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Discontinuous functions

We already saw a square (one of plane figures) is given by

equation8

with absolute function |x|. There is an another equation using tex2html_wrap_inline162 which is given by

  equation10

in other work of mine (see ``plane figure equations''). This provides a resort to study discontinuous functions with linear calculus.

The expedient is as follows.

  1. Suppose the problem in question contains discontinuous functions.
  2. Express discontinuous functions as a continuous functions with parameters (as n in equation (2)) so as to approach the discontinuous functions under the limit of the parameter. We call them pseudo functions.
  3. Study the problem with the continuous pseudo functions instead of the discontinuous functions.
  4. Take a limit of introduced parameters in the results of pseudo functions.


next up previous
Next: Examples for and Up: Discontinuous functions Previous: Discontinuous functions

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