Math for engineers

Discussion in 'Math' started by fila, May 17, 2011.

  1. fila

    Thread Starter Member

    Feb 14, 2011
    Hello everyone!

    I've been doing a lot of math this semester, Fourier transformation, and Laplace transformation. Through last three semesters we have had three Math courses, Mathematics 1,2 and 3. We have covered matrix calculus, differential equations, integrals, nabla (del) operators, etc. So as you see, a lot of mathematics. I love math, I always did but not until a few days ago I asked myself - why? Why am I learning all this stuff? A lot of things I have already forgot. The main reason is poor lecturing by math teachers that really don't know or don't care about the application of math. When they talk about math they think about theorems and not about application. To be sincere at first I wanted to study math but I wanted to see math (and physics) in action so I chose electrical engineering. I could have chosen mechanical, same thing. But instead of seeing math in action I feel like I math student solving some math problems that don't mean anything to me.
    Without further ado I want to ask the real engineers on this forum. In your everyday life and dealing with real problems what mathematical tools are you using? In the end are we all going to buy some ''math program '' like Matlab or Mathematica for problem solving? Are Fourier and Laplace useful?
    Maybe one question is the most important. Because I love math and love seeing it work I don't intend to stop learning it. What I would like is that you tell me on what should I be more focused and what mathematical tools will help me in understanding the problems I come across and eventually in solving them.
    What are your experiences with mathematics in electrical engineering?

    Thank you.
  2. steveb

    Senior Member

    Jul 3, 2008
    My experience with mathematics in engineering is that it is a critical and invaluable tool. Many of my most creative solutions to problems have come by way of mathematical insight that was only possible because of years of study in math. Further, aside from the insight obtained from mathematical training, proving that the insight was (in fact) useful by actual implementation in simulations and prototypes required further mathematical skill.

    As far as software tools, they are great, but only useful when you have the mathematical background to back it up. What's the point of doing symbolic integrals or derivatives in Mathematica if you don't even know what an integral or derivative represents? How can you utilize an FFT calculation in Matlab if you don't know what linearity means and don't know the physical relation between frequency and time?

    Every field has a standard set of tools that belong in the toolbox. Where would the plumber be without a wrench, or a soldier without a rifle? For engineers, the maths we are taught form a critical tool set, and the more math you know, the more tools you have. As far as the question "which math is useful?", trust in the years of experience engineering schools have. The math taught in accredited programs is the most important. You won't use it all every day. Some, you may only use once a decade. But, when you need it, you need it. Perhaps, you may have forgotten the details of what you need, but knowing that the tool is available is critical, because when you don't know what is possible, you don't even know that you missed an opportunity.

    That said, math is not the "be-all and end-all" of engineering. In really depends on the field of specialization and the person doing the work. I always like to point out the example of Faraday. He used no math at all. The "Faraday's Law" we talk about in integral or differential form is the formulation we get from Maxwell, and that is Faraday's discovered experimental truth, expressed in mathematical language. Faraday was skeptical of the use of mathematical formalism for most of his life. Very late in life he began to see its value, but did not really use math seriously himself. Time has proved the value of math in physics and engineering. But, Faraday proved the value of intuition, experiment, clear thinking and hard work as equally important tools a good engineer should throw in a box and drag to work every day.
  3. Georacer


    Nov 25, 2009
    Wait until you get in the university. After four years in it, I wish I could return to the plain, stand-alone highschool math.

    Now, we have tables, homogenous transformations, complex differential equations, optimum control, you name it.

    Joking aside, you will see that highschool has only taught you about math as much as you know about life in A-Centauri. Preliminary math in the first semesters of each college are very important. Learn them well and you will see that they will serve you well while trying to understand electrical engineering theorems and practices.

    EE schools will blend math and practice in later semesters. Unless you understand your math well, you will be wandering "why on earth did the manufacturer/scientist/professor do that?" all the time. Math can explain lots of things.

