Numerical Differentiation and Integration Revisited

When data to be differentiated or integrated contain random errors (usually experimental errors), it can be advantageous to first fit the data to an appropriate function using regression techniques. Then, the fitted function can be differentiated or integrated analytically. Example 7.5 illustrates this approach. 

Example 7.5 Mean Fleat Capacity of Gaseous Propane 

FIGURE 7.15 Heat capacity data for propane gas (reference temperature = 50 K). 

Integrating this function between limits of 50 and 1500 K and dividing by the 

Exercise 7.3 The Clausius-Clapyron equation relates the latent heat of vaporization to temperature and vapor pressure according to the following equation  

---