And now on to the math... - Page 1
Forum section: electronics / beginners

author: LektroiD
author_rank: Frequent Contributor
timestamp: June 12, 2019, 08:53:22 pm
content: Hi all, I've just passed my Electrical Engineering level 5 course, and have been accepted on a 2 year level 7 & 8 Electronic Engineering course, known in the UK at this level as HNC & HND (you may want to look up the equivalent in your country to find out what that equates to). I managed to get through all subjects at level 5, although maths wasn't my strongest subject (we only went as far as Pythagarus and touched on Trigonometry), now I'm going to skip a level and go straight for level 7. I'm fine with everything, but concerned I may struggle with the maths & formulas (my memory is quite poor when it comes to formulas). Any hints or tips to get myself strong in these areas?I'm aware of Khan Academy, but not sure which areas should I look at. I start in August, so if possible I'd like to do a bit of study over the holidays to get myself up to speed. Any hints or tips are duly welcome.

author: bob91343
author_rank: Super Contributor
timestamp: June 12, 2019, 09:13:46 pm
content: As with anything else, learning by understanding is far superior to memorization. You don't need formulas. If you should need one, you should be able to derive it.Calculus and advanced algebra aren't difficult; it's just that some of the concepts aren't familiar.Integration is adding up values. Differentiation is seeing how values change. Theory of equations is a lot of fun, as you get to play with interesting graphs. Exponentiation and logarithms are important but the more familiar you get with them the simpler they seem.What you can do is get a textbook and, rather than starting at the beginning, go into the book a few chapters and see how much you can get, and if you have a clue to solve the problems. If not, think about it and make sure you see the definitions of any new functions so you aren't totally lost. Follow each derivation so that you see how the author got to the result.

author: NivagSwerdna
author_rank: Super Contributor
timestamp: June 12, 2019, 09:19:06 pm
content: Firstly, Congratulations! Good job.You could do nothing and get them to teach you... that actually might be the best way... if you are too curious I would recommend Thomas' Calculus which can be bought Used on Amazon and other places for much less than new especially if you go for an older edition. (e.g.https://www.amazon.co.uk/gp/offer-listing/0321878965/ref=tmm_hrd_used_olp_0?ie=UTF8&condition=used&qid=1560374286&sr=1-4). I found it useful... but you need to be motivated (and for me it was revision). (You can find dodgy online versions... but for me I need hardcopy of that sort of material).

author: Vtile
author_rank: Super Contributor
timestamp: June 12, 2019, 09:21:27 pm
content: Quote from: bob91343 on June 12, 2019, 09:13:46 pmUnfortunately at my experience the exams are usually build in favor to memorizing vs. derive as they are usually fully booked vs the time available. In the long run the memorizing will loose for the understanding and feedback gained from solving applied problems (even rather simple ones).PS. All of the fancy mathematics will eventually simplify to series of summations and multiplications.

author: rstofer
author_rank: Super Contributor
timestamp: June 12, 2019, 09:24:03 pm
content: You should find a lecture series in PreCalculus. It will be a review of the algebra and trig that you have already taken but, as a guess, in a good deal more depth. Trig identities, all of them, will absolutely be required in Calculus and even more when you get to the Signal Processing course of EE. Lots of sin() and cos() going on.Around here, there are 3 math courses required: Calc I, Calc II and DIfferential Equations. Don't worry, this isn't the end. You will probably have a separate course in Laplace Transforms and Fourier Analysis. You may also have classes in statistics (not likely) and Linear Algebra (more likely but not a given).Khan Academy has an EE track separate from their main mathematics program. You might take a look. Their math series on Laplace Transforms is very good - as is everything else they do.A for cost subscription to CalcWorkshop.com is highly recommended. You can do the series on Limits without charge just to see how the program works. Not everybody wants to pay money for video courses but this one is worth it. It's free and highly recommended. It turns out that much of the math you will do will be based on the idea of limits. Even in non-calculus subjects...3Blue1Brown videos on YouTube are also very good.In EE as in all other engineering subjects, math is everything.And, no, I didn't try to compare the different levels versus out BSEE system. What I wrote above is typical of BSEE programs.

