What Are Dual Functions and How Are They Used in Mathematics or Engineering?

what are dual functions ?

Dual functions result from systems that are related in a certain way. For example if you have a resistor, inductor and voltage source in series, the equation for the voltage is
vin - R*i - L*di/dt=0.
If you have a current source a conductance (G=1/r) and a capacitance in parallel the equation for the sum of currents is
iin - G*v - C*dv/dt=0.

The equations have the same form and are dual.

Search google with: dual circuits

Generally if you take a description of a circuit, and make the following word replacements (as was done above):
current=voltage
resistance=conductance
capacitor=inductor
parallel=serial

then you end up with dual circuits described by equations of the same form.

ok, but i was concerning about digital electronics......

It's a similar concept in digital systems obtained by replacing "and" gates with "nors" (with inputs inverted), and "or" gates with "nands" (with inputs inverted). Then a SOP form becomes the dual POS form.