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:
“Whatever we inherit from the fortunate
We have taken from the defeated
What they had to leave us—a symbol:
A symbol perfected in death.”
—T.S. (Thomas Stearns)
“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)