Math for EE - Page 1
Forum section: electronics / beginners

author: lili
author_rank: Newbie
timestamp: August 29, 2021, 09:23:28 pm
content: Hey folks. I am new to electronics and I want to understand at what level I need to know mathematics to be an electrical engineer. At first glance, it seems that the ability to add, subtract and solve equations is enough, is that so?

author: Benta
author_rank: Super Contributor
timestamp: August 29, 2021, 09:26:06 pm
content: Are you trolling? Is this a joke?

author: wwdwgs
author_rank: Newbie
timestamp: August 29, 2021, 09:35:45 pm
content: All you need to become an Engineer is ability to used smart phone and internet.

author: Zero999
author_rank: Super Contributor
timestamp: August 29, 2021, 09:39:14 pm
content: Quote from: Benta on August 29, 2021, 09:26:06 pmDon't forget, this is the beginners section.Quote from: lili on August 29, 2021, 09:23:28 pmA professional engineer needs to know a lot more mathematics than that. Mathematics is a substantial part of an engineering degree. In fact someone with an engineering degree would probably do quite well if they took a mathematics degree, shortly afterwards.

author: tszaboo
author_rank: Super Contributor
timestamp: August 29, 2021, 09:41:38 pm
content: Just these sort of things:https://en.wikipedia.org/wiki/Argument_principlehttps://en.wikipedia.org/wiki/Maxwell%27s_equationshttps://en.wikipedia.org/wiki/Taylor%27s_theoremhttps://wwwhome.ewi.utwente.nl/~poldermanjw/onderwijs/DISC/mathmod/book.pdfOnce you done with these for the Bachelor, you also need some more for the quantum physics for the Masters degree.

author: TimFox
author_rank: Super Contributor
timestamp: August 29, 2021, 09:43:25 pm
content: After arithmetic and algebra, the bare minimum is calculus (derivatives and integrals) and complex variables.

author: xrunner
author_rank: Super Contributor
timestamp: August 29, 2021, 10:05:29 pm
content: Quote from: lili on August 29, 2021, 09:23:28 pmNo. No it is not so at all. What were you glancing at lili? It may have been an introductory project book perhaps or some basic online projects perhaps. No you have to go higher than basic algebra as others have and will tell you ...

author: Cerebus
author_rank: Super Contributor
timestamp: August 29, 2021, 10:20:28 pm
content: Quote from: Zero999 on August 29, 2021, 09:39:14 pmTrust me they couldn't. At Uni. I shared a flat with someone doing maths and they do mathematics that someone with engineering mathematics just plain wouldn't recognise.Mathematician's (Dad) joke: What's purple and commutes? ... An Abelian grape.If you groaned you're a mathematician. If you're an engineer with a lot of maths under their belt you probably still wonder what the hell that was about.Edit: Sorry, meant to include this:To an engineer doing mathematics "1 + 1 = 2" is a fact, and they almost certainly can't tell you why it is true. To a mathematician why "1 + 1 = 2" is true is a whole field of study and I'd expect a graduate mathematician to be able to make a fair fist of giving a, possibly simplistic, explanation to a layman, just as I would expect an EE graduate to be able to do the same for "Whydoes electricity flow through a wire?".

author: Cerebus
author_rank: Super Contributor
timestamp: August 29, 2021, 10:45:40 pm
content: Quote from: lili on August 29, 2021, 09:23:28 pmIf you're still at the "ohms law" stage of things then yes, it probably does look like that. Get into circuit design a bit though and you'll soon hit a point where to design something you have to be able to solve differential equations. Do a bit more and you'll find systems of differential equations that can't be solved (or can't be solved relatively easily), then you find yourself needing Laplace transforms.If you do it from first principles, even the simple circuit of charging a capacitor, via a resistor from a battery and calculating what the voltage is at a given time is, requires solving a differential equation. If you grab the general answer to that system from a textbook as a formula then you just need the most basic algebra manipulation skills - "fill in the numbers". But if you start out with Ohm's law and knowing that for a capacitor C = Q/V, then you need calculus.If you're talking about the kind of mathematics you need to comprehend before you undertake an EE degree, then I'd say a solid understanding of trigonometry, algebra and basic differential and integral calculus. If you can get on to solving basic differential equations then you'd probably have a step up over other EE undergraduate freshmen. Anything beyond those you'd expect to learn while doing an EE degree.

