Hey Everyone, I am attempting to learn some calculus from the ground up and would like to know of any references that would be auspicious in that regard? Lately I've been studying electronic theory that requires calculus; such as capacitors, op amp differentiators, and op amp integrators. It would be nice to have a form of learning material that includes practical examples for electronics. I will, however, accept any calculus references you deem appropriate for a beginner. I would appreciate any help! Thanks, Austin
Hello, On learnersTV there are some video's on mathematics: http://www.learnerstv.com/lectures.php?course=ltv095&cat=Maths&page=1 More pages like that are found here: http://www.learnerstv.com/course.php?cat=Maths Bertus
I'd suspect that most folks will recommend the text they used for basic calculus, but I'm not so sure that's a good choice, as they're usually intended for the usual year and a half basic calculus course. It's likely you'd be swamped in details. Here are some recommendations. Also check out the recommendations on learning calculus. My favorite calculus book is Courant's two volume "Differential and Integral Calculus", but I didn't find that book until I was a grad student. It was the 2nd ed. from the 1930's and most people will declare it too old. But the basics were known long ago and they don't change. I still use Courant today, but I lost my basic college calculus (Purcell from the early 60's) text decades ago. Here's something to consider: a 12 hour basic calculus video from The Teaching Company. I can't speak from first-hand knowledge as I haven't seen this particular video. However, a relative loaned me a two DVD set on elementary particle physics published by the same company and the lecturer was well-prepared and a superb presenter. The focus was on ideas. My guess is that this basic calculus video would be worthwhile because it would also focus on the key ideas and concepts. This high-level view would then help you drill down into the textbooks for more details when you needed to learn the nuts and bolts -- but you'd have a good conceptual framework to put them in. Most students go through calculus and are presented with lots of seemingly useless techniques -- until they need them in later years. Be careful on choosing texts, as you can get over your head. Some calculus books should be considered "Real Analysis" books, as they are intended for math majors who already have basic calculus out of the way. You also should know about the Dr. Math site. You'll often find your basic math questions answered there -- and there's lots of interesting stuff to browse through. I found some arcane analytic geometry formulas I was trying to derive and that saved me a bunch of time.
Why do you think studying electronic theory requires calculus? I don't know a lick of calculus and I've not had too much difficulty studying basic opamp theory circuits. Most people that know basic algebra and know how to look up the terms and variables present in many electronics circuits can get along just fine without and calculus at all. For the practical person simulators can cover a lot of learning curve as you can play with component values and look at how it effects the circuits.
Thank you very much for all of the useful advice and links! They look extremely helpful! If anyone would like to contribute more, by all means do so.
There will come a time when an engineer on bleeding line research needs that particular tool. Basic functions such as charge curves (both capacitors and inductors) use elementary calculus, but we have the formula's predigested for us so it is not obvious. Even many op amp circuits (such as integrators or differentiators) use pure calculus, and if you ever want to understand a gyrator it is a must (a gyrator converts a capacitance/inductance into a model of the other, making a capacitor act like an inductor for example). Filters are another field that it is extremely useful to have this tool. Someone once said the difference between engineers and techs is the math. I think there is a grain of truth in that. I wish I retained even a little of the calculus I had in college, but it is all gone. I retain enough of the concepts to follow discussions though.
As I've mentioned, take a look at the electronic circuit examples I stated in my first post. I don't think that any of those circuits require calculus, I know they require calculus. Basic op amp theory circuits I've already learned about, such as the non-inverting and inverting amplifier circuits. However, op amp differentiators and integrators do require calculus to examine them effectively. If you look at a thorough EE textbook, which I do happen to have, you will see numerous calculus equations. I don't consider myself to be a practical person. In addition, not only do I want a practical view of how circuits work, but I want a technical view as well; actually even more so. If I want to learn calculus, I'm not going to let anything impede me from continuing.
The math background provides huge insight into electronics but it's only one portion. I'd consider it necessary but I guess it depends on your goals. Personally I would recommend trying to go through an actual electronics textbook which does calculations and if you get stuck on the math refer to a math book briefly. I don't see the advantage of going through a pure math book in any depth. Get the concept from the math book and get the practice from the electronics book. That being said my mind is thoroughly blown that I had an argument about my misinterpreting Maxwell's equations given these new facts...
I recently came across this website that has hundreds of training videos, including many on math, going well into the calculus level: http://www.khanacademy.org/ I've only looked at a few of the videos, but the ones I saw look quite good.
