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Book: Calculus Made Easy


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#1 darnoconrad

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Posted 09 July 2012 - 04:47 PM

I'm working my way through Calculus Made Easy by: Silvanus P. Thompson
Copy and Pastable Version: http://bit.ly/PGwcpKttp://ebit.ly/PGwcpK
PDF Version: http://djm.cc/librar...sy_Thompson.pdf

In it he gives an example:
y+dy = (x+dx)²

and after squaring it gets:

y+dy = x²+2x*dx+(dx)²

I have no clue how he got from one to the other. Maybe someone can explain or show the steps?

Thank you.

#2 ruveyn ben yosef

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Posted 09 July 2012 - 06:00 PM

I'm working my way through Calculus Made Easy by: Silvanus P. Thompson
Copy and Pastable Version: http://bit.ly/PGwcpKttp://ebit.ly/PGwcpK
PDF Version: http://djm.cc/librar...sy_Thompson.pdf

In it he gives an example:
y+dy = (x+dx)²

and after squaring it gets:

y+dy = x²+2x*dx+(dx)²

I have no clue how he got from one to the other. Maybe someone can explain or show the steps?

Thank you.


(a + B )^2 = a^2 + 2*a*b + b^2

That is just algebra.

The real trick is dropping the square of the infinitesimal dx since it is negligible. If dx is teeny, teeny, tiny the square of dx is even teenier and tinier.

ruveyn

#3 darnoconrad

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Posted 09 July 2012 - 06:26 PM


I'm working my way through Calculus Made Easy by: Silvanus P. Thompson
Copy and Pastable Version: http://bit.ly/PGwcpKttp://ebit.ly/PGwcpK
PDF Version: http://djm.cc/librar...sy_Thompson.pdf

In it he gives an example:
y+dy = (x+dx)²

and after squaring it gets:

y+dy = x²+2x*dx+(dx)²

I have no clue how he got from one to the other. Maybe someone can explain or show the steps?

Thank you.


(a + B )^2 = a^2 + 2*a*b + b^2

That is just algebra.

The real trick is dropping the square of the infinitesimal dx since it is negligible. If dx is teeny, teeny, tiny the square of dx is even teenier and tinier.

ruveyn


That solves my problem! Thanks

#4 ewv

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Posted 09 July 2012 - 06:36 PM

...In it he gives an example:
y+dy = (x+dx)²

and after squaring it gets:

y+dy = x²+2x*dx+(dx)²

I have no clue how he got from one to the other. Maybe someone can explain or show the steps?


(a+ b)2 = (a+b)(a+b)
= a(a+b) + b(a+b)
= a2+ab + ba+b2
= a2+2ab+b2

If you don't know algebra at that level then it is too soon for calculus. You should know that result without having to work out it with those steps. Learn high school algebra first.

#5 realitycheck44

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Posted 10 July 2012 - 08:42 PM

Learn high school algebra first.

This.

Though ewv and others on the forum are an excellent resource for math/science related information, physicsforums.com is pretty useful for non-philosophical questions like this one.
"The Priest hated him, for the Viking looked at heaven only when he bent for a drink over a mountain brook, and there, overshadowing the sky, he saw his own picture.
...
A Viking lived, who had laughed at Kings, who had laughed at Priests, who had laughed at Men, who had held, sacred and inviolable, high over all temples, over all to which men knew how to kneel, his one banner - the sanctity of life." -Ayn Rand

#6 darnoconrad

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Posted 10 July 2012 - 09:07 PM


Learn high school algebra first.

This.

Though ewv and others on the forum are an excellent resource for math/science related information, physicsforums.com is pretty useful for non-philosophical questions like this one.


Right on! Thanks.




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