如何在数理方法教学中培养学生综合运用知识的能力——以留数定理在傅里叶级数展开问题中的应用为例  

On fostering students' capacity of synthetically utilizing knowledge in teaching of the methods of mathematical physics—Taking the application of residue theorem in Fourier series expansion for example

作　　者：朱爱东[1] 王洪福[1] 田莲花[1] 张英俏[1] 

机构地区：[1]延边大学理学院物理系,吉林延吉133002

出　　处：《延边大学学报（自然科学版）》2014年第2期163-166,共4页Journal of Yanbian University（Natural Science Edition）

摘　　要：培养学生对知识的融会贯通、综合运用的能力是数学物理方法教学的重要教学目的之一.通过运用留数定理方法求解一类复杂周期函数R(cos x,sinx)的傅里叶级数展开问题与常见的解题方法的比较,说明了知识点融合对学生理解和掌握数学物理方法以及对学习后续课程的重要影响.教师在数学物理方法教学中应注重知识点的有机融合和注重培养学生综合运用知识的能力,并提出数学物理方法教学应以培养学生的发散性思维方式和对知识的综合运用能力为首要目的.The most important teaching aim of the methods of mathematical physics is to foster students＇ capacity in synthetically utilizing knowledge.By using the residue theorem to solve the problem of Fourier series expansion for a type of complicate periodical function,and comparing with the common method,we discuss the organic integration of the knowledge points in the lesson＂methods of mathematical physics＂,as well as fostering the students＇ capacity of synthetically utilizing knowledge.The important effects of the organic integration of the knowledge points on grasping this course and learning the other subsequent courses are illustrated.Moreover,we propose the ideas that the lesson of methods of mathematical physics should aim at fostering the divergent thinking mode and the ability of synthetically utilizing knowledge.

关 键 词：留数定理 傅里叶级数 数学物理方法 

分 类 号：O411.14[理学—理论物理] G642[理学—物理]