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Serie de taylor

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Serie de taylor

1. 1. TAYLOR SERIES<br />BY:DUBAN CASTRO FLOREZ<br />NUMERICS METHOS IN ENGINEERING<br />PETROLEUM ENGINEERING<br />2010<br />CONSTRUIMOS FUTURO <br />1<br />
2. 2. TAYLOR SERIES<br />In mathematics, the Taylor series is a representation of a function as an infinite sum of terms calculated from the values of its derivatives at a single point. If the series is centered at zero, the series is also called a Maclaurin series. It is common practice to use a finite number of terms of the series to approximate a function. The Taylor series may be regarded as the limit of the Taylor polynomials.<br />CONSTRUIMOS FUTURO <br />2<br />
3. 3. CONSTRUIMOS FUTURO <br />3<br />TAYLOR SERIES<br />The Taylor series of a real or complex function ƒ(x) that is infinitely differentiable in a neighborhood of a real or complex number a is the power series:<br />which can be written in the more compact sigma notation as:<br />where n! denotes the factorial of n and ƒ (n)(a) denotes the nth derivative of ƒ evaluated at the point a. The zeroth derivative of ƒ is defined to be ƒ itself and (x − a)0and 0! are both defined to be 1.<br />
4. 4. 4<br />TAYLOR SERIES<br />orderzero<br />orderone<br />ordertwo<br />order n<br />CONSTRUIMOS FUTURO <br />
5. 5. CONSTRUIMOS FUTURO <br />5<br />MACLAURIN SERIES<br />In the particular case wherea = 0, the series isalsocalled a Maclaurin series:<br />
6. 6. 6<br />EXAMPLE<br />For f(x) = arccos (x) <br />a) to Write the polynomial of Mclaurin P3(x) for f(x).<br />CONSTRUIMOS FUTURO <br />
7. 7. CONSTRUIMOS FUTURO <br />7<br />b) to Complete the following chart for P3(x) and it stops f(x) (to Use radianes).<br />
8. 8. CONSTRUIMOS FUTURO <br />8<br />
9. 9. CONSTRUIMOS FUTURO <br />9<br />BIBLIOGRAPHY<br /><ul><li>http://en.wikipedia.org/wiki/Taylor_series
10. 10. CHAPRA, Steven C. y CANALE, Raymond P.: Métodos Numéricos para Ingenieros. McGraw Hill 2002</li>