2006-09-13 01:36:25 · 9 answers · asked by siliqua 2 in Science & Mathematics ➔ Mathematics
The best book which will help you to understand calculus is by Thomas/Finney. Simple and illustrative examples are the highlight of this book.
2006-09-13 02:52:49 · answer #1 · answered by Anonymous · 0⤊ 0⤋
Differentiation By Substitution
2016-11-16 21:01:37 · answer #2 · answered by robichau 4 · 0⤊ 0⤋
Acually in differential calculus there's the chain rule of differentiation which might be what you're referring to.
it implies for two functions f and g in a single variable(for simplicity) z
then for,
f[g(z)] the derivative of this function
d{f[g(z)]} / dz = g'(z) . f'[g(z)]
this also implies that when given x= f(t) and y= g(t)
dy/dx = dy/dt * dt/dx
this isn't really a removal of a facor but it works much like that.
also dx/dt = 1 / (dt/dx)
In integral calculus (consider it as the opposite of differentiation, i.e antiderivatives) you have 'integration by substitution' which is the equivalent of the chain rule of differentiation. Actually it's the backward process. However to understand this you have to master differentiation and appreciate the backward development from it.
Read Gilbert Strang's Calculus or GH Hardy's A course in Pure Mathematics, both are pretty good. The first is available for free download on MIT, try
http://ocw.mit.edu/ans7870/textbooks/Strang/strangtext.htm
Hope this helps!
2006-09-13 05:00:46 · answer #3 · answered by yasiru89 6 · 0⤊ 0⤋
if at all differentiation can be done by substitution it again ends up to be the same thing .&there is no need for any substitution while differentiating
2006-09-13 17:22:32 · answer #4 · answered by punith r 1 · 0⤊ 1⤋
do you mean integration by substitution?
or do you mean differentiation using the chain rule?
there is NO such thing as differentiation by substitution
2006-09-13 02:18:57 · answer #5 · answered by Anonymous · 0⤊ 1⤋
In order to improve your basic knowledge in differentiation you must go through the book ("Prime Mathematics" from d.r sharma ) and r.d sharma booklet both books r different. If u r looking forward for competitive exams then go for R.D sharma objective booklet.
2006-09-13 02:21:41 · answer #6 · answered by varun 1 · 0⤊ 0⤋
You should learn about limits first. Limits lead very naturally into derivatives. That'll keep you busy for a few weeks!
2016-03-17 02:10:49 · answer #7 · answered by ? 4 · 0⤊ 0⤋
i thought there was only integration by substitution method. but i guess i could be wrong (:
2006-09-13 01:46:34 · answer #8 · answered by boogiesbottom 3 · 0⤊ 1⤋
good luck.
2006-09-13 01:43:24 · answer #9 · answered by paisa_de_la_muerte 1 · 0⤊ 2⤋