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Any advice about integration appreciated.

  1. Aug 26, 2006 #1
    Me and integrals fell out:frown: and as my course is nearing an end I'd like some advice on where I could learn more about Integration and the techniques involved. I'm pretty sure I will still pass as I did very well in other areas, but my tutor admitted this was the hardest part of the course and that it was inherently difficult learning material solely from a text book.

    Unfortunatley I couldn't attend tutorials as they conflicted with work. As I'm looking to study physics further and understand integrals are a very important part of physics both classical and quantum, I'm keen to get a good grounding before I start the physics diploma in a little over a year. So I've decided to spend the next 3 months before my next maths course starts getting to grips with an area I obviously didn't get to grips with the first time round.

    My basic problem was that I had trouble following the rules and remembering them all and knowing when exactly and sometimes how to apply them, I also made mistakes in certain steps that lead to the whole thing being very innacurate, also time was a factor and I spent a deal of time trying to confer with my tutor by email, this was a lenghty process, that meant I didn't get real satisfactory answers quickly enough to meat the deadlines of the assigned assesments.

    The texts I used were excellent but sometimes they didn't show all the steps in solving an integration problem and I found it hard to follow exactly what had happened. As an example I showed a problem to a friend at work and he solved it in about nine steps, and it was very straight forward, the book did it in four and it left some questions. Needless to say work is not a good environment to learn, and I can't rely on getting satisfactory advice in the 45 minutes of personal time alotted at work. They expect you to work :smile: the cads!

    I guess what I'm looking for is good introductory work into integration at the 'A' level or advanced level(this is high school calculus in the US but is college level in the UK as college starts at 16) I already have a good grounding in the basics from the course so it doesn't have to be completely introductory, but it'll probably be most helpful if it involves me working through a shed load of problems to get me fluent in the approach.

    It can be on line or in book form anything, as long as it isn't too expensive, I can't afford to pay out hundreds of pounds on material for this as I'm saving up for my next course. I am well aware though that learning is almost never free, so, as long as it's within reason advance anything :smile:

    Any tips for learning or advice would also be very welcome.

    Thanks alot in advance.:smile:
     
    Last edited: Aug 26, 2006
  2. jcsd
  3. Aug 27, 2006 #2
    I've found that whenever I have a hard time with an integral it's usually because my algebra and trig skills are not up to par.

    There are a lot of little algebra and trig tricks that the authors of math books assume every math student is aware of. The problem is, a lot of us had very poor algebra and trig courses so, it makes learning calculus a lot harder then it should be.
     
  4. Aug 27, 2006 #3
    practice them over and over. Start at your current skill level and do as many as you can, then move on to the next technique and repeat. I used this site a lot. http://archives.math.utk.edu/visual.calculus/
     
  5. Aug 27, 2006 #4

    mathwonk

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    are you talking about techniques for guyessing antiderivatives? if so the only important ones are substitution and parts.


    i thought stewart was pretty clear on this stuff, maybe thomas and finney, say 9th or 10 edition.
     
  6. Aug 27, 2006 #5
    Thanks alot kdinser/math-chick_41/mathwonk, already there are some nice sources for study here. I won't be able to actually study the 'till my course is finished, but I'd say my essential problem is practice of which I had very little, the basic theory's in there now hard wired about what integration actually involves and how it works, I just need to back it up with a deal of reading learning and practice. :smile: Much appreciated advice.

    Special mention to math-chick_41, that site looks exactly what I'm looking for cheers :smile:
     
    Last edited: Aug 27, 2006
  7. Aug 27, 2006 #6
    I think I mentioned this to you before, but I could be wrong. Check out Maple's integration tutor. It will walk you through step-by-step for solving integrals. You can also make up as many integrals as you want, and it will show you how to solve them, step-by-step. It's nice because you can try a lot of different integrals, and you may find that maple will not solve them (in the tutor anyways), and you can see why this is. Some integrals look very simple, but you cannot solve them with elementary functions, it's nice to know why.
     
  8. Aug 27, 2006 #7
    Get Schaum's "3,000 Solved Problems in Calculus" - it has basically all the usual tricks. Read the problems and try to solve them; if you can't do one, star it, read its solution and move on to the next one. Then attempt the starred ones again and again, until you manage to get them all.
     
  9. Aug 30, 2006 #8
    I ordered this second hand 45 pounds from Amazon, :eek: what does it cost new?

    @Frogpad, you did thanks again.:smile:
     
  10. Aug 30, 2006 #9
    I see it there for £10.
     
  11. Aug 31, 2006 #10
    Thanks I'm trying to cancel the order on Amazon but for some reason even though it's dispatched in a weeks time you can't cancel it? what the:confused: stern email asking for cancelation, I'll wait for a confirmation and then order the 10 pound version. Thanks for that.

    That's funny what does it cost new 10 pounds what does it cost 2nd hand 45 pounds, right that makes sense? What is it a friggin antique :biggrin:
     
    Last edited: Aug 31, 2006
  12. Aug 31, 2006 #11
    Sounds like you ordered it from a marketplace seller? I don't think you can cancel those transactions, though I would complain to Amazon about price gouging if that is indeed the same book. Maybe it's a first edition Schaum's outline. Wowee.
     
  13. Aug 31, 2006 #12
    Get calculus by Spivak and do chapter 18, once you've done that chapter there is hardly any integrals that you can't do...
     
  14. Aug 31, 2006 #13
    They had a contact email for the supplier so I sent them an email, if they dont cancel it I can return it for a refund as well apparently, although they'd better cancel it or let's just say I'll be writing several more stern letters to both them and Amazon. I'm in no mood to be ripped off, I don't like throwing money at people. A difference of 35 pounds is daylight robbery etc.

    Spivak is 25 quid, I might try that if the tenner Schaum thing falls down.
     
    Last edited: Aug 31, 2006
  15. Aug 31, 2006 #14
    Spivak is one of the hardest calculus texts out there. I do not recommend it if you're already struggling with integrals, because what you want is a lot of solved examples, and Spivak does not have many of those. Although chapter 19 does have plenty of integration exercises, and some are even solved at the back, it's just not the same as Schaum's.

    But if you want to buy Spivak go ahead. It's definitely a top knotch calculus text -- and one of my 2 favorites (the other being Courant). You can learn a great deal of rigorous introductory mathematics from that book.
     
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