Symbol Manipulation
Suppose we want to solve the differential equation
Treating these symbols as ordinary algebraic ones, and without giving any justification regarding the validity of this step, we take reciprocals of both sides:
Now we take a simple antiderivative:
Because this is a formal calculation, we can also allow ourselves to let and obtain another solution:
If we have any doubts about our argument, we can always check the final solutions to confirm that they solve the equation.
Read more about this topic: Formal Calculation, Examples
Famous quotes containing the words symbol and/or manipulation:
“The glance is natural magic. The mysterious communication established across a house between two entire strangers, moves all the springs of wonder. The communication by the glance is in the greatest part not subject to the control of the will. It is the bodily symbol of identity with nature. We look into the eyes to know if this other form is another self, and the eyes will not lie, but make a faithful confession what inhabitant is there.”
—Ralph Waldo Emerson (1803–1882)
“The basic tool for the manipulation of reality is the manipulation of words. If you can control the meaning of words, you can control the people who must use the words.”
—Philip K. Dick (1928–1982)