    Senior Member

    Jun 29, 2010
    OP is Right...........
  5. wmodavis

    Well-Known Member

    Oct 23, 2010
    I am a retired electrical engineer who went through lots af math in my schooling just as you are doing. It is good stuff though I can't say I loved it like you do. That is definitely to your advantage. Whether you use all or only some of the math you are learning is IMO not the real issue. And whether the math classes 'make it interesting' or 'practical' is practically irrevelant again IMO. Math teaches you to think and helps you solve problems. What are the knowns and unknowns and relationships. That will lead to solutions to problems IF you have the mentality for it.

    Some engineering requires and uses lots of that math and some does not. If you are good at it it is an extremely useful tool but not the end, only a means to the end. The end (so to speak) is solving problems using math and all the other tools you will pick up along the way.

    I didn't like math but I loved electrical engineering. If I got hung up on the profs who weren't interesting or who didn't make it practical etc etc I'd just believe lots of it was a bunch of wasted time. BUT IT WASN'T. Some of that won't catch up to you for years. Some day maybe you'll be able to say 'I sure wouldn't have figured that out if I couldn't integrate or differentiate or whatever'. There is some math I have never used in my engineering but it was not a waste of time. When I interviewed and hired engineers, if they bitched and moaned about worthless, uninteresting, uninspiring, waste-of-time, irrevelant classes I let someone else hire them because they will probably think those same thoughts about what ever they are assigned to do. And all of the real world electrical engineering is not stuff to keep you on the edge of your seat. A lot is hum-drum. Like some of those classes.
  6. santos4eva

    New Member

    Oct 30, 2010
    Mathematical tool is a veritable tool in electrical engineering. You'll not see the need until you decide to be a designer. I had faced some challenges in designing, only mathematical intuition & tools that makes it solveable. For instance, the Jacobian concept in mathematics is used in load flow studies of a countries grid network. On thing is important, knowing how to relate a maths variable to electrical quantity. The concept of reverse engineering used by Japan is through maths. Allocation of resources during the second world war by Britain using linear programming concept is an application of maths. I don't know which part of the world you are, but maths is an inevitable tool in electrical engineering if and only if you'll become a designer, because maintenance engineering don't apply much of maths concept.
  7. ErnieM

    AAC Fanatic!

    Apr 24, 2011
    First off, I'm a circuit designer first and foremost. I call myself a digilog engineer as I am best (and happiest) when designing embedded systems clear thru from the analog front end to the central processor into the code and back out to whatever peripheral is out there. I've got products out there from some medical sensors to military power controllers. Plus the test fixtures for them: one has 11 pics working together to test 10 timing circuits together, another literally you press the DELETE key on a PC and a laser files and blows stuff up.

    OK, tiny stuff but it is still vaporized! Its for custom IC die processing.

    Design a 60dB amplifier at 3 MHz? Done that. Program a PIC to process the results in assembler? Check. Digilog: part digital, part analog. Specialization is for insects!

    One recent project entailed making a power controller for a LED. Customer wanted a LED replacement for an incandescent bulb he could drop into the same hole, so it needed to have the same brightness as a bulb when between 10 and 28 VDC was applied (just for fun in either polarity). Oh, and it all had to fit inside a tube smaller then the metal end of a number 2 pencil. I did remember from way back that interpolation polynomials would fill in the in-between data points not specified, but I didn't work it out; I used Open Office to do it for me (Excel is my best friend but that feature there has always had a bug).

    But no higher maths were involved there. Basic algebra is typically the only math tool I need. I can't remember the last time I needed an integral or a derivative.

    Yesterday I spend an hour getting some internal part numbers assigned to my project. My first boss and mentor told me any engineer is lucky to spend 10% of his time doing stuff he learned in school. I think he was a bit optimistic there.
  8. fila

    Thread Starter Member

    Feb 14, 2011
    I agree with all of you about the utility of math but I've heard things like this countless times:

    Some of you say that mathematics is great to develop reasoning skills and helpful in solving real problems that aren't intuitive but how can math be useful to me in that way when professors are just throwing theorems and mathematical formalism in my face. EernieM says that basic algebra is all he needs. When dealing with circuits I think that's true.
    How many of you engineers had to deal with Fourier transformation or Laplace transformation? Is it something that you use frequently when designing, fixing stuff? Or is basic algebra really enough? And what tools do you consider by basic algebra?
  9. Wendy


    Mar 24, 2008
    As a lead tech a lot of what I did was experience and knowledge, not math. My signature is from an old buddy who worked his way up as a tech to an engineering profession, and there is a heck of a lot of truth to it.

