“偏微分方程”課程中的高階學(xué)習(xí)探索
摘 要：本文以本科“偏微分方程”教學(xué)中涉及的格林公式與高斯公式為出發(fā)點，通過復(fù)數(shù)乘積的幾何解釋，將格林公式與高斯公式在積分形式上統(tǒng)一為無空間維數(shù)要求的散度定理。進而引入一般的分部積分公式，使學(xué)生對抽象積分有一個初步的了解，達(dá)到在“偏微分方程”課程中進行高階學(xué)習(xí)探索的目的。
關(guān)鍵詞：偏微分方程；數(shù)學(xué)物理方程；高階學(xué)習(xí)
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”又稱為數(shù)學(xué)物理方程，是大學(xué)本科學(xué)習(xí)的重要課程［12］。（剩余4623字）