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Math Help - What would be helpful to review before taking Calculus III?

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    What would be helpful to review before taking Calculus III?

    I'm taking a Calculus 3 (the standard US course) course this summer and I'm wondering what particular topics from Calculus I, II or any other level of math would be useful to review since the course is going to be accelerated. For example, is a topic like series going to be used a lot? Thanks.
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    Quote Originally Posted by Carbon View Post
    I'm taking a Calculus 3 (the standard US course) course this summer and I'm wondering what particular topics from Calculus I, II or any other level of math would be useful to review since the course is going to be accelerated. For example, is a topic like series going to be used a lot? Thanks.
    If your Calculus III is the same as mine was it is vector calculus.
    You will want to review are
    1. Know how to take derivatives.
    2. Know how to integrate things.
    a. u substitutions.
    b. integration by parts.
    c. Trig substitutions.
    3. Just to emphasize what I said above you will need all of you 1-d calculus the above is just the basic stuff.
    4. Know your Vector algebra. If you have taken linear Algebra review How to take determinants especially 3 by 3 matrices.
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    If you know the textbook you'll be using, I suggest looking over its TOC in detail. Usually it is an introduction to vector calculus. Certainly there are specific topics you cover briefly that stem from earlier courses, but at least in my class it was like one week on dealing with polar coordinates again. You'll face the fun double and triple integrals. Frankly, I found Calc III to be the easiest and most fruitful. If you know your Calc I and Calc II, the third was hardly mysterious once you got used to vector stuff and its notation. But the idea is that you should be comfortable with the sorts of derivatives and integrals you'll deal with, and to be able to use the basic and advanced integration methods taught in calc II. The real difficulty of Calc III is merely the multiplication of work. A triple integral can look daunting, and trying to interpret it can be a challenge, but really it is not that difficult from all the work you've already done. It's just an extended application of what you did previously. If you can take a "calc IV" (vector analysis at my university), it just goes another level of up in abstraction, requiring some knowledge of proofs, and simplifies the notation a lot. I wish I had taken it right after Calc III because I was so unfamiliar with calculus by the time I took it, I had to relearn a lot of stuff. Also, physics helps understand vector applications a lot. It wasn't until electromagnetism when I finally understood that whole vector analysis class.
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