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sir or madam, [Anyone] Could you please say me the proceedure in studying and approaching towards the CHAPTER CALCULUS. Could you say me what is the mark that we must get for choosing what we want rather than accepting what they give . I don't know that i must say or not but by the force of my father i had joined and got my ambition melted and shaped in his way now .It took much time ,could you please sujest me.I am an O.C as regard to regulations are applied for reservations so please say me. If any thing wrong excue me.

sir or madam,                             


          [Anyone] Could you please say me the proceedure in studying and approaching towards the CHAPTER CALCULUS.


         Could you say me what is the mark that we must get for choosing what we want rather than accepting what they give . I don't know that i must say or not but by the force of my father i had joined and got my ambition melted and shaped in his way now .It took much time ,could you please sujest me.I am an O.C as regard to regulations are applied for reservations so please say me.


                  If any thing wrong excue me.  


         

Grade:11

1 Answers

Vasanth SR
askIITians Faculty 1310 Points
3 years ago
The most important thing to have going into a calculus course is a damn good knowledge of algebra. As Richard Feynman says in the first chapter ofFeynman's Tips on Physics:

What we have to do is to learn to differentiate like we know how much is
3 and 5, or how much is 5 times 7, because that kind of work is involved so
often that it's good not to be confounded by it. When you write some­
thing down, you should be able to immediately differentiate it without even thinking
about it, and without making any mistakes. You' ll find you need to
do this operation all the time-not only in physics but in all the sciences.
Therefore differentiation is like the arithmetic you had to learn before you could
learn algebra.
Incidentally, the same goes for algebra: there's a lot of algebra. We are
assuming that you can do algebra in your sleep, upside down, without mak­
ing a mistake. We know it isn't true, so you should also practice algebra:
write yourself a lot of expressions, practice them, and don't make any errors.

His point is that you should be able to do algebra in your sleep. There's too much thinking in calculus already. Don't waste time trying to remember how logarithms work. I can't really think of any other important things you need to prepare for calculus.

One comment I will make, though, is that, whereas differentiation (the first topic in calculus) is a set of mechanical rules you will learn and follow, integration (the second topic) requires much more creativity. It's exactly analogous to the difference between multiplying polynomials and factoring them in algebra. The first one you always know how to do, the second one you sort of need to "see it".
Example:

(2x+3)(4x+7)=8x2+12x+14x+21(2x+3)(4x+7)=8x2+12x+14x+21
=8x2+26x+21=8x2+26x+21

We just did a bunch of distributing and rearranging. Nothing too crazy.
However, if I asked you to factor the equation, in the end, it wouldn't be so easy to work backward. How would you know to split up 26 into 12 and 14?

Try this one: factor10x2+14x−1210x2+14x−12.

So you should try to review factoring like this just to get comfortable with having to play around with a problem and weasel your way toward an answer instead of following some algorithm.

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