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Calc I: Possible to Self-Teach?

  1. May 28, 2007 #1

    Cod

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    Well, the thread title pretty much says it all. I never made it higher than college algebra and trigonometry in my high school days. I'd really like to learn calculus, but do not that much about it going into it. I want to teach myself calculus, if at all possible, but I'm unsure of the proper and most effective ways to teach yourself a new subject. What are the best methods for self-teaching? Any tips for learning math at home?

    Any help is greatly appreciated.
     
  2. jcsd
  3. May 28, 2007 #2
    are you in school or working?
     
  4. May 28, 2007 #3
    Yes it is definitely possible to self-teach yourself Calc I at home as long as you have the required strength in algebra and trig. The best way to learn for me is to just grab a textbook and sit down and learn! I tried to make sure that I understood all the concepts in their entirety even if it meant staring at some cryptic page for 2 hours until the concept sunk in.

    Any of these textbooks I can personally suggest, but the textbook you choose depends on the level of mathematical rigor you want from the text.

    http://www.amazon.com/Single-Variab...ef=pd_lpo_k2_dp_k2a_2_txt/103-9630758-3061400
    http://www.amazon.com/s/ref=nb_ss_b...as=stripbooks&field-keywords=Apostol+Calculus
    http://www.amazon.com/Calculus-Analytic-Geometry-Seventh-Larson/dp/0618239723

    Stewart lacks rigor but if you just want to know how to use calculus, its fine. Larson is a bit more rigorous than Stewart, all theorems are proved and its my personal favourite. Apostol is very very rigorous, starting with axioms dealing with the real number system and working with them to introduce calculus. Its not for the faint of heart. (although I think it is impossible to finish Apostol and not understand calculus, which is a good thing). I haven't fully read Apostol, but have read the Calc I portions of both stewart and larson.

    You may want to just rent out a textbook by larson or stewart from the library, most libraries seem to have at least one copy.

    edit: also, if you get stuck on a concept you can always ask about it in the homework help section here..
     
    Last edited: May 28, 2007
  5. May 28, 2007 #4

    G01

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    I liked Stewart when I used it. It is not rigorous but it definitely does the job for physics or engineering majors.

    If you want to become a mathematician or gain the knowledge of a mathematician instead of becoming, let's say a physicist, then I suggest starting with Stewart's but eventually moving on to a more rigorous book.
     
  6. May 28, 2007 #5
    even if you are aiming for physics&engineering i dont see any harm in learning it rigorously from books of authors such as: courant,spivak,apostol.
     
  7. May 28, 2007 #6
    and courant's also has applications to geometry and physics and it's rigourous enough. (although there are some topics which are connected to topology which he doesn't really elaborate as rigoursly as one would like to).
     
  8. May 28, 2007 #7
    im self teaching myself linear algebra over the summer, and that'll probably be kind of hard.
     
  9. May 28, 2007 #8

    Cod

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    I'm in the military, but I have some free time at night.

    Thanks for all the advice and book choices. Do y'all have any advice for going through the book(s)? Should I take notes on each section? Highlight?

    Any further help is greatly appreciated.
     
  10. May 28, 2007 #9
    Newton and Gauss both had to teach themselves calculus.

    A few years ago the physics students society where I was going to school had an ongoing correspondence with a prison inmate in Florida who was teaching himself first-year math and physics. So you can certainly learn on your own.

    Go through the proofs and derivations done in the textbook and write out the steps. Get a book that has a lot of sample problems - if you screw up or get stuck, the textbook explains how to do them.
     
  11. May 29, 2007 #10
    also, i find it easier to try and learn the mechanics of the steps first, and become comfortable with solving problems before trying to get the theory and concept in your head. It just gave me a headache, and doing peroblems is just repeating a certain order of steps. After that, the concepts should be easier to grasp after you just start doing the math.
     
