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Wasting time with Spivak? Engi major to-be

  1. Jul 13, 2012 #1

    I am going to major in engineering physics come fall and purchased Spivaks' "Calculus" after seeing it recommended a lot (here amongst other places). I expected it to be hard but it's excruciatingly so.
    I have done some HS calculus before but that was more memorizing how to solve a particular type of problem and then doing it over and over. Never done any proofs based maths before (closest to a proof I have come is some trig equalities) so the style of this book is obviously quite new to me.

    I'm actually enjoying my time with the book, only on chapter two and I can spend hours on a single exercise. I find myself getting help from solutions or the back of the book for more questions than I manage on my own while some I have a lot of trouble getting even with the solutions/I understand what is done but it's a 100% "Not a chance I'd come up with that". Feels like such a victory when I do get something right though.
    If I had all the time in the world and nothing else going on I'd stick with it, but as the pace I'm getting through it at is so slow I doubt I'll have gotten much actual calculus done come fall.

    I'm essentially just wondering if I would be much better off using some less rigorous book that's easier to work through and isn't as proof based (I'm spending plenty of time just learning how proofs work here). I have my dads old Robert Adam's "Calculus: A Complete Course 3rd ed." (later edition is used in my uni as a supplement to their own material) and I've considered purchasing Stewart's "Calculus": Hell I could spend some time getting familiar with linear algebra, looking at the theory it seems to start off simple enough.

    Any input would be appreciated, really quite at a loss here.
    Sorry if it's in the wrong board, not quite sure where this would go.
  2. jcsd
  3. Jul 13, 2012 #2


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    I fear that Spivak might be the wrong book for you. First of all, Spivak is a book intended for math majors. As such, it spends most of the time on proofs and less on what might be useful to engineers.
    Second of all, Spivak is actually a book intended for people who know calculus and who are familiar with proofs. As such, it is more an "introduction to real analysis" than a calculus book.

    The book is quite hard if you're not familiar with proofs and calculus. Especially the exercises can be very daunting.

    I think it might indeed be best to get yourself an easier book for now.
  4. Jul 13, 2012 #3


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    I essentially parrot what micromass has said, and will just note that all the extra 'real analysis'-y stuff in this book is almost certainly unnecessary to you as an engineer. So simply, do not expect all of your hard work to somehow pay off in your engineering classes. But since it seems like you are enjoying it, by all means pick it up again after you've had an exposure to calculus!
  5. Jul 13, 2012 #4
    Thanks for your thoughts. Leaning towards abandoning Spivak then. Would be one thing I had to trudge through this eventually but if it's more or less not at all useful for what I'll be doing in the next few years it doesn't seem like the most effective use of my time.

    Will definitely give it another crack in the future when I have more maths under my belt. Was fun to give it a try at least, got to say, a bit humbling as well. Couldn't quite drop the "how much harder can it get?" feeling until I started with Spivak.
  6. Jul 13, 2012 #5
    Not so fast! I am also an Engineer ( Aerospace) and It is my opinion that you aren't wasting your time on Spivak. As you, I am also revisiting Calculus with Spivak and I can certantly relate with your strugles and feelings of acomplishment. Well, if you have got the time needed for it (as you have experienced, it needs alot of time) it is enlighting to see math at this level. altough I might agree, that a diferent book woud be more suibatle, Spivak allowsus to grasp things differently. If feel the need to be good at solving exercices, rather than givin proofs, don't worry. Search for " Calculus Exercices" on google, and you shall find countless exercices.
  7. Jul 14, 2012 #6
    What would be a good book to learn about proofs?
    I already know "engineering calculus" but I was interested in learning more about math as a hobby
    I got Spivak but it seems to assume I know some things I don't.
  8. Jul 17, 2012 #7
    ttt, no tips for me?
  9. Jul 17, 2012 #8


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    If you are interested in learning about doing proofs (and the thought processes involved), I would recommend "How to Read and Do Proofs" by Daniel Solow. When I was pursuing my BS in math, I found this book quite useful.
  10. Jul 17, 2012 #9

    George Jones

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    Maybe there is no practical connection between engineering and the epsilons and deltas of analysis, but I think there is a conceptual one.

