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Applied Mathematical Methods by Bhaskar Dasgupta

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Advanced Topics in Numerical Integration*

In the previous chapter, we covered Newton-Cotes quadrature formulae and developed some sophisticated practical methods for integration of functions. In the present chapter, we develop an exposure to methods that arise out of composite ideas. We start with an introduction to Gaussian quadrature, which provides a rich collection of tools to tackle problems in numerical integration. Next, we develop the elementary tools for multiple integrals, based on classical ideas and a stochastic technique known as the Monte Carlo method.

Gaussian Quadrature

A typical quadrature formula comes in the form of a weighted sum as, where fi’s are the function values at sampled points and wi’s are the corresponding weights. ...

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