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Calculus Formulas

  1. Sep 15, 2003 #1
    I despise taking notes in school, and never do, so I was wondering if anyone knew of an online list of all formulas relating to Calculus so I can just highlight the ones we're learning as we go along in school. (I'm taking AP Calculus BC)

    Thanks
     
  2. jcsd
  3. Sep 16, 2003 #2
    You should get used to taking notes. Math isn't about memorizing formulas. You can't get good at math by watching someone else do it. You have to do it yourself.
     
  4. Sep 16, 2003 #3

    chroot

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    Since there are an infinite number of "formulas relating to calculus," I'd suspect you'd have a hard time finding a list of them on the internet. Do what Stephen tells you -- get used to taking notes.

    If you just hate taking notes in class, you might be able to get away with just listening to the lectures, and then going home and taking notes while reading your book. Either way, Stephen is right: you can read a book or listen to a speaker and have no trouble follow along for the entire ride -- but you won't be able to remember a single thing unless you actually use it.

    - Warren
     
  5. Sep 16, 2003 #4
    Taking notes isn't 'getting good at something by doing it yourself' though.. it's just copying down exactly what you see BEING done, and I prefer just listening, and listening that much harder b/c I dont have to focus on movements of my hand. Anyway it's all good 'cause I found a site with them
     
  6. Sep 16, 2003 #5
    There's tons of sites, it just depends on your preference. Google it. Plus, your book should already have most of them, and if not, many teachers let you write them in on the covers, or in the pages near the back cover where nothing's written. Of course, writing them your self in your notes ensures that you'll understand them, and help you remember them as well.
     
  7. Sep 16, 2003 #6
    i stopped taking notes and found it more helpful to try to prove the theorems on my own rather than listen to the trite old methods for proving them.

    i believe dr. nash didn't even go to class at all, much less take notes.

    it's kinda like becoming a mechanic. there are essentially two ways. one way is to go to school where you learn how to do everything except anything new. one way is to teach yourself; that way, your only experience is what is with what is new, new to you at least.

    cheers,
    phoenix
     
  8. Sep 16, 2004 #7

    mathwonk

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    Here is a compromise I recommend: Go to every class and listen in class as closely as possible. Then immediately afterwards go to the library, take out some paper and write out everything you remember in as much detail as possible. This way you think through everything again, and also produce useful notes. You also remind yourself of what you forgot, and make a note to review it somewhere. If it seems you are not able to remember much, you might need to take notes in class, or listen more effectively.

    Another tactic is to read the material the night before to make effective listening easier.

    Anyone addicted to memorizing formulas may be interested in viewing the play "The Lesson" by Ionesco.

    The main point people are making here though is the unavoidable truth that reading notes is not nearly as effective for learning as writing notes is. When I write out an outline for my class of the material we have covered, I learn it very well by doing so. They on the other hand learn much less by merely reading my outline, so I always advise them to write their own.

    Anyone who seeks to learn math by imitating the behavior of Professor Nash by skipping class however, does so at his/her own risk. It may be that Nash was more talented, and more eccentric, than some of the rest of us. At least missing class seldom worked for me, especially since I usually spent the time saved by playing "hearts".
     
    Last edited: Sep 16, 2004
  9. Sep 22, 2004 #8

    JasonRox

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    I find this to be true.

    On the other hand you have to take notes of important things, like definitions and what not. Examples or metaphors to help you understand the math is not necessary to write down. You should sit back and try to understand, and not take most of your time writing notes. My notes are really messy, and are barely readable, but I re-write them neatly after class.

    Note: I am fortunate enough (well not really) to have a hearing disability, which isn't really noticeable when I put my hearing aid. Because of this, I went for "Help for Disabilities" for the first time this year, and they hooked me up with a notetaker. Although I'm doing fine now because it isn't anything I haven't seen before, I am doing this because later on when I see new material I don't miss anything. Basically, I listen and write sloppy notes, re-write notes, read notetakers notes, read textbook, and try exercise questions.

    Also, I find that understanding the material is the only way you can succeed in math. Memorizing will get you past the first term, and then you're toast. Obviously lots of people forget the "Quadratic Formula", but those who experienced on how to deduce it themselves will remember for the rest of their lives (until alzheimers kicks in). :biggrin:
     
  10. Sep 22, 2004 #9
    Exactly. One of my teachers would always say that math is not a spectator sport.

    Besides, I think it would take quite a bit of work to memorize the Taylor Series of Expansions.
     
  11. Oct 11, 2004 #10
    Unless you are being taught very poorly the course shouldn't be entirely comprised of the notes anyway. You should probably be able to get away without the notes, but it is usually the concepts that are taught that are the important thing anyway. No copying down examples from class/lectures doesn't improve your skills, but it does give you an idea of how to solve certain types of problems so when you run into them, you may remember a certain mathematical trick or two.
    If you are dead set against copying out notes then just go to class and listen, if there is something that you feel is worth remembering then copy it down, otherwise prepare to have the world's largest memory.