author: Bud
author_rank: Super Contributor
timestamp: August 29, 2021, 11:47:08 pm
content: Quote from: lili on August 29, 2021, 09:23:28 pm"To be an electrical engineer" - do you mean to study the EE discipline or just to get hired to do EE work? It is likely not possible in the West to be hired without a respective university degree but in some other parts of the world engineering roles may be nominal and not require mandatory educational credentials. So this is why i am asking.

author: rstofer
author_rank: Super Contributor
timestamp: August 30, 2021, 12:36:24 am
content: Semester long courses:Calculus I -- this assumes you are proficient with algebra, geometry and trigonometry from advanced high school classesCalculus IICalculus IIIDifferential EquationsLinear AlgebraNumerical Analysis-- classes that are just math classes in disguise:Fourier AnalysisLaplace Transforms and Control SystemsField Theory and Maxwell's EquationsSignal ProcessingYou might only need 30 units of math so, if we assume 4 units each, you only need 7 or 8 of the above. Or, maybe a couple are combined. There will be some kind of math class every single semester and you hit the road running with Calc I and work up from there.Here is one such program:https://catalog.pacific.edu/stocktongeneral/schoolofengineeringandcomputerscience/electricalengineering/#majortextWait! What happens if you aren't up to speed on Algebra, Geometry and Trigonometry? You slept through high school... There is a program at most Junior Colleges called Pre-Calc I and II and it is a 2 semester program (figure a full year) so not only does the EE program take 5 years but there is the potential for adding another year for Pre-Calc. Hint: Do not try to take Pre-Calc I or II during the abbreviated summer semester.ENGINEERING is ALL math!The list above isn't meant to discourage but rather to acknowledge just how much the graduate EE actually has to know. Those working EEs that hang around here really understand a ton of math. They may not use it every day but they knew it when they graduated.Another hint: Calculus is easy, it's the Pre-Calc that will bury you. You absolutely have to be rock solid in Pre-Calc.All of the above is for the US, particularly California. I'm just guessing but for the Russian Federation, it may be different but I expect it is equally rigorous. If not more rigorous. Check with one of your local universities.

author: rstofer
author_rank: Super Contributor
timestamp: August 30, 2021, 01:50:32 am
content: If you're going to do this EE thing, there are a few sites you may find usefulwww.symbolab.comfor solving all kinds of math problems. If you subscribe (donate?), you get detailed steps for solution. Otherwise, you just get the answer. I donated a few years ago...www.desmos.comfor graphing equationswww.khanacademy.orgfor math tutorialswww.khanacademy.org/science/electrical-engineering-- math for EEswww.youtube.com/channel/UCYO_jab_esuFRV4b17AJtAw-- 3blue1brown... all kinds of higher level mathYou will also need to use LTspice for circuit simulation and MATLAB (free to some students, inexpensive for individuals, expensive for business) or Octave (free MATLAB work-alike) for problem solving. wxMaxima and Mathematica are also useful.You may have local equivalents...

author: xrunner
author_rank: Super Contributor
timestamp: August 30, 2021, 01:56:59 am
content: Quote from: rstofer on August 30, 2021, 12:36:24 amThat's true! I am actually been reviewing some refresher courses on differential equations because, well, I have not used in some time and I think it's fun.

author: Cerebus
author_rank: Super Contributor
timestamp: August 30, 2021, 02:40:26 am
content: Quote from: rstofer on August 30, 2021, 12:36:24 amA warning, those are from a US perspective whereallthe above are undergraduate courses. In the UK and other European countries you'd be expected to have covered something like Calculus I & II from ages 16-18beforeyou go to university. I just checked those Calculus I & II courses at Pacific, and they arepretty much what was in my A-level maths courses (examined at age 18). The prerequisite "advanced high school classes" above are what we'd studied up to O-level (examined age 16) and I'd presume that current European syllabi were similar.

