The document discusses using Taylor series to understand truncation errors in numerical approximations. It explains that Taylor series allow using approximations by adding additional terms to increase the order of approximation. Starting with a zero-order approximation, adding a first-order term allows a linear adjustment, and generalizing the Taylor series allows for better approximations of functions through higher-order terms in the series expansion. The Taylor series is used to estimate the characteristics of truncation errors that result from using approximations rather than exact mathematical procedures.

1. SERIES CONTRIBUTION TO THE NUMERICAL APPROXIMATIONSMARCELA FERNANDA GARZON TORRESMETODOS NUMERICOSCONTINUACION CAPITULO 2

2. Truncation errors are those that result from using an approximation rather than an exact mathematical procedure, hence to obtain knowledge of these errors characteristics, makes use of the series.

3. TAYLOR ‘SERIES CONSTRUCTIONTo the Taylor ‘series construction makes use of approximations, what allows us to understand more about them. Initially requires a first term which is a zero-order approximation f(x1)=f(x2) (f value at the new point is equal to the value in the previous point).LA SERIE

4. If (xi ) is next to (xi+1),then F(xi) soon will be equal to F(xi+1):

5. To achieve greater approach adds one more term to the series; this is an order 1 approximation, which generates an adjustment for straight lines.

6. To make the Taylor ’series expansion and to gain better approach generalizes the series for all functions, as follows:

7. BIBLIOGRAPHYNumericalMethodsforEngineerswith Personal ComputerApplicationswww.virtualum.edu.co/metrum/raices .htm

8. Note: With the Taylor’ series we can estimate the truncation errors.