If you could do it over - how would you learn Maths in prep for engineering wrk?

[monster_of_electronics]

From the stand point of job utility, what are some useful techniques for learning fundamental math applicable to many modern engineering jobs on a day to day basis? (i.e. calculus and beyond)

Immersing oneself in math and making it a lifestyle?  Consistent short, broken up study sessions and work on non-math heavy stuff in between?  A lot of tutoring?  Deep introspection of fundamental concepts?  What works best?  What work pretty well?  What doesn't work well?  I find it initially draining to learn new math until I fully understand how something functions and/or find its utility in its application to everyday problems.  When I find this application, it's annoying when I don't completely understand it but spent hours memorizing some other stuff to get an A.

Most people I've spoken to learned math to get the grade.  I am not looking to become a mathematician but I also sense that's it's fundamental to any engineering work.  I've never been great in academic setting, so a 4.0 GPA at MIT isn't happening but I might as well hedge my bets on understanding the stuff that's most useful as best I can instead of just trying to get an A or a B.

[monster_of_electronics]

If you use it or will use it, you will learn it. As you progress with signal theory, circuit theory and control theory, you inevitably use math.
Also when you learn math, some thing must be dependent on something else, and that is also a good reason to learn both.
Learning without actually practicing in real design will inevitably end up with forgetting.

Thanks for your insight blueskull, a lot of engineering courses and such seem to require calculus, I haven't taken even Calculus I yet, what sorts of courses would be useful to take in parallel with calculus I to ensure ongoing application of math?

[Mechatrommer]

Learning without actually practicing in real design will inevitably end up with forgetting.

but getting it back up will be much much faster than learning it from zero. i find it forgetting is not something got to do with "not practising", but something got to do with "not interesting". i find it less probable for me to totally forget engineering stuffs that i learnt within the span of few months many years back, but more probably of forgetting people's name that i just met few hours ago.

[Kappes Buur]

My problem always has been that I need to be able to visualize everything in my mind before
anything sinks in. Even now, that I am retired, I find it difficult.

However, since coming across https://www.khanacademy.org/math I finally have a grasp of the
more advanced concepts.

Which proves that it's never too late.

[danadak]

Not a recipe for every engineer, but most commonly applied math I find
is simple algebra and a little geometry. And for me a fair amount of Laplace,
albeit that's primarily algebra. And with analog increasingly sampled data
Z transform helpful, but again that's mostly algebra in application.

School was highly theoretical. I found that my best learning, like former poster,
also visualization, add to that solving a practical problem. I also now rely heavily
on Mathcad, Spice, to do the heavy lifting. Not ideal, but fast. I have also
noticed more recent physics and EE books much better visual practical examples.

One technique I am not proficient yet is signal flow graphs. They inherently
lead to an understanding of what circuit elements have significant impact on
signal flow. Additionally the algebra is canonical in many senses, getting at
a T(s) for example very rapid, vs traditional methods of node and loop equations.

One area that comes with experience is relating math to time domain results.
In the backward direction, meaning observing time domain signals and knowing
how its related to the frequency domain. Eg, phase margin, transmission line
behavior......


Regards, Dana.

[TheAmmoniacal]

My one and only advice in learning mathematics is to make sure you understand the basics . So much of math is rearranging and manipulating expressions, know your order of operations, know your log rules, know your exponential rules, factorization, fractions.. Recognize trig identities.

Work on problems, lots.

[rstofer]

Before you even think about Calculus, make sure your pre-calculus skills are up to date.  Compared to pre-calculus, calculus is a piece of cake.

There are a number of online sites that provide videos of various math subjects (Purple Math and Khan Academy are my favorites).  I also bought several video courses from http://www.thegreatcourses.com/ but only when they were on sale!

The EE program in college will require at least up through Differential Equations plus specialty subjects like Laplace Transforms and Fourier Analysis.  Like Calculus, these topics are mostly about slinging polynomials - the stuff they teach in pre-calculus.

I am fortunate in that I get to do the courses over as my grandson progresses through college.  We are just wrapping up the first half of pre-calculus.  The college has decided to make pre-calc a 2 semester course because students find their way into calculus without a sufficient foundation.  Makes sense to me!

