Advanced Math in Electronics Engineering

[Legion]

General question for the engineers out there. How often do you directly use advanced math (differential equations, fourier analysis, etc.) in your job?
By "directly use" I mean if you were put in a differential equations for engineers course, for example, would it be trivially easy cause you do this stuff everyday, or would you need to go back and leaf through the textbook for a while to remember?

[IanB]

Not an EE, but quite a lot. That's because I work in the area of simulation/computation where mathematics is both important and necessary.

[Legion]

Not an EE, but quite a lot. That's because I work in the area of simulation/computation where mathematics is both important and necessary.

Do you use software tools like Matlab and/or Maple to help?

[IanB]

Do you use software tools like Matlab and/or Maple to help?

Generally not. I either use Excel or I write code in C++ or C#. I'm in the software business so code is the end product of what we do (we create commercial tools that allow engineers to do simulation).

[mtdoc]

I believe Dave said in a recent video (or AmpHour podcast?) that he has never needed to use calculus or other higher level math in his career as an EE.

[EEVblog]

General question for the engineers out there. How often do you directly use advanced math (differential equations, fourier analysis, etc.) in your job?
By "directly use" I mean if you were put in a differential equations for engineers course, for example, would it be trivially easy cause you do this stuff everyday, or would you need to go back and leaf through the textbook for a while to remember?

Never used advances math like that once in 20+ years in the electronics design industry. But YMMV, some people use it daily.
Yes, I'd have to look up the textbooks to remember any of it.

[Fsck]

fractal antennae come as an easy example for using math in electronics design.

[EEVblog]

fractal antennae come as an easy example for using math in electronics design.

How many design engineers would have to design their own fractal antenna?

IME the majority of electronics design engineers will rarely, if ever have to use advances math. It's usually statistics, or concepts like integration are needed, rather than actually solving integrals or whatever.

[Fsck]

fractal antennae come as an easy example for using math in electronics design.

How many design engineers would have to design their own fractal antenna?

IME the majority of electronics design engineers will rarely, if ever have to use advances math. It's usually statistics, or concepts like integration are needed, rather than actually solving integrals or whatever.

industry, no clue. I guess I forgot to type out my longer answer:

for most people in "electronics engineering", as typically defined (industry & selftaught/Bachelors level stuff [which is most], excluding theoretical research [yes, there are theoretical researchers in ElecE!]), >90% of people will not use advanced math. you can probably forget how to do anything manually above first year univ math. any higher level stuff, you'll probably just have a computer to do it for you, if it needs to be done at all.

[IanB]

I think it is hard to answer this question properly without defining what "advanced math" is. It will surely mean different things to different people?

For instance, if you are in Grade 10, then first year college math will seem like "advanced math" to you. If you are in the first year of college, then the subjects covered by graduate students will seem advanced. It's all relative.

But as to fundamental areas of applied mathematics like ordinary and partial derivatives, differential equations, integration, vectors, matrices, complex numbers and so forth, then I think most engineers should expect that to be part of their world at least some of the time.

One way to answer this question is to look at the mathematical content of the American EIT/FE (Engineer in Training/Fundamentals of Engineering) exam. The material in the FE exam is considered by the exam admininstrators to be foundation knowledge for engineers of all specializations.

[Rick Law]

General question for the engineers out there. How often do you directly use advanced math (differential equations, fourier analysis, etc.) in your job?
By "directly use" I mean if you were put in a differential equations for engineers course, for example, would it be trivially easy cause you do this stuff everyday, or would you need to go back and leaf through the textbook for a while to remember?

Let me add some fruit for thought - or random thoughts if you will.

I am not an EE person.  I am trained in Physics (Master Degree).  I have never worked a day in Physics after graduate school, but I use the skills I learned in Physics in every job.  The problem solving skills I learned, the analytical skills I learned...  In the 30+ years I have worked, I have taken on many roles, from junior to executive level.  The skills I learned as a Physics student are skills I used everyday.

Mathematics is a language on its own.  It is a form of expressions and thus a form of communication.  The more mathematics you learn, the more ways of approaching (thinking about) a problem you got.

There is no such thing as too much knowledge.  Eat it up.  It will only help.

Rick

[EEVblog]

But as to fundamental areas of applied mathematics like ordinary and partial derivatives, differential equations, integration, vectors, matrices, complex numbers and so forth, then I think most engineers should expect that to be part of their world at least some of the time.

IME of practical PCB and system level electronics, I've found that not to be the case, and am struggling to think of any colleagues who have needed to do so either (and I've asked them over the years too, as I've often wondered this myself). I'm also struggling to think of any instances where I have seen it documented in any company engineering documents, and being from a big military background, that's all we did, document stuff, including all calculations and equations etc. Granted, I'm just one case having only worked at a half dozen companies.

I do know of some that have used such advanced math is basic research and the like with in the company. But that's pretty rare. Usually it's done once and then you spend 5 years design engineering the actual product and into production.
Of course I've had to understand the concepts behind it all and know when such things apply etc, but the actual calculations I've left up to pre-written routines that do the advanced number crunching or simulation packages etc.

