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Should I bother with this last chapter of my Linear Algebra text?

  1. Dec 17, 2015 #1
    Intro to Lin. Alg via MIT OCW 18.06 (part of Electrical Engineering), by Gilbert Strang.

    I've been doing it as independent study before starting my BSEE next year. I'm getting to the end. Chapter 9 is titled "Numerical Linear Algebra", and is concerned with the heavy, intricate computational side of applied linear algebra, principally in how poorly conditioned matrices are handled and how efficiency and accuracy of solutions are optimized and traded off in actual real world algorithms.

    None of what's in Ch 9 appears on the final exam and isn't really relevant to Electrical Engineering (maybe for CS, but not for EE broadly speaking...at least, I think so). Ch 9 really seems like an introduction to the sort of thing an Applied Math major would want to master in order to get a job at Mathworks.

    Does an EE focus need this deeper look into the "under the hood" aspects of numerical linear algebra?
     
    Last edited: Dec 17, 2015
  2. jcsd
  3. Dec 17, 2015 #2

    Study what's going to be on the test.
     
  4. Dec 18, 2015 #3

    Krylov

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    I could imagine that numerical LA could be useful for the analysis of large electrical circuits, complicated linear control systems or power networks, but maybe indeed it is not part of the core material for someone starting his undergraduate studies. However, I'm not an EE, but I just ran into one, though. Maybe you can ask @Domenico94 for an opinion.

    Maybe it's also better when you change the title to something like: "Should a undergraduate EE learn numerical linear algebra?". It may attract more knowledgeable customers.
     
  5. Dec 18, 2015 #4

    FactChecker

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    It sounds like you have already skimmed it and know what the issues are. That is enough. Concentrate on the required material. The fact that you can self-study means that you can pick it up later if you ever need it.
     
  6. Dec 18, 2015 #5
    As an EE student, I don t think that going too much deeply into theory would help much, since engineers tend to apply what mathematicians and physicists already studied, but I d suggest him to better study the applications of numerical methods, for example like Euler's-method is used in circuits involving diodes, or how this method can be used to have the response of an RLC circuit. But while you re in college, no teacher will actually ask you: I have a system with these variables. Please solve them numerically. Studying that would serve as an insight, by the way
     
  7. Dec 18, 2015 #6
    I don't think I can edit the title at this point.
     
  8. Dec 19, 2015 #7

    Student100

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    You can actually take those open courses for credit? That seems odd.

    I've leant out my copy of the 4th edition, but if memory serves me then the information in Chap 9 would be okay to skip as an EE for right now. The iterative methods may be something you want to revisit later on when you start programming in Matlab more. Chapter's 8 and 10 are incredibly useful, however, FFT's playing a major role in signal processing. That is something EE's should be very concerned about.

    If you're just self studying the material, and final exam isn't a real final exam, I would just say go ahead and grind through it now.

    Strang's book is excellent for the applications of LE, but I hated his videos.
     
  9. Dec 20, 2015 #8
    In preparing for your final you should focus on material thats going to be on the exam.

    However, afterwards spend some time to study this last chapter. I strongly disagree with the statement the numerical linear algebra is irrelevant to engineering. In my opinion this is one of the most important subjects in linear algebra for engineers. There are numerous problems in engineering that require you to invert large matrices. In many cases you'll probably use a numerical library. However, knowing the basics behind how these methods work will help in selecting the right method for a particular job. Also when things break it helps to know whats "going on under the hood."

    In general spending a few days to learn new material can only open doors. However, ignoring a subject because you decided that it is irrelevant closes doors.
     
  10. Dec 21, 2015 #9

    mathwonk

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    I would skim it to know what are the issues, and to know where to go back to if you ever need it. Thats all I did as a pure mathematician and I have never needed it, not having ever taught the numerical courses afterwards. remember though, sometimes numerical topics are where the jobs are.
     
  11. Dec 21, 2015 #10

    Student100

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    I just got my copy of the 4th edition back, I'd definitely recommend you do chapter 10, even if it isn't required. 9.1 and 9.2 are short and have some good information, while 9.3 is probably okay to skip for now. Good luck with your final.
     
  12. Dec 22, 2015 #11
    Oh I've done chapter 10. Good to see FFT and unitary matrices, even if I don't fully understand FFT.
     
  13. Dec 22, 2015 #12
    I don't strictly disagree with you, but in a qualified sense I do, re: opening and closing doors. Not covering those numerical LA chapters would not transform into leisure time. It would be spend doing other study that might benefit me more. Since I haven't started my BSEE yet, I might be better off devoting those few weeks (as I also work full time at the moment), to broadening my programming knowledge, doing more physics, more advanced diff eqs stuff like Laplace Transforms that I want to at least have a rudimentary understanding of before I begin the course.
     
  14. Dec 22, 2015 #13
    When I was in the EE major we had a required numerical analysis course in sophomore year that was built almost entirely on linear algebra. I think it would be a good use of your time to get acquainted with the subject, though wait until after the final if it's not going to be on your test.
     
  15. Dec 22, 2015 #14
    When I was a student, I barely had time to eat, let alone explore beyond what was required of us.

    Before finals:
    I think it is best if you focus on just the material for which you are responsible. Anything that distracts you from that task may hurt your mark.

    After finals:
    Go ahead and learn all the additional info you can. It can't hurt. And there is a chance, if you find the material interesting, it may stimulate you to learn more in the CS field. Even if it doesn't, Electrical Engineering students do a lot of programming and this material may be helpful later.
     
  16. Dec 23, 2015 #15
    Thanks for the replies, it's much appreciated.

    One annoying thing about these extra sections (referring in particular to Chapter 9 and sections 8.6 and 8.7), is that they feel very much like an afterthought. Something tacked on, and not really well fleshed out. Informally the text itself explicitly stated that SVD was the climax of the text. This was at the end of Chpater 6. chpater 7 on Transformations was reasonably well fleshed out and structured, but also based very much on familiar concepts cast in a different light. Chapter 10 on complex, matrices, complex operations and Fast Fourier Transform was a bit difficult but not so much of an afterthought, as Chapter 10 was meant within the syllabus to be covered part way through Chapter 6. But Chapter 9 is only vaguely on the reading list, not on the final exam, and has this feel of being an afterthought; plenty of gaps in the explanations; the same being true of 8.6 (LA in Stats and Probability) so far...I haven't gotten to 8.7 (Computer Graphics) yet.

    I'd love to get a more solid grounding in these very important real world applications of LA, but this text seems to be treating these things as an afterthought following its self-admitted climax at the SVD.
     
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