关于数值积分的几点教学注记

Several Teaching Notes on Numerical Integration

摘要: 本文对常用的数值积分公式给出了相关教学注记。首先，我们引入Newton-Cotes公式，并利用该公式证明了例1中定积分的数值估计。此例说明数值积分公式在数学理论上的有趣应用，为此，我们给出教学注记。然后，我们引入Gauss求积公式，通过例2比较了Newton-Cotes公式，Gauss求积公式和Clenshaw-Curtis公式的数值模拟过程，并且基于数值积分公式的代数精度，数值稳定性和收敛性给出了相关详细的教学注记。

Abstract: This paper gives relevant teaching notes on commonly used numerical integration formulas. First, we introduce the Newton-Cotes formula and use it to prove the numerical estimation of the definite integral in Example 1. This example illustrates the interesting application of the numerical integration formula in mathematical theory. To this end, we give teaching notes. Then, we introduce the Gauss quadrature formula and compare the numerical simulation processes of the Newton-Cotes formula, the Gauss quadrature formula and the Clenshaw-Curtis formula through Example 2. Relevant detailed teaching notes are given based on the algebraic precision, numerical stability and convergence of the numerical integration formula.