向量微积分

当前位置:首页 > 自然科学 > 数学 > 向量微积分

出版社:世界图书出版公司
出版日期:2008-5
ISBN:9787506292269
作者:马修斯 (Matthews P.C.)
页数:179页

内容概要

作者:(英国)马修斯(Mattews P.C.)

书籍目录

1. Vector Algebra
1.1 Vectors and scalars
1.1.1 Definition of a vector and a scalar
1.1.2 Addition of vectors
1.1.3 Components of a vector
1.2 Dot product
1.2.1 Applications of the dot product
1.3 Cross product
1.3.1 Applications of the cross product
1.4 Scalar triple product
1.5 Vector triple product
1.6 Scalar fields and vector fields
2. Line,Surface and Volume Integrals
2.1 Applications and methods of integration
2.1.1 Examples of the use of integration
2.1.2 Integration by substitution
2.1.3 Integration by parts
2.2 Line integrals
2.2.1 Introductory example: work done against a force
2.2.2 Evaluation of line integrals
2.2.3 Conservative vector fields
2.2.4 Other forms of line integrals
2.3 Surface integrals
2.3.1 Introductory example:flow through a pipe
2.3.2 Evaluation of surface integrals
2.3.3 0lther forms of surface integrals
2.4 volume integrals
2.4.1 Introductory example:mass of an object with variable density
2.4.2 Evaluation of volume integrals
3. Gradient,Divergence and Curl
3.1 Partial difierentiation and Taylor series
3.1.1 Partial difierentiation
3.1.2 Taylor series in more than one variable
3.2 Gradient of a scalar field
3.2.1 Gradientsconservative fields and potentials
3.2.2 Physical applications of the gradient
3.3 Divergence of a vector field
3.3.1 Physical interpretation of divergence
3.3.2 Laplacian of a scalar field
3.4 Cllrl of a vector field
3.4.1 Physical interpretation of curl
3.4.2 Relation between curl and rotation
3.4.3 Curl and conservative vector fields
4. Suffix Notation and its Applications
4.1 Introduction to suffix notation
4.2 The Kronecker delta
4.3 The alternating tensor
4.4 Relation between ijk and ij
4.5 Grad,div and curl in suffix notation
4.6 Combinations of grad,div and curl
4.7 Grad,div and curl applied to products of functions
5. Integral Theorems
5.1 Divergence theorem
5.1.1 C:onservation of mass for a fluid
5.1.2 Applications ofthe divergence theorem
5.1.3 Related theorems linking surface and volume integrals
5.2 Stokes’S theorem
5.2.1 Applications of Stokes’S theorem
5.2.2 Related theorems linking line and surface integrals
6. Curvilinear Coordinates
6.1 Orthogonal curvilinear coordinates
6.2 Grad,div and curl in orthogonal curvilinear coordinate systems
6.2.1 Gradient
6.2.2 Divergence
……
7. Cartesian Tensors
8. Applications of Vector Calculus
Solutions
Index

编辑推荐

《向量微积分》由世界图书出版公司出版。

作者简介

《向量微积分》主要内容:Vector calculus is the fundamental language of mathematical physics. It provides a way to describe physical quantities in three-dimensional space and the way in which these quantities vary. Many topics in the physical sciences can be analysed mathematically using the techniques of vector calculus. These topics include fluid dynamics, solid mechanics and electromagnetism, all of which involve a description of vector and scalar quantities in three dimensions. 
This book assumes no previous knowledge of vectors. However, it is assumed that the reader has a knowledge of basic calculus, including differentiation, integration and partial differentiation. Some knowledge of linear algebra is also required, particularly the concepts of matrices and determinants.

图书封面


 向量微积分下载 更多精彩书评



发布书评

 
 


精彩书评 (总计1条)

  •     书名叫向量微积分,就是所谓的矢量分析。目前国内的单独成书的矢量分析并不多见。这本书讲矢量分析对物理意义讲的很清楚明白,在计算上引入了张量,但又不像一些张量分析的书让人觉得恶心,结果是由于张量的引入让一些矢量分析的等式的证明变得相当容易。这本书强烈推荐给学物理的同学。

精彩短评 (总计20条)

  •     好书,不太厚,容易阅读。
  •     基本上就是教你怎么算的一本书。几个向量微分算子的定义以及相应积分定理的证明(如果还能叫定义和证明的话)很不靠谱
  •     这里的目录只显示最前面的一小部分,关键的部分看不到。
  •     刚接触外文书籍,看这本书刚好,就是没有纯数学化,没有看见定理和证明,总是说明性文字
  •     楼上的评论极不负责任,目录看不到是卓越的事,和这本书的好坏无关,你不晓得到实体书店去看啊?这是我见过的最好的矢量分析教材之一,书的纸张也很好,象原版书一样。不再是世图以前那种印得象盗版的书另外还有一本很经典的矢量分析教材,Div, Grad, Curl, and All That: An Informal Text on Vector Calculus, Fourth Edition by H. M. Schey也是非常经典,但是中国没引进
  •     看了前几章,比较简洁易懂。另外辟一下谣,这本书不像影印版,字迹非常清楚,纸张也可以。前面那位说印得不清楚的不知道为啥说瞎话,这种印刷如果还不清楚就没有清楚的了。
  •     通俗易懂。第四章和第七章尤其精彩。
  •     看看英文原版开眼界,能学到些国内教材上没有的东西。
  •     用分量形式来写Nabulu算子,分析明了简洁。
  •     两百页也不够,比较薄,从外表看上去没有太大压力。可以学到的东西包括scalar field, vector field;grad, div, curl;tensor;etc. 阅读更多
  •     mark, 7 days to finish
  •     买了没看,比较基础。
  •     习题有点难,不过解答很详细。
  •     以后Springer的书还是国内买影印吧,再贵也比amazon上买原书便宜。
  •     这本书真心赞!!!
  •     讲得很全,推荐在大一下学期前后读完
  •     前几张看得很顺利,从第五章开始迷糊了
  •     尽量别买,印刷质量太次了,都看不清楚。
  •     比老毛子的书简单,两下就弄完了~
  •     书名很吸引人但是内容一般这种书国内很多没必要买英文版。
 

外国儿童文学,篆刻,百科,生物科学,科普,初中通用,育儿亲子,美容护肤PDF图书下载,。 零度图书网 

零度图书网 @ 2024