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Any good self-teaching Calculus materials?

  1. May 29, 2012 #1
    Hey, next year I'm going into University. I will be taking a more computational-style calculus course, I believe the textbook will be by James Stewart: Single Variable calculus (my assumptions), and I will also be taking Physics. I'm wondering if you guys could give me a list of helpful websites on the internet, as well as, textbooks that can improve my Calculus/Physics skills.

    Also, could you guys give me any tips over the summer while studying Calculus/Physics. Should I take it easy and review material a couple times a weak. Or would a 2 hour study session everyday be really helpful for University?

  2. jcsd
  3. May 29, 2012 #2
    Mathematical Methods in the Physical Sciences - Mary Boas
    This is one of, if not, THE best undergrad 'methods' books out there, I'd marry Boas if I had the chance :biggrin:
    Whilst you're doing that Kleppner has a good book called introduction to mechanics which you may like.
    Once you know the material in Boas' book, you could have a little look at Landau and Lifgarbagez book on classical mechanics, the first of their ten part 'course of theoretical physics'. It's also one of the best introductions to the more formalised physics.

    Before I went to university I studied for pretty much all of the time I was awake, 2 hours a day would be more of an off day!
    I started off with Boas' book, Gilbert Strangs 'Introduction to Linear Algebra' (if you intend to follow physics, you'll learn to love linear algebra) and Kelppners book on alternating days. Once those were finished I went onto 'How to Prove it - A Structured Approach' by Velerman(sp?) and Hoffmans linear algebra and finally onto the Bourbaki groups Theory of Sets which is by far one of my favourite mathematical texts.

    I've kind of gone off on a tangent..
  4. May 29, 2012 #3
    As far as textbooks are concerned, you should check out "A First Course in Calculus" by Serge Lang. If you struggle with that and are in need of some pre-calculus review, I would recommend "Basic Mathematics" by Serge Lang as well. "Calculus: Early Transcendentals" by James Stewart is also pretty good (in my opinion).

    As for Internet resources, google patrickjmt and khanacademy...they're both pretty great. I would post the links, but apparently you're not allowed to post links until you've made at least 10 posts (which is a great idea, by the way).
  5. May 29, 2012 #4
    I see what you did there :tongue2:
  6. May 29, 2012 #5


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    If it were me, I would study from the Stewart book you will be using.
  7. May 29, 2012 #6
    If it's something you enjoy, by all means knock yourself off and read as much as you want! If, on the other hand, you want to study so that the material is easier when you start taking classes, I would recommend two things:

    1. Forget about the textbooks and enjoy your summer. You have an academic life full of studying time ahead of you :biggrin:

    2. If you reaaaally want to start right now, just take it easy. Make sure you don't study so much that it becomes a chore :wink: Make sure you understand something before you go to the next, because math builds intensely on previous knowledge and understanding. Finally, take notes! You will be surprised at how often you will forget things that you struggled for hours to understand. Taking a few minutes to write down your "accomplishments" and how you came to them, can boost you a lot in the long term. If you have a memory that is like a Swiss cheese like me that is :biggrin:
  8. May 29, 2012 #7


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    You make a good point, but I think one can do both, relax and prepare. I went to Germany for several weeks after senior year, went to the opera almost every day, visited churches and art galleries, and also read several chapters of Kelley's General Topology. As a result the first few weeks or months of topology were trivially easy in the Fall.

    For most people goofing off is overrated. It is really enlightening to see how enjoyably the well prepared person goofs off after doing well in school, getting a good job and earning the big bucks.

    Those of us who insisted on goofing off big time before getting our education may wind up trying hard to catch up our whole lives.

    I was very unfocused as a kid, but I am almost 70 now, only recently retired, and that rather modestly. Some of my younger friends who worked hard as youngsters and saved their $ have been retired and goofing off now for some 15-20 years already, and in a style that I will never attain.
    Last edited: May 29, 2012
  9. May 29, 2012 #8
    ^^+1. I read 400 pages of tensor calculus during Christmas and it was quite fun actually :biggrin:

    I too have been catching up for 3 years since I graduated, and I already see some wasted opportunities there. However, I have developed a love and sincere interest in understanding what I read, that simply wasn't there when I was a student, so I know that it often takes time to get your engine started :tongue: I have found that this usually works when you are not stressing over passing an exam, but when you actually study in order to learn.
  10. May 30, 2012 #9
    Before reading your about me I always pictured you as a well matured late 20s to early 30s guy :redface:
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