Posted 9 Jul 2012 · Report post I'm working my way through Calculus Made Easy by: Silvanus P. ThompsonCopy and Pastable Version: http://bit.ly/PGwcpKttp://ebit.ly/PGwcpKPDF Version: http://djm.cc/library/Calculus_Made_Easy_Thompson.pdfIn it he gives an example:y+dy = (x+dx)²and after squaring it gets:y+dy = x²+2x*dx+(dx)²I have no clue how he got from one to the other. Maybe someone can explain or show the steps?Thank you. Share this post Link to post Share on other sites

Posted 9 Jul 2012 · Report post I'm working my way through Calculus Made Easy by: Silvanus P. ThompsonCopy and Pastable Version: http://bit.ly/PGwcpKttp://ebit.ly/PGwcpKPDF Version: http://djm.cc/librar...sy_Thompson.pdfIn it he gives an example:y+dy = (x+dx)²and after squaring it gets:y+dy = x²+2x*dx+(dx)²I 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^2That 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 Share this post Link to post Share on other sites

Posted 9 Jul 2012 · Report post I'm working my way through Calculus Made Easy by: Silvanus P. ThompsonCopy and Pastable Version: http://bit.ly/PGwcpKttp://ebit.ly/PGwcpKPDF Version: http://djm.cc/librar...sy_Thompson.pdfIn it he gives an example:y+dy = (x+dx)²and after squaring it gets:y+dy = x²+2x*dx+(dx)²I 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^2That 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.ruveynThat solves my problem! Thanks Share this post Link to post Share on other sites

Posted 9 Jul 2012 · Report post ...In it he gives an example:y+dy = (x+dx)²and after squaring it gets:y+dy = x²+2x*dx+(dx)²I have no clue how he got from one to the other. Maybe someone can explain or show the steps?(a+ ^{2} = (a+(a+ = a(a+ + b(a+ = a^{2}+ab + ba+b^{2} = a^{2}+2ab+b^{2}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. Share this post Link to post Share on other sites

Posted 10 Jul 2012 · Report post 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. Share this post Link to post Share on other sites

Posted 10 Jul 2012 · Report post 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. Share this post Link to post Share on other sites