Things are so much easier today (I graduated in '73) with programs like Microsoft Mathematics, MatLab and several other mathematics programs.  Graphing functions is fundamental to understanding what they represent and these math programs do a great job.  So do the graphing calculators.  I am partial to HP calculators (I prefer RPN) but the TI Inspire is also very nice.

The big problem that most everyone has is working word problems.  Everybody hates word problems.  The thing is, engineering IS a word problem.  Spend a lot of time on these.

I'm also a visual learner and I need to see how things work before I understand the math.  These days, I play with Ordinary Differential Equations as a game.  MatLab w/ Simlink allows me to set up these equations and plot the results.  I can also add knobs and dials to allow me to play with the parameters.  All of a sudden, the mass/spring/damper 2d order DE makes a lot more sense.  I also built a small analog computer for modelling such things.  There's nothing like a hardware solution to a set of DEs.

Good luck!

[Tomorokoshi]

There are a number of online sites that provide videos of various math subjects (Purple Math and Khan Academy are my favorites).

Yes, Khan Academy is a good resource. Use multiple resources.

It may also help to spend some idle time watching through various YouTube resources like Numberphile. For me it helps with some of the background-noise of math concepts. Occasionally one will apply with other work I'm doing.

[chris_leyson]

I would say learn basic algebra, learn how to manipulate equations, geometry and trigonometry and as TheAmonical said Trig Identities, they can be very useful at times. Log and exponentials both in base e and base 10 or in fact in any number base. Complex numbers are a must for electrical and electronic engineering and then you get to learn very poweful techniques like Laplace transforms, of course you have to think or freqency in radians/second rather than cycles/second or Hz, it makes the math easier. When yo have to analise larger circuits or systems then polynomials become important, most people can do polynomial multiplication but polynomial division is also a useful skill. Approximation of functions and series can come in very handy, that can simplify a lot of math. Then there is calculus and differential equations, I think I'll stop there for now.
The most important thing is understanding the basic principles and then knowing how to apply the mathematical short cuts and not the other way around as it is sometimes taught.

[orin]

Before you even think about Calculus, make sure your pre-calculus skills are up to date.  Compared to pre-calculus, calculus is a piece of cake.

There are a number of online sites that provide videos of various math subjects (Purple Math and Khan Academy are my favorites).  I also bought several video courses from http://www.thegreatcourses.com/ but only when they were on sale!

Our local library carries a good selection of these.  I sure wouldn't pay full price.

If you want to review calculus, I suggest starting with the following course on Coursera: https://www.coursera.org/learn/single-variable-calculus

It will give you a thorough workout!  Prof Ghrist has put a lot of time into his lecture slides and animations which are entertaining in their own right.  My only criticism is that he talks really slowly and I usually ran his lectures at at least 1.5 speed.  I'd look at basic calculus on Khan Academy before starting this course.  You'll want to know what a Taylor series is or you'll be quickly lost.

I liked this course on differential equations on edX: https://www.edx.org/course/introduction-differential-equations-bux-math226-1x-0

I highly recommend it if they ever run it again.  It lays the foundations of what you are doing to solve differential equations, before going onto some of the tricks of the trade.  It even says that in some cases, you are basically guessing the answer, calling the technique "The method of the lucky guess".  Another thing to note is the mention of the "No wrong answers" principle - you can always check your answer against the original problem simply by differentiating it one or more times.  If you have done this course, RC, RL and RLC circuits in EE will be a breeze.

[rstofer]

I liked this course on differential equations on edX: https://www.edx.org/course/introduction-differential-equations-bux-math226-1x-0

I highly recommend it if they ever run it again.  It lays the foundations of what you are doing to solve differential equations, before going onto some of the tricks of the trade.  It even says that in some cases, you are basically guessing the answer, calling the technique "The method of the lucky guess".  Another thing to note is the mention of the "No wrong answers" principle - you can always check your answer against the original problem simply by differentiating it one or more times.  If you have done this course, RC, RL and RLC circuits in EE will be a breeze.

When working with DEs, you almost always 'assume' a solution and try to back into getting it to work.  The fact is, most DEs can't be solved by analytical means.  It's all based on a guess!

The nice thing is that most people have a computer and MatLab can model DEs quite well.  LTSpice can be coerced into doing it also.  Just create an integrator using an ideal capacitor and op amp.  Today, we have excellent tools for a course that was fairly difficult back in '73.