I found vodka very useful when learning calculus....I think Actually, I encourage you to learn what you can of calculus and trig and anything that relates to what you want to do. Dont listen to the nay-sayers, as they usually dont know what they are missing because they haven't learned how it can make a difference. It is a VERY important practice and if you REALLY want to know whats going on in those little flecks of silicon, your on the right path.
I truly appreciate all the encouragement and useful resources! All of the links that were provided look fantastic, and I'll definitely start reading! Thank you very much!
You too? In Ukraine/Russia, where I'm from they give you free vodka on calculus exams, that's why our country is so good in math. I have been teaching Electronerd some basic calculus over instant messenger. He is waaaaaay ahead of other people his age, and a great learner. I found basic calculus pretty easy, its vector calculus with all those 3d plots and functions of 300 variables that scare me. Circulation integrals anyone? Integrating a 3d surface. Nightmarish stuff. Even Einstein hated that stuff. I'm pretty sure this quote is about multi-variable calculus. "Do not worry about your difficulties in Mathematics. I can assure you mine are still greater." You know who I blame? Maxwell. He just HAD to stick all those circulation integrals into his equations.
If only my mother would let me imbibe vodka! Seriously Volta, you're giving me too much credit! A lot of the kids my age are probably in calculus already, I know at least one that is. Hopefully capacitors, op amp differentiators, integrators, and filters require basic calculus?
Filters require Laplace transform, which is a method to bypass using calculus. For filters go learn complex numbers and about impedances and reactances. All you gotta know from calculus to deal with capacitors is what the formula for capacitor current is. I(t) = C dv(t)/dt, and then you gotta learn to forget that, and replace it with impedance Zc= 1/jwC. Then you learn that jw = S, and the whole thing turns into simple algebra. So concentrate more on complex numbers than calculus man.
Eh, I think both are important. Impedances etc. help you actually calculate things but the calculus itself gives a lot of insight which is very easy to visualize. If you're comfortable with integrals you can easily figure out voltage and current relationships in capacitors and inductors, such as from looking at a waveform on a scope. Recognizing slopes (seeing derivatives) lets you see where you'll get slew rate limiting with op amps. With transfer functions you need to be very comfortable with limits to see what the equations are telling you quickly. You often need calculus to manipulate transfer functions especially if you want to go back to the time domain. I wouldn't want to be dealing with these things without a background in calculus. There really isn't all that much you need but being comfortable with basic integrals and derivatives, especially visually, is extremely useful no matter what you do.
The statement someone made about the difference between techs and engineers was just the math has a grain of truth. However, the engineers with the math will go on to learn concepts the techs won't be prepared for. I'm not an EE, so I can't speak with authority, but I did have to take a network theory class and sat in on a communications class by the same teacher (he was excellent). The math was relatively straightforward (mostly Laplace transform stuff, differential equations, and Fourier series/integral/transform stuff). However, getting facility with that stuff leads to understanding that a technician isn't going to have. For example, if I designed something and needed an EE to design a circuit in conjunction with this design and specified the PSD must be less than such-and-such a curve (and gave the reasons why and the trade-offs), the EEs I used to work with would run off and tackle things. Some would even politely argue with me over the design -- and that's a good thing. Where I used to work (HP, Varian, Perkin-Elmer), there would be few techs that would have those capabilities, although some of them were excellent circuit designers. Another common example (as Ghar intimated) would be that the EEs would be conversant with stuff in e.g. an E&M class because of their math background. The techs might have some knowledge of stuff (especially if they were hams), but won't be able to handle e.g. a design task that was specified by a mathematical statement without some coaching and help. Now, I'm certainly not "down" on techs; I'm just pointing out that the math training gotten by the engineers typically exposed them to more technological concepts and gave them tools to figure out more problems. So I think Electronerd's efforts to learn more math are excellent. However, remember Hamming's quote at the beginning of his book on numerical analysis: "the purpose of computing is insight, not numbers". I'm paraphrasing, as I may not remember it exactly, but it gets the spirit. The same thing is true with the math -- it helps you get more insight; you don't learn it for its own sake.
The good news is that I have already learned about complex numbers. I'll start learning the math involved for caps, thanks!
I agree completely! Math has always been a favorite subject for me, because I like to solve challenging problems. The fact that I can do so much with math and predict results accurately has always inspired me to continue, especially since it applies to my passion of electronics. While our universe can be described in numerous ways, I believe mathematics describes our universe the best!
Mathematics is indeed a very effective language. You have the wisdom to see that it is more than just a tool. As a language, it enables communication with others, communication with ourselves, new insights for creative solutions and paths to obscure knowledge. Keep studying and your fluency will increase over time.