Partial Differential

Alkmene · November 8th, 2009, 11:13 pm

*warning - very elementary and boring*Although I am quite familiar with the definition of a partial differential I can't really think of an example where there is a the difference between a "normal" and a "partial" differential.Can someone give me a very simple example (preferrence is to exclude trigon as I am very weak in this area)?e.g.,del(a*b)/del(a) = bd(a*b)/d(a) = bWhat happens in the casea=f(b)b=f(c)d(a)/d(c) = d(a)/d(b)*d(b)/d(c)but what about del(a)/del(c) and why?Thanks,Alk

ehremo · November 9th, 2009, 7:58 am

suppose we have a function f(t,T). Thend f(t, t) / d t = del f(t, t) / del t + del f(t, t) / del Ttherefore assuming that the second term is non-zero they're not the same thing

dariobovina · November 9th, 2009, 11:34 pm

Hi,for a function of a single variable the partial derivative is equal to the 'normal' derivative.In your case:a=f(b)b=g(c) , namely a=f[g(c)]you correctly computed d(a)/d(c) = d(a)/d(b) * d(b)/d(c)I think that writingdel(a)/del(c) = del(a)/del(b) * del(b)/del(c)is the same!