Numerical Integration

  • Vilmos Komornik
Part of the Springer Undergraduate Mathematics Series book series (SUMS)


For his celestial mechanics Newton had to evaluate complicated integrals. He and his followers generalized the trapezoidal rule \(\int _{a}^{b}f(x)\ dx \approx \frac{f(a)+f(b)} {2} (b - a)\) and Simpson’s rule \(\int _{a}^{b}f(x)\ dx \approx \frac{f(a)+4f(\frac{a+b} {2} )+f(b)} {6} (b - a)\) by seeking approximations of the form \(\int _{I}f(x)\ dx \approx A_{1}f(x_{1}) + \cdots + A_{n}\,f(x_{n})\) where the points x k and coefficients A k do not depend on the particular choice of the function f.


Asymptotic Expansion Orthogonal Polynomial Trapezoidal Rule Celestial Mechanic Compact Interval 
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Copyright information

© Springer-Verlag London Ltd. 2017

Authors and Affiliations

  • Vilmos Komornik
    • 1
  1. 1.Department of MathematicsUniversity of StrasbourgStrasbourgFrance

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