    I've had a lot of discussions with new engineers who wanted to over analyze a problem that I already had a solution for. In a production environment my ideas were used more often than not, and when they weren't I usually learned something new.

    I've frustrated several engineering students at this site by being able to pick out a capacitor value without being able to explain why, and it worked. There really is an intuition to problem solving that can only be learned in the real world and experience. Long before college I was working with electronics. I missed the electronics Vo Tech courses in high school studying college bound subjects. It was a waste. I don't count the math in that category though.
  10. someonesdad

    Senior Member

    Jul 7, 2009
    It's pretty common for engineering and science students to get frustrated with the math as taught by math departments. Part of the problem is that any discipline has few really good teachers. You're interested in using the math as a tool, not seeing theorems proved. But you don't realize that mathematicians often value the proof as much as the theorem. This is hard for students to understand because they haven't climbed those mountains in discovering new theorems for themselves. I remember discovering a nifty thingy in my research when I was a student and my adviser called me on the phone and we talked about it for two hours one evening, both being quite excited about it (alas, I can't even remember what it was now). There is great excitement about seeing something new that others haven't seen before -- and a good proof shows you something about the path that the explorer took to get there and demonstrates insight and creativity.

    Once you're out in the workforce, the use of mathematics as a tool varies widely. I worked at a big Fortune 50 company known for hiring the top EEs and saw a wide variety of math used by engineers -- some used little and some used a lot. I found I probably used math models more than the engineers, mainly because I often worked on things that weren't built or were in the design phase -- and we didn't have enough experimental data to help us make decisions on how to proceed. Thus, we'd build mathematical and computer models of things and use those to help make decisions. As an example, at one place I worked in the 70's, we were building a complicated ultrahigh vacuum chamber. Someone decided that we should have an electron beam evaporation option in this chamber, so we had to design the positioning of the electron beam guns, shutters, etc. inside the chamber and estimate what kind of deposition uniformity we'd get over a GaAs wafer in that chamber. There was no way to do an experiment, as the chamber hadn't been built, so we set up a math model for the evaporation uniformity (as I recall, it was a reasonably hairy double integral). I couldn't evaluate it analytically, so I had to beg some computer time from the EEs and their CP/M systems. That was my introduction to computers, as most of the people in my department in school in the 60's had "turned our noses up" at computers in college (all that was available was card-punch FORTRAN systems over in the engineering college).

    I do have some advice though on some math courses I'd recommend you take. First, take a good engineering statistics class. Learn something about experimental design and decision making. You'll use these skills through the rest of your career and you'll have a leg up over your colleagues. Most of the work you'll do helps you and others make decisions, so it makes sense to learn how to make good, objective decisions with the least amount of resources.

    Second, take a Finite and Combinatorial math class from the computer science department. It is material rarely studied by EEs, but you'll find tools you'll use later in your career.

    Third, this isn't a math class, but you're going to use computers a lot. I strongly recommend every engineer and scientist take a Data Structures and Algorithms class, also from the computer science department. The reason is that computer use and programming will probably be heavy in your career, so it benefits you to know how to use and analyze data structures and algorithms. You'll learn interesting things along the way too.
  11. BillO

    Distinguished Member

    Nov 24, 2008
    Yes, they are. However, more important is knowing about them and other applications. Depending on the turns your career takes you may depend heavily on the knowledge of mathematical applications you are now learning, or perhaps not. The future will determine that. After 35 years of not using Fourier transforms I was recently asked to do a study on the feasibility of making hand help voice replacement device. Something that you could hold in your hand, talk or sing into and out would come the same phrase in someone else's voice. It turns out that, no, tis is currently not feasible, but for 3 months I lived and breathed mathematical applications, including Fourier transforms, trying to design and optimize models for the human voice.

