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Book: Calculus Made Easy

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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/library/Calculus_Made_Easy_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.

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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

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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

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...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.

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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.

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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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