author: radiolistener
author_rank: Super Contributor
timestamp: August 30, 2021, 03:58:36 am
content: Quote from: lili on August 29, 2021, 09:23:28 pmif you're familiar with differential equations and other stuff likeSchrodinger equation, it will be a nice background for electrical engineer, but this does not cover all needs, so be ready to learn some more math for electronics...

author: rstofer
author_rank: Super Contributor
timestamp: August 30, 2021, 12:40:43 pm
content: Quote from: Cerebus on August 30, 2021, 02:40:26 amYes, in general terms, the US is behind the world in math and science at the high school level. I went to a private high school and we did do Calc I and Calc II but unless a student signs up for the more advanced programs, they won't take these courses, they are not mandatory. It has been nearly 60 years but I don't recall that the high school level Calculus courses were anywhere near as involved as the university level classes.And that's why we have Pre-Calc at the Junior College level. Think of it as a 'make up' program.The one thing we do well is offer a Junior College (often called Community College) program. If an EE degree takes, say, 150 semester units, the first 60 or so are 'General Education' and there is no requirement to take these in the College/University program. These Community Colleges are a lot cheaper and often more local than state Colleges or Universities.There too, we have two levels of public colleges in California (and probably other States). There is the Cal State system and the University of California system. Cal State Stanislaus is a lot less notable than UC Berkeley. The concept is that the universities are more involved with research.There is some movement with the idea of having undergraduate degrees available from Community Colleges. That would leave them in competition with the state College system. I don't know if they are going to offer all undergraduate degrees or just a subset. Locality is important because living expenses can dwarf tuition.

author: Cerebus
author_rank: Super Contributor
timestamp: August 30, 2021, 02:02:59 pm
content: Quote from: rstofer on August 30, 2021, 12:40:43 pmEquivalency of qualifications or educational attainment levels around the world is a mess. Europe is better for this than some places, but more by accident than design. We all tend to be a bit parochial about about the education system and assume everybody else's is the same as our local ones - which of course they are not. Youdidqualify that what you were saying might not apply in Russia but it wasn't in the lede, so I just wanted to point it up lest the OP get misled.It's difficult to judge from a brief course summary quite how it compares with what I was taught, but on a bullet point by bullet point comparison those calculus I & II course taken as whole look much like part of the content of my grammar school maths syllabus. Of course, like you, I'm talking about some time ago (the 70s in my case) and things will have changed. I did take a quick look at the UK national schools syllabus before commenting, and it looks roughly the same as in my day (perhaps a little dumbed down, but I would say that wouldn't I) and seems comparable to those undergraduate courseson a bullet point by bullet point comparison.

author: rstofer
author_rank: Super Contributor
timestamp: August 30, 2021, 02:31:52 pm
content: I spent a little over a year living and working in Singapore and their educational system impresses me to no end. I worked with some of the smartest engineers I have ever known. Their National University is world class and their Polytechnic does amazing work.I used to go to a McDonalds from time to time and it was just staggering to watch the middle school students sitting quietly at the tables in the rear, all working diligently on their homework. No grab-assing, just solid work! Expectations are high, failure is not an option.In the US, it is possible to graduate from highschool without knowing how to read or write much less calculate. Good thing we are a service economy.In the end, it all works out. Those who are destined for greatness have every opportunity in the US. We don't seem to come up short on the Nobel Prize thing and we can all remember July 20th, 1969. We'll be fine...

author: rstofer
author_rank: Super Contributor
timestamp: August 30, 2021, 02:40:42 pm
content: Quote from: Cerebus on August 30, 2021, 02:02:59 pmI think my list is accurate in terms of content, it may be wrong in terms of timing. In the end, those are the topics a graduating EE will be expected to know. There is certainly a ton of math that is taught in the Applied Mathematics and Mathematics curriculums that I didn't include but I'm pretty sure that my list is reasonably complete for undergrad.

author: Cerebus
author_rank: Super Contributor
timestamp: August 30, 2021, 02:51:47 pm
content: Quote from: rstofer on August 30, 2021, 02:31:52 pmYeah, but y'all like to pretend 12 April 1961 didn't happen.