    ( can and is being done with varying degrees of success...however, not real-time, and not in a hand-holdable format.)

    Mathematics itself is the greatest tool. What you have likely been learning is applied maths. The difference between applied mathematics and pure maths is like the difference between instruction pipelines, data caches, asynchronous memory, dynamic mapping, processing vectors, and, running Word on a PC. A Fourier transform is something you can do with mathematics, but it does not give you a very good look at mathematics. If you love maths, I'd suggest a more thorough program in mathematical analysis, theoretical algebra and geometry/topology.

    I used a lot of math in the above mentioned project, as well as the following placements in my career;

    • In a stint in academia running labs in electronics for the physics department of the U of T.
    • In a stint as an electronics technologist in the sound industry designing custom filter networks.
    • In another stint as an electronics technologist in the communications industry designing error detection and correction algorithms.
    • As a systems engineer in the marketing industry designing sorting, selecting, searching, collating and summarizing routines.
    • As a mathematician working for the environmental department of the Ontario provincial government reviewing papers for publication and advising the environmental scientists that wrote those papers.
    • As the local vice president of support for a multinational software company analyzing statistical information (well, I had folks that did the actual analysis, but I directed them...:p)
    You may actually do more math than me, as some of my friends from University have wound up doing, or less, as others have. It's best to be prepared. Besides, the more math you do, the better you will understand everything else.
  12. fila

    Thread Starter Member

    Feb 14, 2011
    Thanks for the replies. :)
  13. retched

    AAC Fanatic!

    Dec 5, 2009
    What's math?
  14. sa.doublex

    New Member

    Jun 16, 2011
    though I didn't go far in my studies but what I've discovered is that most of the math I did in my study is only applied in design work, is laplace transforms and fourier, matrices but not just in the real industrial field but some are abstract.
  15. MrChips


    Oct 2, 2009
    To fila,

    The answers to your questions are Yes, Yes and Yes.

    You may not see the relevance now while you are in school but stick to it, it will be worth it. Math, Fourier Transforms, Laplace Transforms - You will be amazed how much you will use them - not just to work things out but to give you a solid understanding of what you are doing.
  16. MrChips


    Oct 2, 2009
    Just got back from having an MRI brain scan. All of this would not be possible without engineers with a solid background in Math, Fourier Transforms, Laplace Transforms and computers. Think about it.
  17. mcasale


    Jul 18, 2011
    Hi there. I echo a lot of what's been said, but you should not rely on any software packages to do your work for you - except maybe Excel. I've been doing EE stuff for nearly 40 years (OMG!). I have done many control applications (using feedback) and the Laplace Transforms are essential. If I want to simulate a system or get a frequency response, I'll write out the equations by hand and then enter them into a spreadsheet for grunt calculations. Also, if you wind up working in a small company, or for yourself, you won't have the money to buy expensive software. Learning the underlying math is GOOD. I still have my text books - though they are written on parchment :).
  18. #12


    Nov 30, 2010
    I get most of my work done with algebra and trig. Every day that I plug in the soldering iron, I will use algebra. My neice holds up "the sign of the cross" when she sees me doing math. Funny! She acts like it's witchcraft :)

    A side note, Albert Einstein and I both failed algebra the first time we took the course!

    It is very useful to be able to write a program to do what somebody called, "grunt" work. Having some subroutines to do math saves a lot of time. I learned Basic and Fortran, but I suspect spreadsheets are easier. Besides, handing over a printout of the program and the answers makes a believer out of the most difficult people.

    Knowing where to find it is important. Notice the names of the formulas. I was in a backwoods town without my books, so I told a local to get the high school math teacher to get me Hero's formula so I could double check a land survey. The customer gained 17,800 square feet of land because I was able to name the formula I needed and find the errors in a surveyors map.

    You never know when the opportunity to use math will get the job done!