CH E374 Lecture Notes - Richardson Extrapolation, Royal International Air Tattoo, Propagation Of Uncertainty

• School: University of Alberta
• Department: Chemical Engineering
• Course: CH E374
• Professor: Joe Mmbaga

Document Summary

Definition of the derivative of a function f of x at x = x0: (1. 1) Derivatives are therefore approximated by differences: stays finite (does not really go to (1. 2) An important theoretical result (known as mean-value theorem): in the interval there is a point for which exactly with generally unknown. Suppose we know the function f at positions h we distinguish three approximations to the derivative at. Forward difference: that are spaced by a distance. From figure 1c, we get the impression that the central difference approximation is the most accurate. This we can prove" by means of taylor expansions: The (1. 3) (1. 4) indicates that the leading order of the terms left out of the expansion is: equation (1. 3) can be rewritten such that (1. 5) This means that the forward difference approximation of the first derivative has an error proportional to. In numerical jargon: the forward difference approximation of the first derivative is first-order accurate (accurate to.