在流体力学课程中认识张量结构

Understanding the Tensor's Structures in the Fluid Mechanics Teaching

大学本科力学专业的流体力学课程涉及大量的张量分析知识。深入认识张量结构,对学好流体力学具有重要的意义。作者在流体力学课程教学中,提出利用集合及传承性思想来解释张量,并给出三阶张量的拓扑结构以及张量的维数与阶数的结构意义。通过认识三阶张量的结构,学生能够深刻理解流体力学中张量代表的复杂行为,并且能调动学生思维积极性。最终能够提高学生对流体力学学习的兴趣与信心。

The subject of the Fluid Mechanics for the undergrad-uates in the engineering specialty involves a great deal of the knowledge of tensor analysis. An in-depth insight into the ten-sor＇s structures is important for an in-depth learning of the fluid mechanics. The set and generic theory was used in the author＇s teaching for description of tensors and explanation of the meaning of the dimension and order for the tensor. Better understanding of the complex behavior represented by the tensor was achieved through observation of the structures of the third order tensor. The proposed method contributes to inspire the student＇s minds, en-hance the interest and confidence in learning of the fluid me-chanics.