  12. May 31, 2007 #11
    I taught myself Calc 1 before I went to Uni to take it again. I orderd it as a correspondance course via my provincial goverment. It was a great idea, it was pretty difficult, but the key is to set aside time everytime and just do it. Im glad I did, it paid off
     
  13. May 31, 2007 #12

    JasonRox

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    I did it to without any trigonometry experience at all. After I was done, I had it down for sure. I was better prepared than other students in university!
     
  14. May 31, 2007 #13
    Calculus by Larson is excellent.
     
  15. May 31, 2007 #14
    Now comes a no-brainer question by me. Since I am not a native english speaker I would like to ask an offtopic question which has been bothering me since I got in this forum. What exactly is calculus? What does it mean?

    By calculus we mean physics probems and calculations? Again sorry for the offtopic question.
     
  16. May 31, 2007 #15
    Calculus is a lovely tool used to solve certain fundamental problems. The mian ones are the area beneath an arbitrary curve, and the other is the slope of a tangent line. Let me give you an idea as to how to do this. Say you're driving in your car and you want to know how fast you're going... What you do is divide the distance travelled by the time elapsed, BUT the problem is that this is only an average. One has to be more precise. So you take a smaller distance and the corresponding time elapsed, and this should be a better approximation for the speed at which you're travelling because it varies less in a smaller amount of time. now as if you let the time elapsed become smaller and smaller(along with the distance) the average vlocity converges to the velocity at a certain point in time. So more generally you take the slope of a curve and let the change in x approach zero.

    The area under a curve can be found ina similar way, which i'm sure we've all thogfuht of. Take rectangles and approximate an area with it. As you increas the number of rectangles and decrease the base of each it becomes more accurate as the height varies along the base of each rectangle. If you let the base of eachrectangle approach zero it converges to the area, because the height barely varies along the base when its very small.

    These two thing are called differentiation and integration repsectively and are related via the funadamental theorem of calculus.

    Yes its possible to teach yourself calculus one. It actually very simple.
     
  17. May 31, 2007 #16
    If you'd like a classroom setting to accompany your learning, look for universities that offer OCW (open courseware), it's literally an entire class uploaded on the internet (with exams and quizzes, some of them like MIT even have a whole year's worth of lectures on video for free).

    the new itunes comes with a thing called "itunes u," where they have a whole bunch of OCW lectures to download for free; I'm sure there's calculus lectures in there or if there isn't there will be (since it's a new feature, i just got it today with the update).

    I use this book:
    http://www.amazon.com/Calculus-Gilb...8317433?ie=UTF8&s=books&qid=1180669749&sr=1-1

    the book is available for free on the MIT OCW website, it's pretty solid and at the same time written in a casual tone.
     
  18. Jun 1, 2007 #17
    No, it isn't very simple. I am working on calculus for two months now and I only know how to differentiate and integrate an arbitrary function. :cry:
     
  19. Jun 5, 2007 #18

    mathwonk

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    i recommend cheap books.

    heres one: li like:
    Calculus Made Easy (ISBN: 0312114109)
    Bookseller: thriftbooks.com
    (Auburn, WA, U.S.A.) Price: US$ 1.00
    [Convert Currency]
    Quantity: 1 Shipping within U.S.A.:
    US$ 3.99
    [Rates & Speeds]
    Book Description: 1970. Book Condition: Acceptable. All of our items ship within 24 hours. 100% Satisfaction Guaranteed! Spend Less - Read More. Bookseller Inventory # G0312114109I5N00


    heres another one:

    Introduction to Calculus and Analysis, Volume 1
    Richard Courant; Fritz John
    Bookseller: Goodwill Industries of Central Indiana
    (Indianapolis, IN, U.S.A.) Price: US$ 19.79
    [Convert Currency]
    Quantity: 1 Shipping within U.S.A.:
    US$ 3.00
    [Rates & Speeds]
    Book Description: Interscience Publishers, 1965. Hardcover. Book Condition: Good. Bookseller Inventory # mon0000031763



    those two together will be enough for a lifetime.
     
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