摘要
国内很多“数学物理方程”教材在讲述分离变量法时,解答的第一步设y(x,t)=X(x)T(t),让初学者产生疑问,为什么方程的解具有乘积形式?加法形式的解是否可以?这里给出一个比较浅显的解释,以期让初学者能够比较容易地理解.
Many students in science will study the course partial differential equations in college.In most textbooks,when mentioned the method of separation of variables,they assume at the beginning that y(x,t)=X(x)T(t)without any explanation,while solving a homogeneous partial differential equation with a homogeneous boundary condition and an initial condition.This puzzles most students.They will have many questions even after consulting with the teachers,such as,why the general solution is the product of two functions?Could the solution be the sum of two or more functions?A clear explanation which seems easier to understand is presented.
作者
李文伟
LI Wenwei(School of Information and Mathematics,Anhui International Studies University,Hefei 231201,China)
出处
《大学数学》
2024年第3期102-113,共12页
College Mathematics
基金
安徽省高等学校省级质量工程项目(2020kcszjxtd34,2022xsxx081)
中国高等教育学会高等教育科学研究规划课题“教育数学实践研究”课题(23SX0425)。
关键词
数理方程
分离变量法
傅立叶方法
partial differential equation
method of separation of variables
Fourior method
