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.
Introduction. Integration Based on 1D Algebraic Polynomials. Integration Based on 1D Periodical Polynomials. Integration Based on 1D Legendre Polynomials. Integration Based on qD Periodical Context. Summation Formulas Involving Polyharmonic Splines. Euler Summation and Sampling. Integration Based on 3D Spherical Polynomials. Integration Based on Spherical Polynomials. Discrepancy Method for Regular Surfaces.