[ablacon64]

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Sorry, very good topic but I couldn't help myself!

[vk6zgo]

fractal antennae come as an easy example for using math in electronics design.

 Among RF folk,fractal antennas are largely regarded as a "gimmick" offering no advantage over conventional designs.

Of course,they do contain that magical word "fractal" in their name!

The real antenna "gurus" do extensively use high level maths,but most of us lesser folk rely upon
well established design rules for antennas.

[Fsck]

fractal antennae come as an easy example for using math in electronics design.

 Among RF folk,fractal antennas are largely regarded as a "gimmick" offering no advantage over conventional designs.

Of course,they do contain that magical word "fractal" in their name!

The real antenna "gurus" do extensively use high level maths,but most of us lesser folk rely upon
well established design rules for antennas.

the problem is when you're trying to save every mm^2 in your design, or when compressing your circuit into the smallest area possible you've left a very oddly shaped space available for antennae.

[nuhamind2]

I'm sure things like making robot require a hell lot of control theory.

[T3sl4co1l]

If you're content to just "look it up" on everything, yes, damn near everything has been derived at one point or another, and all you really need is a search engine, or a good solid data book.

But if you're the kind of person who needs to understand things, and wants to see theorems proven in class, and wants to derive things yourself, you will need it.

Personally, I use arithmetic daily; algebra frequently, during design (most often playing with resistor dividers, AC steady state filters, diodes and transistors, etc.); and calculus and diff eq occasionally (more at complicated coupling networks, time-domain stuff, certain models of reality).

I use Fourier and E&M (except for special cases for transformers) extremely rarely, however they are always intuitively present in my mind.  Two cases where manual calculation is almost useless, but knowledge and intuition with their properties is invaluable.  Practical calculations are almost exclusively computed, for example DFT on time series data, or FEA on E&M.

The most recent diff eq I looked at was this problem:
Suppose you have a heat source in the center of a round metal plate.  The heat source has a radius r1 and the plate, r2.  Thickness and conductivity do not matter directly, but the product, the heat spreading coefficient rho, does.  The surface has a thermal conductivity to the surroundings defined as p = T(r) * k, where p is power density (W/m^2 or whatever), T(r) is the temperature at radius r (0 <= r <= r2) and k is the heat transfer coefficient.  (This is at best a poor approximation of radiation -- which goes as Tabs^4, and a poor approximation of convection, which is nonlinear in the T^2 range or so, depending on airflow and awful stuff like that.)  So, a transistor bolted to the chassis and how it heats up, simplified.

Setting up the equations is fairly straightforward, the trouble comes when trying to solve it... it turns out to be of the form of the Bessel function.  So you kind of have to compute it, or pick it out of a table or whatever, to do much with it.

Another thermal conductivity problem I've done is uniform power (W/m^2) into the face of a conductor, which sinks the heat laterally (no surface dissipation or crap like that to deal with).  It's a differential equation again, but easy to solve this time; it's a parabola, with the vertex at the hot end.  The temperature at the end is simply the sum of all temp rises along the conductor (which, at a given point, is the sum of all power dissipated by that point, which is linearly cumulative).

Tim

[Legion]

Thanks for the responses. I enjoy math but I find if I don't use it, it's quickly forgotten. As my time gets more limited I have to prioritize the things I study.

[tszaboo]

I daily use advanced math, like multiplying stuff... Jokes aside, the worst mathematical problems came for me from error analysis, and filter design, thermal design. None of which requires integration, or any kind of university math.
Avoiding complex mathematical problems is part of the engineers job. If you can simplify an integration to multiplication with 10% accuracy, you will do it, because usually it doesn't matter. To say one example, you calculate an oddly shaped waveform dissipation on a resistor, to say if you need 63mW 125mW or 250mW one. There is no point, just point at the average of the signal, calculate the dissipation, add like 50% (which you need anyway) choose resistor.

[TheRuler8510]

General question for the engineers out there. How often do you directly use advanced math (differential equations, fourier analysis, etc.) in your job?
By "directly use" I mean if you were put in a differential equations for engineers course, for example, would it be trivially easy cause you do this stuff everyday, or would you need to go back and leaf through the textbook for a while to remember?

The strongest advise I can give you is to remember to actively manage your career as you progress through it, or else it will manage you. You can easily manage it in such a way that you never see advanced math, or never see an electronic component for that matter.  Having the math background can give you insights into some problems you may not otherwise have had--even if you never actually use the math.

Whatever you do, you should gravitate toward what you enjoy doing the most--but also use foresight into where that will lead you. Don't get pigeon-holed doing something that will cause you to be unemployable in ten years--I have seen that happen to people.

Good Luck,

[t3chiman]

General question for the engineers out there. How often do you directly use advanced math (differential equations, fourier analysis, etc.) in your job?
...

I concur with the consensus: the daily grind of a workaday EE involves scant reference to the higher-order math so beloved by academics.

But, say you find yourself putting CPUs into your circuits, and writing software to control interprocessor communications. Then, the situation changes. Personally, I found the switch from circuits to networked processors jarring. Even after pursuing (and getting) an MSCS, still I felt an intellectual void when weighing design alternatives. It took years to dispel my worries, and reach a conclusion.

