X is true about the slope of Y=X^2 for all X.

Jon

Reply to
Jonathan Kirwan

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