Maths reading list/books - Page 1
Forum section: electronics / beginners

author: Frankenstein
author_rank: Newbie
timestamp: September 14, 2020, 08:39:27 pm
content: Hi all’ could anybody tell me the very minimum!!maths I really need to study circuit analysis to a good level .possible ONC-HNC level I may sign up for a distance learning course at teeside uni in the uk ,I need to start to get up to speed quickly...I am a newbie I am currently learning to repair PCB and am dedicated to cracking the Maths Many thanks !!

author: radiogeek381
author_rank: Regular Contributor
timestamp: September 14, 2020, 09:44:34 pm
content: First, the math can be intimidating at the start. Good news! You don't have to learn it all at the start. Take your time. If you can find a good teacher it will all be much easier. Most of the math in a US EE curriculum is taught in parallel with the EE stuff.I am not familiar with the certificate levels in the UK, but the math involved in the various EE areas in a US undergrad program will cover a pretty fair range. The distinction is going to be how far you want to go, and whether we're talking about "gut" understanding (that looks like a low pass filter) or analytical chops (that's a low pass filter with a cutoff of X Hz).Better folks than I can talk about the first. For the second category:1) Algebra is pretty important for passive circuits. It can even get you through things like op-amps. Capacitors and inductors will be a bit of a trick, but Algebra is a good basic start. Nothing fancy -- up to solving quadratics, and enough to understand how to solve simple systems of a few variables.Along the way, it is useful to gain some understanding of complex numbers and trigonometry. This will come in handy later on. But it won't be necessary for simple circuits without L and C.Calculus is underneath most of the stuff that follows. (if not all of it). Lots of people get tied up in their shorts here. Calculus may come easy to you, it may not. But the basic notions that come out of it that are important:we can manipulate functions that tell us about "qualities" of the functions (ragged, smooth, growing, shrinking, perpetual...)we can relate thing A to thing B based on how B is changingwe can use both of these ideas to understand circuits and systems2) Linear differential equations is useful -- though there is a cruel joke that gets played on EEs where we learn a "short cut" through most of this. But familiarity with diff-eqs is a foundation that other things get built upon. It has been forty years, but I think I could still solve some simple diff-eqs without losing too much hair.Diff-eqs come into play with analysis of L-C-R circuits (inductors and capacitors in particular). But then...3) Laplace Transforms -- this is the punch line of the cruel joke: Laplace transforms are a really useful way to reason about and analyze circuits. They are often introduced after a semester or two of diff-eq based instruction in circuits, almost all of which are easier to analyze in the Laplace domain.4) Vector Calculus -- this is about as sophisticated as it gets in the undergrad curriculum. The subject is central to really understanding electric and magnetic fields, wave propagation, and "life the universe and everything."That's most of the trajectory. Some would add in Fourier analysis (useful in communications and other things), probability and statistics (useful in lots of things), and some others. But these seem to be the hammer, screwdriver, pliers kind of tools: algebra, diff-eq/calculus, transforms.Some might argue that this is all obsolete in the era of simulators. I won't: the math fundamentals are important to the way I think about circuits.In any case, take your time. For some of us, it took a couple of passes through the material before it really "clicked."

author: Mechatrommer
author_rank: Super Contributor
timestamp: September 14, 2020, 10:09:56 pm
content: Quote from: Frankenstein on September 14, 2020, 08:39:27 pmdont!... i dont want to brag but i already have the necessary skill for some analysis but frankly its not going to be used much. math derivation alone takes time. in the end what actually working does matter (real world application) math is just approximate. the quick replacement for math is spice simulator such as tina-ti spice or ltspice. instead of try to learn theory, try to understand to make a circuit first, learn what is resistor, diode, transistor etc. in case you stumble with math you can just ask directly here such as if you dont understand voltage divider, come here and ask member can provide you online materials and advices... ee is one hell of a universe.. opamp, microcontroller, logic ic, optocoupler, rf synthesizer etc. if you cant pinpoint your field of interest you can go round for eternity. i've been here for like 10 years and currently at the age of 43, i can barely make a circuit. i came from repairing stuffs too.in case you want the math too.. algebra is a must at the very least solving multiple simultaneous equations, this is used in Kirchoff law and equivalent circuit (Thevenin or Norton) nobody here used it anyway we use spice!. if you want to get fancy, matrix algebra and then differentiation and integral, to solve capacitor and inductor circuit. next level is partial derivation taken in degree level, this can be hard you'll need a teacher to babysit you. in ANY circumtances if you find yourself stumbled with math, that is indication you'll need to go down a bit, some basic you are missing. i usually stumbled in Set notations usually found in papers but what the heck. Phasor, z-transform, Laplace et al are another mind bending beasts. fwiw ymmv.

author: Frankenstein
author_rank: Newbie
timestamp: September 15, 2020, 07:11:24 am
content: Thanks very much for such an informative reply I’ll get the books out!

author: Frankenstein
author_rank: Newbie
timestamp: September 15, 2020, 07:13:29 am
content: Thanks very much for such an informative reply!!!

