Carburization Heat Treatment. Write a computer program for calculating carburization heat treatments. The program should ask the user to provide an input for the carbon concentration at the surface (cs), and the concentration of carbon in the bulk (c0). The program should also ask the user to provide the temperature and a value for D (or values for D₀ and Q, that will allow for D to be calculated). The program should then provide an output of the concentration profile in tabular form. The distances at which concentrations of carbon are to be determined can be provided by the user or defined by the person writing the program. The program should also be able to handle calculation of heat treatment times if the user provides a level of concentration that is needed at a specified depth. This program will require calculation of the error function. The programming language or spreadsheet you use may have a built-in function that calculates the error function. If that is the case, use that function. You can also calculate the error function as the expansion of the following series:

In these equations, z is the argument of the error function. Also, in certain situations, you will know the value of the error function (if all concentrations are provided) and you will have to figure out the argument of the error function.
This can be handled by having part of the program compare different values for the argument of the error function and by minimizing the difference between the value of the error function you require and the value of the error function that was approximated.

erf(z) = 1- 1x 3 1x3 x 5 + 2z (27) TTZ + (2z)3 or use an approximation erf(z) = 1- - [() N