author: rstofer
author_rank: Super Contributor
timestamp: August 30, 2021, 03:15:23 pm
content: October 4th, 1957 is the one that scared the hell out of us. I was in 6th grade (IIRC) and the change in elementary school education was sudden and dramatic. October 3rd, we were cruising along in math and science, not paying attention to much. On October 5th we kicked it into high gear. Twelve years later we walked on the Moon. I was there (tangentially) and it was amazing! Every parent wanted their kid to go to college and become an engineer. I dropped out of college November 22, 1963 and didn't restart until 1969. It was a long process but I retired 18 years ago and haven't given one thought to working.Some dates stick with you!

author: Per Hansson
author_rank: Unknown
timestamp: August 31, 2021, 06:03:30 pm
content: Since the OP seems absent but the discussion is going on and seems to interest some math guys I need to ask a question that bugs me:I have read allot of Wikipedia sine wave articles and their related articles (you know how it goes, you read, and click, and read and it never ends)But I never understood the reason or why this statement it true: Peak voltage = RMS x √2 (I.e. 230V RMS x √2 = 325v peak AC voltage.Or for that matter 230 x √3 = 400V which just happens to be the line to line voltage, but then this is RMS, not peak, the peak is again:400v RMS x √2 = 565v peakCan some kind soul please explain this relationship for someone that had trouble with math in elementary school?Example statement from Wikipedia article:https://en.wikipedia.org/wiki/Mains_electricity_by_country"All voltages are root mean square voltage; the peak AC voltage is greater by a factor of √2, and the peak-to-peak voltage greater by a factor of 2√2."My question is: why is it so?

author: Stray Electron
author_rank: Super Contributor
timestamp: August 31, 2021, 07:00:01 pm
content: This! This! This! Weak math skills are THE biggest reason that people drop out of the EE course. I don't know what level school that you're in currently but get started taking some serious math courses as soon as possible. If you're in the equivalent of high school in the US, then you need to take the most advanced math classes that they offer.I'll add one more course to rstofer's list: Matrix algebra. If you do any circuit analysis you'll certainly need it. You'll also need to know Bessel functions and Fourier analysis, I don't know if those are covered in any of the math courses that restofer named but you will almost certainly need to understand them.In the US, every college and university has what they call a "college catalog" that list every course that they offer and the prerequisite courses that students are Required and/or Recommended to take before taking the main course. The catalogs also list what courses are Required in order to earn each degree that they offer. Contact the schools that interest you and get a copy of their catalog and those will tell you what math and other courses that you will be required to take. Beware that the graduation requirements and the catalog change every year.Quote from: rstofer on August 30, 2021, 12:36:24 am

author: Cerebus
author_rank: Super Contributor
timestamp: August 31, 2021, 07:02:43 pm
content: OK, here goes:First why RMS at all? The RMS value (root mean square) of an alternating voltage is the same as the DC voltage that would produce the same power as the AC voltage when fed into a resistive load. So 1V DC applied across a 1 \$ \Omega \$ resistor produces 1W of heat, so does 1 V RMS AC.The squared bit comes from \$ P = \frac {V^2}{R} \$, the power P produced in a resistance R by some particular voltage V. The mean (average) bit comes from the fact that you're dealing with a voltage that changes over time and you need to compare it with a DC voltage that doesn't - the AC voltage takes many values over time, the DC just one, so we use an average to get a single figure. The root falls out from going back from a squared voltage (from calculating equivalent power between AC and DC voltages) to just a voltage.Now, the proper way to show how this all comes about is write an equation for (AC power = DC power) and to dive into some calculus involving a sine wave \$ A \sin{(\omega t + \phi)} \$, but that's not exactly going to be a very friendly way of dealing with someone who "had trouble with math in elementary school". For someone of that ilk it's probably best to say that if you apply calculus to the whole problem you come out with the result that the ratio of the peak voltage of a sine wave and a DC voltage that produce the same heating effect in a resistor is \$ \sqrt{2} \$. Itonlyapplies to sine waves, use a different waveform and the ratio is different.The \$ \sqrt{3} \$ thing comes about, going via a similar route to avoid trigonometry this time, when the phase angle involved (\$ \phi \$) is 120 degrees between two sine waves. Again, this is a property ofsine(or cosine)waves but doesn't necessarily hold for other waveforms.I'm aware that this contains handwaving, but there isn't really any alternative other than "trust me that's how it works (with handwaving)" or "here's the maths, enjoy".

