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:
“A pool is, for many of us in the West, a symbol not of affluence but of order, of control over the uncontrollable. A pool is water, made available and useful, and is, as such, infinitely soothing to the western eye.”
—Joan Didion (b. 1934)
“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)