《张量分析基础及连续介质力学—Heinbockel经典》

《张量分析基础及连续介质力学—Heinbockel经典》 Introduction to Tensor Calculus and Continuum Mechanics This is an introductory text which presents fundamental concepts from the subject areas of tensor calculus, dierential geometry and continuum mechanics. The material presented is suitable for a two semester course in applied mathematics and is flexible enough to be presented to either upper level undergraduate or beginning graduate students majoring in applied mathematics, engineering or physics. The presentation assumes the students have some knowledge from the areas of matrix theory, linear algebra and advanced calculus. Each section includes many illustrative worked examples. At the end of each section there is a large collection of exercises which range in diculty. Many new ideas are presented in the exercises and so the students should be encouraged to read all the exercises. The purpose of preparing these notes is to condense into an introductory text the basic denitions and techniques arising in tensor calculus, dierential geometry and continuum mechanics. In particular, the material is presented to (i) develop a physical understanding of the mathematical concepts associated with tensor calculus and (ii) develop the basic equations of tensor calculus, dierential geometry and continuum mechanics which arise in engineering applications. From these basic equations one can go on to develop more sophisticated models of applied mathematics. The m ...