“偏微分方程”课程中的高阶学习探索
摘 要:本文以本科“偏微分方程”教学中涉及的格林公式与高斯公式为出发点,通过复数乘积的几何解释,将格林公式与高斯公式在积分形式上统一为无空间维数要求的散度定理。进而引入一般的分部积分公式,使学生对抽象积分有一个初步的了解,达到在“偏微分方程”课程中进行高阶学习探索的目的。
关键词:偏微分方程;数学物理方程;高阶学习
Advanced Learning Exploration in the Course
of "Partial Differential Equations"
Yu Hao Yang Yunlong
School of Science,Dalian Maritime University LiaoningDalian 116026
Abstract:Based on the Green's Formula and Gauss's Formula involved in the teaching of undergraduate partial differential equations,this paper unifies the Green's Formula and Gauss's Formula in integral form into a divergence theorem without spatial dimension requirements through geometric interpretation of complex product.Then,the general integral by parts formula is introduced to enable students to have a preliminary understanding of abstract integral,so as to achieve the goal of highorder learning and exploration in the course of partial differential equations.
Keywords:partial differential equations;mathematical physics equations;highorder learning
一、概述
“偏微分方程”又称为数学物理方程,是大学本科学习的重要课程[12]。(剩余4623字)
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