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Serie de taylor
Serie de taylor
Serie de taylor
Serie de taylor
Serie de taylor
Serie de taylor
Serie de taylor
Serie de taylor
Serie de taylor
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Serie de taylor

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  • 1. TAYLOR SERIES
    BY:DUBAN CASTRO FLOREZ
    NUMERICS METHOS IN ENGINEERING
    PETROLEUM ENGINEERING
    2010
    CONSTRUIMOS FUTURO
    1
  • 2. TAYLOR SERIES
    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.
    CONSTRUIMOS FUTURO
    2
  • 3. CONSTRUIMOS FUTURO
    3
    TAYLOR SERIES
    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:
    which can be written in the more compact sigma notation as:
    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.
  • 4. 4
    TAYLOR SERIES
    orderzero
    orderone
    ordertwo
    order n
    CONSTRUIMOS FUTURO
  • 5. CONSTRUIMOS FUTURO
    5
    MACLAURIN SERIES
    In the particular case wherea = 0, the series isalsocalled a Maclaurin series:
  • 6. 6
    EXAMPLE
    For f(x) = arccos (x)
    a) to Write the polynomial of Mclaurin P3(x) for f(x).
    CONSTRUIMOS FUTURO
  • 7. CONSTRUIMOS FUTURO
    7
    b) to Complete the following chart for P3(x) and it stops f(x) (to Use radianes).
  • 8. CONSTRUIMOS FUTURO
    8
  • 9. CONSTRUIMOS FUTURO
    9
    BIBLIOGRAPHY
    • http://en.wikipedia.org/wiki/Taylor_series
    • 10. CHAPRA, Steven C. y CANALE, Raymond P.: Métodos Numéricos para Ingenieros. McGraw Hill 2002

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