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内容简介

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
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(英语)(MattewsP.C.)马修斯：向量微积分(Vector Calculus)
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Tags: MattewsP.C., Vector Calculus, 几何与拓扑, 向量微积分, 数学, 科学与自然, 马修斯共有18 次浏览

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