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# Series contribution to the numerical approximations

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### Series contribution to the numerical approximations

1. 1. SERIES CONTRIBUTION TO THE NUMERICAL APPROXIMATIONS<br />MARCELA FERNANDA GARZON TORRES<br />METODOS NUMERICOS<br />CONTINUACION CAPITULO 2<br />
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.<br />
3. 3. TAYLOR ‘SERIES CONSTRUCTION<br />To 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).<br />LA SERIE<br />
4. 4. If (xi ) is next to (xi+1),then F(xi) soon will be equal to F(xi+1):<br />
5. 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.<br />
6. 6. To make the Taylor ’series expansion and to gain better approach generalizes the series for all functions, as follows:<br />
7. 7. BIBLIOGRAPHY<br />NumericalMethodsforEngineerswith Personal ComputerApplications<br />www.virtualum.edu.co/metrum/raices .htm<br />
8. 8. Note:<br /> With the Taylor’ series we can estimate the truncation errors.<br />