授课:68学分：4第七章常微分方程的数值解法7.1引言包含自变量、未知函数及未知函数的导数或微分的方程称为微分方程。在微分方程中,自变量的个数只有一个,称为常微分方程.。自变量的个数为两个或两个以上的微分方程叫偏微分方程。微分方程中出现的未知函数最高阶导数的阶数称为微分方程的阶数。如果未知函数y及其各阶导数都是一次的,则称它是线性的,否则称为非线性的。(),,,ynyy在高等数学中，对于常微分方程的求解，给...
Chapter6IntroductiontoPartialDifferentialEquationsAllofthedifferentialequationswhichhavebeenstudiedinthepreviouschaptershaveonefeatureincommon.Theyalldescribethestateorthemotionofaquantitywhichdependononlyoneindependentvariable.Hencethedifferentialequationsareordinaryones.Inthischapterweshallstudyequationswhichdescribethemotionorchangeofstateofquantitieswhichdependonmorethanoneindependentvariab...
Chapter5*QualitativeAnalysisandStabilityofSolutionsWhentheactualsolutionsofadifferentialequationorsystemcannotbeobtained,weoftenconsidersomemethodofapproximatingsolutions.Althoughthiscandeedhelpusobtainingsomeapproximatesolutions,weoftenfeeltroublesome.Infact,itisnotnecessarytoobtainmaterialformofeachsolution.Whatwhichweneediscorrelativeinformationwiththesolution,namely,theentirehistoryofamotio...
