Differential Equations
For a first order system of differential equations
where bold indicates vector quantities, a scalar-valued function H(r) is a conserved quantity of the system if, for all time and initial conditions in some specific domain,
Note that by using the multivariate chain rule,
so that the definition may be written as
which contains information specific to the system and can be helpful in finding conserved quantities, or establishing whether or not a conserved quantity exists.
Read more about this topic: Conserved Quantity
Famous quotes containing the word differential:
“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)