I had to crack open the old discrete structures book. After some reflection, I realized that relational algebra, finite state automata, regular expressions, parsers--all are merely different aspects of algebraic semigroups. Following such an insight led to high-confidence forays into areas that working programmers tend to avoid: formal specification, automated testing, even metaprogramming (very dramatic when it's used judiciously).

Think that algebraic semigroups will never affect your daily work? Think again. Last week, I happened upon www.systemsafetylist.org. One topic: the Toyota firmware lawsuit. The expert witness for the class action plaintiff had posted his direct examination. It went something like this:
Q: How many global variables did the Toyota firmware exhibit?
A: Over 10,000.
Q: How many would good software engineering practice dictate?
A: Zero.
Etc., etc. Went on for days.

Toyota had to settle, cost them millions.

Thing is, control logic is modelled completely by a Reactor/Proactor pattern. And the sparse decision trees typical of real-time control programs are straightforward to generate with logic programs (After all, EEs don't really use the karnaugh mapping techniques shown in their circuit texts; it's all automated.). As for the thousands of global variables, who knows? I am skeptical. But I did not see any online cross examination of the expert.

So, if you are an EE, and find yourself writing software that describes occasionally communicating finite state machines (sound familiar?), it would behoove you to get smart on your relational algebra, regular expressions, first order predicate calculus, and parser/generator logic. You will then be well prepared when the boss asks for formal specifications--you will have been there long before. As for metaprogramming, you can put it off for a while. But it is absolutely shocking to see an expert write a program that writes your program, I can tell you.

Hope this helps.

[Rick Law]

Thanks for the responses. I enjoy math but I find if I don't use it, it's quickly forgotten. As my time gets more limited I have to prioritize the things I study.

Mr. / Ms. Legion,

I am glad to see your response here "I enjoy math..."  Good for you!

My earlier response "eat it up, there is no such thing as too much knowledge..." was in part mistakenly thinking the original post may be a case of "looking for an excuse to avoid doing it".

I place a lot of weight on "thinking".  Math helps one think different and that alone is a lot of value.  If you enjoy doing it, eat it up, do it.  Knowledge in and of itself is valuable.

Rick

Sidebar 1 : It may be of interest to know: During WWII, one of USA's 5-star general was Omar N. Bradley.  Omar Bradley did integral calculus for relaxation.  This is according to his aide Chet Hansen in one of those History Channel shows about WWII.

Sidebar 2 : An education series call TED Talk (The 2011 series on Inexplicable Connections), one episode is "Dan Cobley: What Physics Taught Me About Marketing"  This is not a great episode per se, but it really high lights how knowledge in one field can be applied to solve problems in something totally unrelated.  Dan Cobley is the current UK/Europe Google Marketing boss.

http://www.ted.com/talks/dan_cobley_what_physics_taught_me_about_marketing

[Neilm]

The only application I have had for advanced maths was measuring an unknown capacitance. The capacitor was discharged through a resistance - a voltage was tapped off this resistance (using the resistor as a divider) to charge up another capacitor (which of course began to discharge when the voltage on the load capacitor was low enough). We had to work out the algorithm to workout what the original capacitance was.

[Kohanbash]

I'm sure things like making robot require a hell lot of control theory.

In robotics there is a fair amount of math when getting into things like autonomy, machine learning, and data analysis. A lot of it comes down to implementing a mathematical idea. A lot of times the math (equations) look tough, but the ideas are easier to understand.

For example to go back and forth from position, velocity, and acceleration you need to know the ideas of differentiation and integration.

Some common uses of math are:
Advanced Statistics - For machine learning stuff such as classification algorithms
Approximation/Interpolation - Working with sensor data and motion planning
Linear Algebra - computer vision, building maps

edit: The TI-89 calculator is great for higher level math classes (and for those of us who forgot calculus and need to use it)

[Phaedrus]

The most recent diff eq I looked at was this problem:
Suppose you have a heat source in the center of a round metal plate.  The heat source has a radius r1 and the plate, r2.  Thickness and conductivity do not matter directly, but the product, the heat spreading coefficient rho, does.  The surface has a thermal conductivity to the surroundings defined as p = T(r) * k, where p is power density (W/m^2 or whatever), T(r) is the temperature at radius r (0 <= r <= r2) and k is the heat transfer coefficient.  (This is at best a poor approximation of radiation -- which goes as Tabs^4, and a poor approximation of convection, which is nonlinear in the T^2 range or so, depending on airflow and awful stuff like that.)  So, a transistor bolted to the chassis and how it heats up, simplified.

In that case I would say, "Ok, what's the peak and average power output? 10W and 6W respectively? And we need four of 'em? Ok, I need an aluminum heatsink aboooouuuut this mass, and since we're doing mass production the stamped one is ok. Add a thermal pad and we'll tweak the fan speed curve once we build the EVT sample.

It's a lot easier. There are times when you need to use higher math, but in 90% of cases, unless you're working on the bleeding edge or doing extreme optimization, rule of thumb works fine.