author: TimFox
author_rank: Super Contributor
timestamp: August 31, 2021, 07:04:21 pm
content: Please refer to any elementary textbook on electricity.A sine wave has the equationV(t) =Asin(2pif t)whereAis the "amplitude", or peak voltage.RMS means "root mean square", which is the square root of the average (over one cycle or all time) of the voltage squared.The proof of the factor 1/(21/2) can be found in these textbooks, or check Wikipediahttps://en.wikipedia.org/wiki/Root_mean_squareRMS values of waveforms are useful since the square of the RMS is the mean-square value. If you square the voltage and divide by the (constant) resistance, the mean of that gives you the mean power, which can be compared to the power in that resistor from a DC voltage equal to the RMS value of the waveform. Besides periodic waveforms such as sinusoids, the RMS value is also useful for measuring random noise.Note that the power defined byP=V2/RwhereVis the RMS voltage is the mean power (averaged over one cycle or all time),not the RMS power(regardless of the audio industry and its misnomers). The RMS power is useless but well-defined, and equals (3/2)1/2= 1.225 times the mean power.

author: Per Hansson
author_rank: Unknown
timestamp: August 31, 2021, 08:14:08 pm
content: Quote from: Cerebus on August 31, 2021, 07:02:43 pmThanks, I should have clarified that part in my question myself since I know it, but I am sure it can be helpful for someone else Googling thisQuote from: Cerebus on August 31, 2021, 07:02:43 pmThank you, I guess I had kind of reach this explanation myself, but it helps when someone tells you it is really so.I.e. since we are working with true sine waves we can take a shortcut and not involve complex math, but in the real (Engineering) world it will not work like this, only in a simulation.Another way to look at it is the difference a RMS vs TRMS multimeter will show on something which is not a true sine wave.The TRMS meter does the complex math, the RMS meter cheats and just uses an algorithm which is similar to my question.

author: rstofer
author_rank: Super Contributor
timestamp: August 31, 2021, 10:21:07 pm
content: Quote from: Stray Electron on August 31, 2021, 07:00:01 pmLinear Algebra usually deals with matrix math.A*x=b becomes a very important concept. MATLAB -- MAtrix LABoratory was made for this kind of thing. Octave too, of course!Completely irrelevant but here is a nice 6x6 matrix problem that I would not necessarily want to solve by hand. The matrix is fairly sparse so a hand solution isn't out of the question but MATLAB does it better.Code:% A football stadium has a capacity of 100,000 attendees% Ticket prices:% Student = $25% Alumni = $40% Faculty = $60% Public = $70% Veterans = $32% Guests = $ 0% A full capacity game netted $4,987,000% Let S = number of students, A = number of alumni, F = number of faculty% P = number of public, V = number of veterans, G = number of guests% S A F P V G = valueM = [ 1 1 1 1 1 1 100000; ... % total number of attendees25 40 60 70 32 0 4897000; ... % total revenue0 1 -1 0 0 0 11000; ... % 11000 more alumni than faculty0 1 0 1 -10 0 0; ... % public + alumni = 10 * veterans-1 1 1 0 0 0 0; ... % alumni + faculty = students1 0 1 0 -4 -4 0]; % faculty + students = 4 (guests + veterans)A = M(:,1:6); % extract 6x6 matrixB = M(:,7); % extract value column vectorP = M(2,1:6); % ticket price by attendee typeR = inv(A)*B; % compute number of attendees by typeT = sum(R); % check total attendees = 100,000 CHECKU = P*R; % total revenue = 4,897,000 CHECKV = R'.*P; % revenue by attendee type - transpose R from 6x1 to 1x6% then do element by element multiplication%% fancy output, all previous default output semicoloned%label = {'Students' 'Alumni' 'Faculty' 'Public' 'Veterans' 'Guests'};for i = 1:6fprintf('%-8s%7d @ %2d = %7d\n',string(label(i)),...round(R(i)),...M(2,i),...round(V(i)))endfprintf('\nTotals %6d %8d\n',round(T), round(U))%{Students 25000 @ 25 = 625000Alumni 18000 @ 40 = 720000Faculty 7000 @ 60 = 420000Public 42000 @ 70 = 2940000Veterans 6000 @ 32 = 192000Guests 2000 @ 0 = 0Totals 100000 4897000%}

