向量微积分

《向量微积分》是2008年世界图书出版公司出版的图书，作者是(英来自国)马修斯(Mattews P.C.)。主要讲述了Vector calculus is the fundamental language of 360百科mathem那介波试现群极atical physics. It provides a way to describ老e physical quantities in three-dimensional space and the way in which these qua吸刘新移谈模父回ntities vary. Many topics in the physical sciences 早象落项can be analysed mathemati草cally using the t厂八换沙echnique响s of vector calculus. These t数爱一滑技强再械空opics include fluid dynamics, solid 环mechanics and electromagnetism, 太all of which involve a description of vector and scalar quantities in t区hree dimensions.

• 书名 向量微积分
• 出版时间 2008年
• 页数 179 页
• 装帧 平装
• ISBN 9787506292269

图书信息

　　出版社: 世界图书出版公司; 第1版 (2008年5来自月1日)

　　外文书名360百科: Vector Calculus

　　正文语种: 英语

　　开本: 32

　　条形码: 9787506292269

　　尺寸: 22 x 14.8 x 1.包千吃弦称短座宽集2 cm

　　重量: 240 g

作者简介

　　作者:(英国)马修斯(Mattews P.C.)

内容简介

　　《向量微积分》

　　This book assumes no previous knowledge of vectors. However, it is assumed that the reader has a knowledge of bas沿济交继威持张使病善轴ic calculus, including differentiation, integration and partial 内要相划心differentiation. Some know厚鲜任纪ledge of linear algebra is also required, particularly the concepts of matr来自ices and determinants.

目录

　　1. V构江汉笔胶山逐独ector Algebra

　　1.1 Vectors and scalars

　　1.1.1 Definition of a vector and a scalar

　　1.1.2 Addition of vectors

皮话谁等米理异志越　　1.1.3 Components of a vector

360百科　　1.2 Dot produc谁t

　　1.2.1 Applic班再消ations of the dot product

　　1.3 C干娘ross product

　陈单长拉派频宪牛奏队　1.3.1 Appli还零cations of the cross product

料染哥否手状者执袁富　　1.4 Scalar 清沿农括于王triple product

　　慢燃压超看1.5 Vector triple product

　　1.6 Sc良必往叫状另很料措室生alar fields and vector fields

　　2. Line，Surf而多属速菜眼ace and Volume Integrals

　　2.1 Applications and methods of integration

　　2.1.1 Examples of the use of integration

　　2.1.2 Integration by substit冲新留即边科旧轻岁ution

　　2.1.吸祖3 Integration by parts

　　2.2 Line integrals

　　2.2.1 Introductory example: 距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