    As for equation lists. Math, like every other subject, tends to like to make equations have insane amounts of subscripts and notations so I don't think you could pay somebody enough money to take the time to put them all in a nice neat organized order.
     
  12. Oct 28, 2004 #11
     
    Last edited: Oct 28, 2004
  13. Nov 30, 2004 #12

    mathwonk

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    why am I not surprized this is the same guy who "forgot his book" the night before the test.
     
  14. Nov 30, 2004 #13

    JasonRox

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    mathwonk, you burned this fellow bad. LOL.
     
  15. Nov 30, 2004 #14

    mathwonk

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    well let me admit, i was much worse than he as a student. i once got a D- in calc 2 and when i reviewed my notes found that I had only been to class once per month that semester.

    i am very tough on this behavior because it cost me 10 years of my professional life wasted, when finally i learned better. so i am like the "repentant" sinner who goes around blasting everyone else for sinning.

    even now i have work i could be doing. so my apologies to basketdan. hang in there young man. please remember however that being smart is something of a curse.

    i.e. you have succeeded so far without working because you must be very bright. but there will come a day of reckoning, when the "bottom end of the curve" has dropped out of the course, and all the competition is both smart and hard working.

    as my basketball coach told one guy, "do your self a favor big fellow and play hard on both ends of the court."

    good luck.
     
  16. Dec 15, 2004 #15

    mathwonk

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    it is that time of year:

    when I marvel that all my students know a vector basis is a set which is both "independent and spanning" but few know what either term means.

    at least some know that a function is integrable if its "upper and lower sums" can be made arbitrarily near, but no one can define an upper sum correctly.

    most know a riemann sum is a sum of products f(xi*)delta(xi) but few know what either (xi*) or delta(xi) mean.

    most know the derivatives of x^2 and sin(x), but few know what a derivative is.

    several can state the "limit test" for a global minimum, but none know what a limit is.

    most can state the fundamental theorem of calculus (every continuous function is the derivative of its indefinite integral) but all claim that the continuous function e^(x^2) has no antiderivative, and most do not know how to define a continuous function.

    some say they fully understand "the math", they just don't get the theorems, proofs, definitions, and corollaries.


    it seems hard to change the things people care to learn, to include the ideas rather than just the numbers.

    merry xmas!
     
  17. Dec 15, 2004 #16

    JasonRox

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    Thanks for the review! :biggrin:

    Calculus I Exam next week and Linear Algebra Exam tomorrow.
     
  18. Dec 15, 2004 #17

    mathwonk

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    you are a good man jason rox
     
  19. Dec 19, 2004 #18

    mathwonk

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    here is another remark prompted by giving my final: on test 4 i announced in advance a certain proof would be asked. namely i would ask the class to prove the only function f with f'=rf and f(0) = c, is f(x) = ce^(rx). I gave the complete proof, emphasizing that the first step was to prove that the quotient f/e^(rx) is constant by taking the derivative and applying the mean value theorem, which implies that any function whose derivative is zero is constant. then evaluate the constant by setting x=0.

    everyone did well. then one week later, unannounced, i gave the exact same problem on the final, with the hint: first prove the quotient f/e^(rx) is constant by the usual method. it seemed no one knew what that method was nor had any idea how to proceed, even after I said "remember this is a differential calculus course and we have a special way of recognizing constant functions".

    I could not understand how anyone could have forgotten in only one week a simple idea like taking the derivative to show a function is constant, especially since we had emphasized it all semester. worse yet, to forget a proof which had been learned correctly one week earlier. i guess the only way is if someone just memorized the proof the first time without bothering to do any thinking at all about what the argument meant.


    it is almost as if many students are dragging their feet so hard, trying not to do any thinking at all, that it is really challenging as to how to get them to benefit from what they do as exercises. so the main thing to remember is that as a student one must always work on oneself to try to understand the idea behind the discussion at hand. the whole point is to use a few sample problems that one solves in class as models for a wider class of problems that one will meet elsewhere. this cannot be useful unless one sees how to generalize the idea behind the given exercise to use it in a new situation. this is the goal of all exercises, not just to do as little as possible to slide by the course.
     
    Last edited: Dec 19, 2004
  20. Dec 19, 2004 #19

    JasonRox

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    I barely study for exams at all. For now, everything is pretty easy. I'll go through the theorems and proofs again, but I understand everything.

    One of the coolest things I think, for a Calculus I course, is how you can prove that if something is differentiable at point x, it is also continuous at point x. You can prove it directly through the definition of the derivative, which is kind of neat.

    Yes, students don't think and don't like to think. That's not good for me because I like to just talk math/physics, but unfortunately no one else does.

    I don't know if it was like this before, back in the day, but I do know that it really sucks today.

    Math club... in your dreams.
     
  21. Dec 27, 2004 #20

    mathwonk

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    deltay/deltax converges to some finite limit L if f is differentiable, as deltax converges to zero.

    It follows that deltay converges to L times the limit of deltax, i.e. zero, hence f is continuous.

    this is nice, but there is a lot more going on than this level of argument. if this is what impresses you now, you have not even scratched the surface. you could get a lot deeper with some effort.
     
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