5 - 数值差异计算与积分法
5.1 NUMERICAL DIFFERENTIATION¶
5.1.1 Finite difference formulas有限差分公式¶
1.两点正差公式
由泰勒展开式推导而来
2.三点正差公式
3.二阶导数的三点中心差
5.1.2 Rounding error（不用看）¶
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5.1.3 Extrapolation（ Richardson extrapolation）¶
例题
作业¶
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5.2 NEWTON–COTES FORMULAS FOR NUMERICAL INTEGRATION¶
5.2.1 Trapezoid Rule¶
5.2.2 Simpson’s Rule¶
One numerical integration formula that has at least precision of degree 3 is the composite Simpson's rule.
5.2.3 Composite Newton–Cotes formulas¶
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5.3 ROMBERG INTEGRATION¶
计算定积分的方法可以通过添加数据来进行扩展，直到达到所需的精度为止。隆伯格积分是应用复合梯形规则进行外推的结果。
Romberg Integration is the result of applying extrapolation to composite Trapezoid Rule.
5.5 GAUSSIAN QUADRATURE¶
