"WIND CHILL"
Piecewise defined functions in 2 variables

                                          
Many situations in every day life are modeled by these functions. The number of variables Involved may be more than 1. Calculus of 2 or more variables is studied in Calculus III. One popular everyday example is a model for determining the WIND CHILL (how cold it feels considering both the temperature & the velocity of the wind. This is a complicated model. Other popular 1-variable models are for postal & telephone rates. The latter are in a class called "step functions." The following is a model used for Wind Chill. W(T,V) gives the effective temperature taking into consideration the present temperature, T and the velocity of the wind, V. 
(Adapted from UMAP)


                   T                                                                    for V between 0 & 4 (inclusive)
W(T,V)= {  0.0817(5.81+3.71sqr(V) -0.25V)(T-91.4)+91.4   for  4 < V < 45
                   1.60T-55                                                         for V = 45 or greater


Example:  W(40,20) would represent the perceived temperature (degrees F) with a present temperature of 40 degrees F and wind velocity of 20 mph. V=20 will use the middle line in the above defined function, since 20 falls between 4 & 45.


Substituting T=40 & V=20 in the above (use middle line), we would get 18.3 degrees F. Needless to say, most people using the wind chill temp would not use the formula (many do not know it or once they see it, they would like to forget it quickly). Instead, charts are given showing the results for a wide range of combinations of T & V.

NOTE:  In the Fall of 2001, the National Weather Service revised the formula based on new research on how cold air affects people. Consequently, new charts have been used for wind chill and the numbers will not be consistent with the above formula. They will turn out to be significantly different.

The revised formula for all combinations of T & V is

W(T,V)= 91.4 - (0.474677 - 0.020425V + 0.303107sqr(V))(91.4 - T)

Not a piecewise defined function.