向量微积分
2008-5
世界图书出版公司
马修斯 (Matthews P.C.)
179
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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.
作者：(英国)马修斯(Mattews P.C.)
1. Vector Algebra1.1 Vectors and scalars1.1.1 Definition of a vector and a scalar1.1.2 Addition of vectors1.1.3 Components of a vector1.2 Dot product1.2.1 Applications of the dot product1.3 Cross product1.3.1 Applications of the cross product1.4 Scalar triple product1.5 Vector triple product1.6 Scalar fields and vector fields2. Line，Surface and Volume Integrals2.1 Applications and methods of integration2.1.1 Examples of the use of integration2.1.2 Integration by substitution2.1.3 Integration by parts2.2 Line integrals2.2.1 Introductory example： work done against a force2.2.2 Evaluation of line integrals2.2.3 Conservative vector fields2.2.4 Other forms of line integrals2.3 Surface integrals2.3.1 Introductory example：flow through a pipe2.3.2 Evaluation of surface integrals2.3.3 0lther forms of surface integrals2.4 volume integrals2.4.1 Introductory example：mass of an object with variable density2.4.2 Evaluation of volume integrals3. Gradient，Divergence and Curl3.1 Partial difierentiation and Taylor series3.1.1 Partial difierentiation3.1.2 Taylor series in more than one variable3.2 Gradient of a scalar field3.2.1 Gradientsconservative fields and potentials3.2.2 Physical applications of the gradient3.3 Divergence of a vector field3.3.1 Physical interpretation of divergence3.3.2 Laplacian of a scalar field3.4 Cllrl of a vector field3.4.1 Physical interpretation of curl3.4.2 Relation between curl and rotation3.4.3 Curl and conservative vector fields4. Suffix Notation and its Applications4.1 Introduction to suffix notation4.2 The Kronecker delta4.3 The alternating tensor4.4 Relation between ijk and ij4.5 Grad，div and curl in suffix notation4.6 Combinations of grad，div and curl4.7 Grad，div and curl applied to products of functions5. Integral Theorems5.1 Divergence theorem5.1.1 C：onservation of mass for a fluid5.1.2 Applications ofthe divergence theorem5.1.3 Related theorems linking surface and volume integrals5.2 Stokes’S theorem5.2.1 Applications of Stokes’S theorem5.2.2 Related theorems linking line and surface integrals6. Curvilinear Coordinates6.1 Orthogonal curvilinear coordinates6.2 Grad，div and curl in orthogonal curvilinear coordinate systems6.2.1 Gradient6.2.2 Divergence……7. Cartesian Tensors8. Applications of Vector CalculusSolutionsIndex
《向量微积分》由世界图书出版公司出版。
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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
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。
习题有点难，不过解答很详细。
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。
买了没看，比较基础。
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
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。
尽量别买，印刷质量太次了，都看不清楚。
前几张看得很顺利，从第五章开始迷糊了
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
好书，不太厚，容易阅读。
这里的目录只显示最前面的一小部分，关键的部分看不到。