数值分析课程中插值余项的教学探讨

A Pedagogical Exploration into the Interpolation Remainder in the Course of Numerical Analysis

插值法是数值分析中最基本的数值方法,而插值法的余项又是插值法的核心内容.在教学中需要着重阐述插值余项的来源和证明过程,然后详细说明一些应注意的注解,为函数逼近、数值微积分和微分方程数值解等数值分析内容的学习打下坚实的基础.

Numerical analysis is a course on offer to introduce fundamental theories and basic methods of scientific computing. The interpolation method is most fundamental in numerical methods, while the interpolation remainder is the core of the interpolation method. In the teaching process, the emphasis should be laid on the elaboration of its origin and proof of the interpolation remainder. Besides, a detailed explanation must be given to some notes that are in need of due attention so as to lay a sound foundation for the learning of content like the function approximation, numerical calculus and numerical solutions for differential equation in numerical analysis.