The roles of “to radically reform & to thoroughly overhaul” in the set up of the fundamental mathematical and mechanical knowledge system of the mechanics

• 1、Department of Mechnaics and Engineering Science, Fudan University, ShangHai 200433

Abstract：In this paper, the fundamental mathematical and mechanical knowledge systems of the mechanics are concluded as calculus and modern tensor analysis with continuum mechanics based on it. As referred to the related national and international textbooks and monographs with the first levels, the fundamental constitutions of the above mentioned knowledge systems are presented. It is put forward that the knowledge points with the corresponding knowledge elements are suitable to recognize one knowledge system, and the radical development property of the knowledge system of calculus is expressed. The concept termed as "Mathematical Generality" is put forward that are just some mathematical structures or forms as the so-called knowledge elements of some knowledge points with respect even to different knowledge systems. Mathematics is taken as the systematic ideas and methods to recognize the natural and unnatural worlds in the present paper, and the relationships between mathematical knowledge system and mechanical knowledge system are represented to some extents. Some cases originated from the knowledge systems of calculus, tensor analysis, differential geometry and continuum mechanics are adopted to expound the arguments that are raised in the present paper. The related proof of the Stokes formula in calculus in the unified form, the interpretation of the tensor field's gradient in tensor analysis in the point of view of differential and the definitions of the Lie-derivative in differential geometry viewed from filed argument with the related results are our own cognitions.

Keywords： Knowledge system Knowledge point Knowledge element Mathematical generality Calculus Tensor analysis Differential geometry Continuum mechanics