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:
“In a symbol there is concealment and yet revelation: here therefore, by silence and by speech acting together, comes a double significance.... In the symbol proper, what we can call a symbol, there is ever, more or less distinctly and directly, some embodiment and revelation of the Infinite; the Infinite is made to blend itself with the Finite, to stand visible, and as it were, attainable there. By symbols, accordingly, is man guided and commanded, made happy, made wretched.”
—Thomas Carlyle (1795–1881)
“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)