    "If I have this much play (jiggle room) here, how much play do I have there?"
  11. Jul 17, 2012 #10
    Hmm it seems interesting, thanks for the tip.
    From the description in Amazon seems exactly what I need, I'm not professional mathematician, just wanted to learn some more rigorous math in my spare time.
    I know how to calculate integrals and solve ode's but never got much the theory behind it.
  12. Jul 17, 2012 #11
    Good engineering book is the one by larson. Less proofs and more stuff you need for engineering. There are some puntam problems for the math major inside of you.
  13. Jul 17, 2012 #12
    I can sympathize with your feelings with respect to the exercises; spending hours upon hours doing Spivak's challenging exercises may indeed be impractical. One's time is of course limited, and your intention is to become an expert engineer, a builder and designer of physical things, and not an expert constructor of mathematical proofs.

    So, feel free to largely abandon the exercises.

    However, I would urge you to hold on dearly to the main body of the text. The material in each of his successive chapters is well worth reading for an engineer. If you intend to go into a profession that makes heavy use of calculus, then being able to read dense mathematical prose will be a skill to have if you really want to excel at what you do. It will be useful to you in the way that chemistry is useful to a surgeon, or in the way that knowing French, German, or Latin is useful to a mathematician. You may not use it on a daily basis in an immediate and direct manner, but if you're really serious about what you do then it will still come up on a regular enough basis to be well worth learning. Do you not surely envision a time in your future career when you get stuck on some cutting-edge engineering problem, and have to dig into some deeper texts or papers on mathematics or physics looking for a solution? You won't want the look and feel of dense mathematical prose to be something foreign to you. Perhaps you won't ever have to produce dense mathematical prose, but it will be good to know how to read it with relative ease. The idea is to be as mathematically literate as possible.

    So, if you want my advice, I say this: put Spivak's exercises to the side for now, and instead barrel on through chapter after chapter, just reading and trying to understand. It won't be nearly as hard; the exercises really do put the breaks on things, so take the breaks right off :-)
  14. Jul 18, 2012 #13
    Yeah not going to abandon it altogether, I'll take a peek every now and then when I feel whatever else I use isn't quite enough/I want more understanding of something.
    Just abandoning my "Do Spivak and do/attempt every exercise until fall" plan.

    Keep hearing that the first year of uni will be the filter year and is hard no matter how you twist it, want to lighten the load now when I do have time.
    The book will be close at hand though, I'm expecting the chapters on limits and onwards will be helpful down the line.
  15. Jul 18, 2012 #14
    Simple solution is to do "baby calculus" with Stewart et al, then when you graduate and you'd like to gain deeper insight, pick up Spivak and work at your own pace. It's similar to what I intend to do when I'm out of college, which is to pick up a partial differential equations book and start cranking.
  16. Jul 18, 2012 #15
    That's what I'm doing my friend. It isn't always practical when you're in eng school to waste much time in rigorous math, you have many other things to do.
    By the way, if you guys could choose only 1 book for more advanced calculus what would it be?
    Courant(my professors love this book), Spivak(seems to be the favored here in PF) or Apostol(I think MIT uses it)
    I know all of them are good, but I would like some insight, I got access to all of them btw.
    I liked Apostol because it got 2 volumes, single and multi-variable, I don't know if spivak got multivariable?
  17. Jul 18, 2012 #16
    IMO, the Courant Books (you are talking about the two volume set, right) aren't near as good as Spivak. Spivak's is a great book and he has another one called Calculus on Manifolds which is like his multivariable calculus book.
  18. Jul 18, 2012 #17
    I see, but wouldn't the manifolds book be a little too advanced? Some people claim it's like the hardest book ever to completely grasp. I'm up to a challenge although...
  19. Jul 18, 2012 #18
    Yes, the manifolds book is hard. In fact, I'm working through it now. But it is a good book.
  20. Jul 18, 2012 #19
    Spivak is very rigorous and proofs, while Stewart is all application and very elementary. Stewart is a good book for engineers who have no interest in mathematics and just want to memorize formulas and algorithms, but it seems you want a deep(er) understanding.

    In that case, I'd highly recommend the Salas, Hille, Etgen: Calculus: One Variable. I'd say its the "middle-ground" between Spivak and Stewart, that is a book that has both proofs and computation, although the computations are harder than Stewarts but the proofs are much more elementary than the proofs found in Spivak. That is the book used at my school for math majors who wanted to learn to do proofs but felt they weren't ready for analysis (honors calculus).
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