欧美理科经典力学教材的现代化(三)——现代教学内容的发展

UPDATED MATERIALS IN EUROPEAN AND AMERICAN CLASSICAL MECHANICS TEXTBOOKS FOR SCIENCE MAJORS 3:MODERN CONTENTS DEVELOPED

本文是研究欧美理科经典力学教材内容更新系列论文的第3篇,分析6部经典力学现代教材的理念、内容和特点。这些教材更重视运动微分方程解的定性和定量特性,更重视定性分析方法和数值求解方法。所有教材都增加了混沌的内容。高级力学课程教材还增加了Lagrange力学和Hamilton力学的几何描述,同时包括了必要的整体微分几何基础知识。有些高级力学课程教材包括了经典力学代数结构的基本知识。中级力学课程教材没有代数结构和几何描述的内容。

As the third paper of a series on the content update of European and American classic mechanics textbooks for science majors,this manuscript analyzes the ideas,the contents,and the features of 6 modern textbooks of classical mechanics.These textbooks pay more attentions to qualitative and quantitative characteristics of the solutions of differential equations of motion,and pay more attentions to qualitative analysis and numerical solutions.Chaotic dynamics is introduced into all the textbooks.Some textbooks for the advanced mechanics course include geometric descriptions of Lagrange mechanics and Hamiltonian mechanics with necessary fundamentals of global differential geometry,and essential algebraic structures of classical mechanics.However the textbooks for the intermediate mechanics course do not deal with algebraic structures and geometric descriptions of classical mechanics.