author: rstofer
author_rank: Super Contributor
timestamp: June 12, 2019, 09:29:32 pm
content: If you can remember diddies like "ho di high - high di ho all over ho ho" Calcworkshop is the place to go. Nobody will EVER forget the quotient rule!I find most math books to be unapproachable. Frankly, they are boring and I learn better with videos. A pretty decent text is "Stewart's Early Transcendentals" but I don't want to get into the textbook fray. They are ALL expensive and you'll need to buy one for the classes anyway.

author: IanB
author_rank: Super Contributor
timestamp: June 12, 2019, 09:37:07 pm
content: Quote from: LektroiD on June 12, 2019, 08:53:22 pmSince you're in the UK you should focus initially on the school syllabus. Firstly for GCSE maths and secondly for A Level maths.For example, GCSE already addresses pythagoras and trigonometry in some depth along with algebra and various other subjects. If you don't feel you could ace the GCSE maths exam right now, then you should look to the various teaching materials and revision books for that.After that, look at the A Level maths syllabus (pick an exam board, or look at several such as AQA or Cambridge). You will probably be taught maths at a similar level to A-level during HNC and HND courses, but if you want to get a head start you should look for revision material for A Level maths and see how much of it you can do. Probably you will need some study since it is rather more advanced than you describe your current level to be.

author: LektroiD
author_rank: Frequent Contributor
timestamp: June 12, 2019, 10:00:12 pm
content: Thanks all for your swift replies. I think A-Level is the stuff I'll have missed in Level 6, as level 5 is equivalent to GCSE, so A-level is probably a good starting point. I'll give that a go and see how I get on... I may pop my head into the college and ask one of the the EE lecturers in person too.

author: lordvader88
author_rank: Frequent Contributor
timestamp: June 12, 2019, 10:08:24 pm
content: One's thing's for sure, there's a lot of short and long math video's on line, especially on what 15-20yo's learn in school and then 1st,2nd year of college/university

author: rstofer
author_rank: Super Contributor
timestamp: June 13, 2019, 11:56:17 am
content: Quote from: LektroiD on June 12, 2019, 10:00:12 pmThat is always the best way to go. Enrolled students can be a good source as well.It doesn't seem a simple matter to compare the course structure of the UK based systems with those of the US. We simply don't go for the certificates approach. Around here, a modern BSEE program is usually 5 years starting right after high school (the first 12 years). Should the student only complete the first 2 years, there would possibly be an ASEE degree. The ASEE level is essentially for technicians. Most of the advanced electronics theory happens in the last 3 years. The first 2 years or so are devoted to things like General Education (philosophy and other non-engineering topics) and fundamental math (Calc I, Calc II, Differential Equations) plus the entry level electonics classes (DC and AC theory, probably).The problem with the BSEE is that everybody has one, there is nothing to differentiate job applicants unless their degree is from a higher tier school such as Stanford, MIT or some of the University of California institutions. These days an MSEE is just about entry level.A BSEE takes about 140+ semester units with most courses being 4 or 5 units. We have two semesters per year so 140/4.5 (avg) takes 31 units per year or about 15 units per semester. That's hard core! Four major subjects plus a lab will give the required 15 units. Each unit is 1 hour of lecture per week for about 15 weeks.If you only touched on trigonometry, you will be way behind the curve moving forward. Again, around here, trigonometry is covered in High School and reinforced in Pre-Calculus. Note that Pre-Calc is a two semester course (takes a full school year) and is assumed to be mastered BEFORE the 5 year program starts. Either the student covered the material, in depth, in some kind of Advanced Placement program in high school OR they are going to be spending 6 years to get that BSEE. The student can take a placement exam to prove proficiency sufficient to skip Pre-Calc.It is jokingly said that Calculus is easy, it's the Pre-Calc that will kill you. Well, really, they aren't joking. I never though much of 'partial fraction expansion' until I hit Laplace Transforms. In Algebra, they kind of gloss over it and then beat you over the head with it later on.Somehow, the entire program ties together. It just takes time and effort. Easy for me to say, I'm retired and kicking back.

