Integration and Cubature Methods: A Geomathematically Oriented Course

Willi Freeden, Martin Gutting

© 2017 - Chapman and Hall/CRC
Published November 27, 2017
Reference - 501 Pages - 31 B/W Illustrations
ISBN 9781138718821 - CAT# K32243
Series: Chapman & Hall/CRC Monographs and Research Notes in Mathematics

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  • First book of its kind devoted to geoscientific integration and cubature methods
  • Presents a novel approach to approximate integration
  • Offers a comprehensive foundation for readers to explore the subject
  • Includes innovative integration techniques such as spherical multiscale equidistribution, best approximate integration over manifolds, adaptive multivariate trapezoidal summation, multivariate Romberg cubature, and Paley-Wiener sampling integration.


In industry and economics, the most common solutions of partial differential equations involving multivariate numerical integration over cuboids include techniques of iterated one-dimensional approximate integration. In geosciences, however, the integrals are extended over potato-like volumes (such as the ball, ellipsoid, geoid, or the Earth) and their boundary surfaces which require specific multi-variate approximate integration methods. Integration and Cubature Methods: A Geomathematically Oriented Course provides a basic foundation for students, researchers, and practitioners interested in precisely these areas, as well as breaking new ground in integration and cubature in geomathematics.