Numerical Quadrature

Abstract

In this chapter we discuss numerical approximation of the integral

$$\begin{array}{rcl} I(f) ={ \int \nolimits \nolimits }_{{\mathbb{S}}^{2}}f(\eta )\,d{S}^{2}(\eta ).& &\end{array}$$

(5.1)

The integrand fcan be well-behaved or singular, although our initial development assumes fis continuous and, usually, several times continuously differentiable. Such integrals occur in a wide variety of physical applications; and the calculation of the coefficients in a Laplace series expansion of a given function (see (4.55)) requires evaluating such integrals.