author: IanB
author_rank: Super Contributor
timestamp: June 13, 2019, 05:54:32 pm
content: Quote from: rstofer on June 13, 2019, 11:56:17 amYes, the systems are very different. However, you can get a good idea of the UK course structure and content from exam specifications.For example, here is a specification for what students should learn for the GCSE math exam (taken at age 15/16):https://www.aqa.org.uk/subjects/mathematics/gcse/mathematics-8300/subject-contentSimilarly, here is a specification for A-level (taken at age 17/18):https://www.aqa.org.uk/subjects/mathematics/as-and-a-level/mathematics-7357/specification-at-a-glance

author: LektroiD
author_rank: Frequent Contributor
timestamp: June 13, 2019, 10:45:29 pm
content: Hi again, and many thanks for everyone's input. There's a couple of things I feel I need to elaborate on, firstly, the level 5 course I completed was a fast-track (intensive) course, which only runs for half a year instead of a full year. I needed to do this level of Electrical Engineering to get into Electronic Engineering, but that only starts at level 7.I mentioned we had touched on Trigonometry, the reason I said that was because I don't know how deep the subject goes (due to it being a fast-track course), we covered all aspects of right angle triangles, but no other types of triangle - I'm guessing Trig would cover all types of triangle? That said, I passed that assessment without any problems. In fact I passed all assessments (we had to pass every assessment in all subjects, or we wouldn't have been able to pass the course), I did have to remediate one assessment where I got a formula muddled (my memory isn't great, so finding ways to commit all the formulas to memory was more of a task than the maths itself).It seems the qualifications differ from each part of the UK, being in Scotland, it seems the grades are different from England. This is a guide to the Maths grades in Scotland:https://www.sqa.org.uk/sqa/47419.htmlI'm absolutely determined to take this study as far as possible, so I'm focussing on brushing up on my weakest subject, which is maths.

author: IanB
author_rank: Super Contributor
timestamp: June 13, 2019, 11:14:30 pm
content: Quote from: LektroiD on June 13, 2019, 10:45:29 pmTriangles are geometry, but geometry and trigonometry overlap somewhat. Basic GCSE level studies would include all kinds of triangle, similar triangle rules, the sine rule, the cosine rule, calculating sides and angles of triangles with different unknowns using deduction, sine, cosine and tangent in all quadrants, knowing sine, cosine and tangent for common angles like 30 degrees and 45 degrees, the equation of a circle, calculating the equation of a tangent line to a circle, and more.

author: Wimberleytech
author_rank: Super Contributor
timestamp: June 13, 2019, 11:35:06 pm
content: Quote from: rstofer on June 12, 2019, 09:29:32 pmI never heard that (and I reckon we are about the same age). Funny, I was doing a derivation a couple of days ago and had to apply the quotient rule...had a mental block so I used the product rule. I am gonna remember your little ditty.

author: LektroiD
author_rank: Frequent Contributor
timestamp: June 13, 2019, 11:35:18 pm
content: Quote from: IanB on June 13, 2019, 11:14:30 pmThat's basically what we did, using the SOH-CAH-TOA rule. We don't have GCSE in Scotland, check the link I provided

author: IanB
author_rank: Super Contributor
timestamp: June 13, 2019, 11:47:26 pm
content: Quote from: LektroiD on June 13, 2019, 11:35:18 pmYes I know, you have the Scottish National exams instead. But broadly speaking the same material is studied at the same age level in both Scotland and England.By the way the SOH-CAH-TOA rule is not sufficient. For example, what is the sine of 210° ? (Trigonometry is not about triangles, it is about circles...)

author: 0culus
author_rank: Super Contributor
timestamp: June 14, 2019, 12:05:20 am
content: An old calculus teacher I had said it best about calculus: you have to do the algebra. If you have strong algebra, the rest of it is much much easier.Another thing (and this is purely my perspective as someone with a math degree; YMMV) that really helped my intuition was taking real (and complex) analysis. These are typically rigorous courses intended for majors, but actually going about proving the theorems you took for granted in your calculus courses is super helpful to building intuition. I also went on to do differential geometry and functional analysis which further generalizes everything.

author: vk6zgo
author_rank: Super Contributor
timestamp: June 14, 2019, 02:13:12 am
content: Don't kid yourself that reading through a few pages, thinking "that makes sense" & moving on works for learning new skills.It doesn't,------it's a trapWork through every example in whatever textbook you are using, then do the problems at the end of the chapter.Work,work,work! It's like anything, the more you do, the better you get!Another thing:The people who write these books, also have "weak spots" where they gloss over things by giving you the easiest possible example.When you come up against a more complex one, you can be in trouble.For that reason, I suggest you pick up several cheap secondhand books on the same subject.One will probably have a better explanation.Universities often have book sales where you can buy excellent textbooks which just aren't the one currentlyspecified for their couses.