Vectors, Tensors and the Basic Equations of Fluid Mechanics 英文原版 矢量/向量、张量分析在流体力学上的应用 Rutherford Aris

基本信息

Author Rutherford Aris

Format Paperback | 320 pages

Dimensions 137 x 214 x 16mm | 325g

Publication date 01 Jan 1990

Publisher Dover Publications Inc.

Publication City/Country New York, United States

Language English

Edition Statement New ed

Illustrations note w. figs.

ISBN10 0486661105

ISBN13 9780486661100

页面参数仅供参考，具体以实物为准

内容简介

这本优秀的著作发展并利用了数学概念来阐明物理理论。它主要面向高级本科生和研究生的工程师，物理学家和应用数学家，将笛卡尔和广义张量的数学应用于物理场理论，并主要从流体力学理论方面进行了演示。

本质上是一篇介绍性文章，旨在让读者熟悉部分微分和多重积分的微积分，它首先回顾了必要的背景资料，然后着手探讨笛卡尔矢量和张量的代数和微积分。随后的章节讨论了流体运动，流体中的应力，笛卡尔坐标中的运动和能量方程，张量以及欧氏空间中的流体流动方程。

*后几章讨论了空间表面的几何形状，表面流方程和反应流体方程。两个宝贵的附录介绍了三维坐标几何和矩阵理论的简历，以及另一个隐函数和雅可比行列的简历。大量的练习是演示的组成部分，为操纵和扩展演示的概念提供了许多机会。

This excellent text develops and utilizes mathematical concepts to illuminate physical theories. Directed primarily to engineers, physicists, and applied mathematicians at advanced undergraduate and graduate levels, it applies the mathematics of Cartesian and general tensors to physical field theories and demonstrates them chiefly in terms of the theory of fluid mechanics.

Essentially an introductory text, intended for readers with some acquaintance with the calculus of partial differentiation and multiple integration, it first reviews the necessary background material, then proceeds to explore the algebra and calculus of Cartesian vectors and tensors. Subsequent chapters take up the kinematics of fluid motion, stress in fluids, equations of motion and energy in Cartesian coordinates, tensors, and equations of fluid flow in Euclidean space.

The concluding chapters discuss the geometry of surfaces in space, the equations of surface flow and equations for reacting fluids. Two invaluable appendixes present a resume of 3-dimensional coordinate geometry and matrix theory and another of implicit functions and Jacobians. A generous number of exercises are an integral part of the presentation, providing numerous opportunities for manipulation and extension of the concepts presented.

作者简介

Rutherford "Gus" Aris (September 15, 1929 – November 2, 2005) was a chemical engineer, control theorist, applied mathematician, and a Regents Professor Emeritus of Chemical Engineering at the University of Minnesota (1958–2005).