author: CatalinaWOW
author_rank: Super Contributor
timestamp: August 31, 2021, 10:52:37 pm
content: Back to the OPs question. While in many systems, particularly here in the US you almost have to have a degree in engineering to get an engineering job, and those degrees require substantial doses of math. But in my career I observed that most engineers actually employed no math more advanced than algebra. Some of those had to at least understand the concepts of differential and integral calculus, but didn't actually use them.That said, my personal belief is that to be good or exceptional engineer you need much more math. It is a useful tool in many, many areas. The lists by Rstofer are in my opinion an absolute minimum and several other fields deserve attention. I took one or more maths courses every semester through undergraduate and graduate school and have never regretted any of them (although some were very painful at the time) and have on several occasions had to go learn more. MATLAB and other software tools have reduced the grunge work of employing mathematical tools, but you still need to know which tools are applicable and what the limitations of that application are.

author: rstofer
author_rank: Super Contributor
timestamp: August 31, 2021, 11:04:12 pm
content: I am lucky to be able to review math over the last 4 years; my grandson just graduated with a degree in Applied Math. I followed along for a while but he has clearly outstripped me in math. Now he is taking a couple of broadening classes before he heads off to grad school. I'm not sure what kind of math it will be but it should be exciting. He is a whiz with MATLAB and the university requires a class in the first semester.

author: tggzzz
author_rank: Super Contributor
timestamp: August 31, 2021, 11:54:40 pm
content: Quote from: Cerebus on August 30, 2021, 02:40:26 amAh, youngsters. Bless.Everybody in my state school did integration and differentiation of polynomials (except 1/x) for O Levels. And did them a year early (i.e. 15) so you could have a second go if you fouled it up.

author: tggzzz
author_rank: Super Contributor
timestamp: August 31, 2021, 11:58:49 pm
content: Quote from: Cerebus on August 29, 2021, 10:20:28 pmI remember a 1st year mathematics class being asked to prove that 1+1=2. After a lot of fruitless work, they found it couldn't be proved and had to be taken as an axiom

author: Cerebus
author_rank: Super Contributor
timestamp: September 01, 2021, 12:21:12 am
content: Quote from: tggzzz on August 31, 2021, 11:58:49 pmShhh, you're gödel give the game away. Might be able to russell up a solution that works in the end.

author: tggzzz
author_rank: Super Contributor
timestamp: September 01, 2021, 07:53:34 am
content: Quote from: CatalinaWOW on August 31, 2021, 10:52:37 pmAgreed, but I doubt the OP will read that since they seem to have disappeared.I'll note the old observation to the effect that "the best result of advanced maths is that you don't have to use it". In other words the derivation of why the mathsworkscan be forgotten, leaving only the simpler ways ofusingthe maths to be remembered. Examples: the substitutions when integrating/differentiating, or the s-plane equations of common linear components.Sometimes it seems that a lot of advanced maths consists of finding ways to manipulate advanced concepts using addition, subtraction, multiplication (and rarely division) operators.

author: rstofer
author_rank: Super Contributor
timestamp: September 01, 2021, 05:53:14 pm
content: Quote from: CatalinaWOW on August 31, 2021, 10:52:37 pmI used the FFT exactly once in my entire career. BUT... I did know what it was and what it was used for and I was able to take the samples and write the C code. For the 12 pulse rectifier, the 11th and 13th harmonics did indeed dominate. Just like the theory.You're right, the rest of the time even high school algebra was all it took. Sometimes a touch of geometry or trig but not all that often.Oh, and one time I modeled a water distribution scheme in Excel to prove that all the branch piping had adequate flow and that the return pipe diameter wasn't too small. Not the kind of thing you want to write home about... EEs working on plumbing can't be a career enhancing task.