author: rstofer
author_rank: Super Contributor
timestamp: September 15, 2020, 05:24:14 pm
content: I am of the opinion that engineering is ALL math. It doesn't matter what kind of engineering, it's math!I would certainly look at Khan Academy for online education. They even have an EE track but they are famous for their math tutorials.https://www.khanacademy.org/https://www.khanacademy.org/science/electrical-engineeringDigilent has a course "Real Analog"https://learn.digilentinc.com/classroom/realanalog/I would make friends with symbolab.com (math solver) and desmos.com (graphing) but, most important, I would learn to use MATLAB (or the open source work-alike Octave). Nobody solves simultaneous equations by hand. Particularly when there are more than 3 unknowns. At my grandson's university, they require a course in MATLAB for first semester engineering students and then they use it throughout the programs. This is great news! It allows the student to work at a high level understanding the problem without getting bogged down in arithmetic.The first topics in Circuit Analysis are Kirchhoff's Laws and Thevenin's Theorem. The Kirchhoff loop and node equations can result in sizable matrices and include complex numbers. NOBODY wants to solve those by hand! wxMaxima is another useful math solver and it is open source as well.Get a decent calculator. I consider the HP 35s to be quite useful and it is sitting right next to the computer keyboard. It is a reproduction of the original HP 35, the very first scientific calculator that came out around '72 when I was in my last year of college. I couldn't afford it... I had managed to get through college with a slide rule. Heck, we went to the Moon using slide rules! It doesn't do graphing but I don't find graphing on a calculator to be useful when I can just go to Desmos.The TI-84 Plus CE is a great calculator and I prefer the "white" version as the legends are easier to see.TI-inspire CS CASHP PrimeThese are all graphing calculators. Maybe look for online reviews.The 35s is more than adequate for my simple needs.Any of these will work and I have them all plus my all-time favorite, the HP 48 GX

author: rstofer
author_rank: Super Contributor
timestamp: September 15, 2020, 07:28:02 pm
content: Mechatrommer has it right! Get very comfortable with LTspice. In practice, there will be differences between simulation and real circuits, particularly breadboarded circuits. Sometimes the difference is modest, other times things oscillate like crazy.Algebra and Trigonometry are the entry level courses. There is actually a 2 semester class called "PreCalc" which covers this stuff as an introduction to Calculus. It turns out that Calculus is easy, it's the PreCalc part that is hard. Note that most colleges assume you have taken the equivalent of PreCalc in high school so, if you need to take them in college, you just added a year to your graduation date. You're going nowhere in Calculus without PreCalc.BTW, simulation isn't understanding. Understanding circuits is a couple of levels higher than being able to simulate something.

author: garethw
author_rank: Regular Contributor
timestamp: September 15, 2020, 08:33:24 pm
content: I'm just starting the 3rd year of my degree in electronic engineering and have had math units in both years.Basic algebra will get you some way to a basic understanding of what's going on in simple resistor circuits, Ohm's law etc. However, you'll soon find the need to want to work with changing voltages and currents such as those in capacitors and inductors. This requires a knowledge of Differentiation and Integration (Calculus). Then Laplace transforms, Fourier transforms/series, Z-transforms......yeah.As has already been said previously, getting to know your way around a spice simulator is a good place to start. I like to compare it to a saying in the quantum mechanics world which is "shut-up and calculate". In other words, don't try to understand it, just trust the math works, or in this case, trust the simulator.

author: Etesla
author_rank: Regular Contributor
timestamp: September 17, 2020, 06:37:37 pm
content: +1 on learning about components and their uses before learning the math. I'm a 4'th year EE senior and I can honestly say that I learned way more practical stuff outside of class building circuits on my own than I did in the classroom. A $200 oscilloscope and some free software will teach you way more than thousands of dollars of textbooks and math courses. I think that the math is cool, but only if you know how to apply it... If you learn the math before you know what you can apply it to, as most kids do, it just doesn't stick. That's why I think the average GPA at my school is a 2.7, and mine is a 3.95... I apologize for sounding cocky, that's not my intention. I just feel strongly that teaching the math before students already have the practical knowledge is a big mistake that wastes a lot of peoples time and money.I learned electronics in the following way:Start by building circuits from tutorials that do things you find interesting.Learn how to read schematics when you realize that's what everyone uses to describe their circuitsBuy an oscilloscope, a multi meter, and a >$10 soldering iron when you realize that you need them.Learn SPICE when you get tired of wiring circuits by handLearn how to read datasheets when you realize building circuits at the discrete level is usually impractical.Learn microcontrollers when you realize most interesting IC's communicate digitallyLearn PCB design when you realize that JLCPCB exists, and that soldering circuits on perfboard sucks.Learn the math when you finally run into problems that others haven't already solved. This happens a while after you start.

author: rstofer
author_rank: Super Contributor
timestamp: September 17, 2020, 07:42:23 pm
content: QuoteI'm not sure the hobbyist approach to learning electronics applies to these levels. OTOH, I'm in the US and have no idea what they mean. We have a 2 year Associate Degree and a 5 year Bachelor's Degree and then it's on to Grad School for a Master's Degree. These programs won't contain much that is practical but they will require a TON of math.The hobbyist approach is fine for learning electronics but it is meaningless on a CV (resume').For the 5 year (10 semester) program, there is a math or math related class every semester starting with Calc I. If you don't have PreCalc skills on entering the program then add another year.