Partial Differential Relations
If three variables, and are bound by the condition for some differentiable function, then the following total differentials exist
Substituting the first equation into the second and rearranging, we obtain
Since and are independent variables, and may be chosen without restriction. For this last equation to hold in general, the bracketed terms must be equal to zero.
Read more about this topic: Exact Differential
Famous quotes containing the words partial, differential and/or relations:
“The only coöperation which is commonly possible is exceedingly partial and superficial; and what little true coöperation there is, is as if it were not, being a harmony inaudible to men. If a man has faith, he will coöperate with equal faith everywhere; if he has not faith, he will continue to live like the rest of the world, whatever company he is joined to.”
—Henry David Thoreau (1817–1862)
“But how is one to make a scientist understand that there is something unalterably deranged about differential calculus, quantum theory, or the obscene and so inanely liturgical ordeals of the precession of the equinoxes.”
—Antonin Artaud (1896–1948)
“All of life and human relations have become so incomprehensibly complex that, when you think about it, it becomes terrifying and your heart stands still.”
—Anton Pavlovich Chekhov (1860–1904)