Chapter 2
Vectors and Scalars
标量简介
Many familiar physical quantities can be specified completely by giving a single number and the appropriate unit. For example, "a class period lasts ...
向量简介
To define some physical quantities, there is a need to specify both magnitude as well as direction. For example, when the U.S. Coast Guard dispatches a ...
笛卡尔坐标系中的矢量分量
Vectors are usually described in terms of their components in a coordinate system. Even in everyday life, we naturally invoke the concept of orthogonal ...
极坐标和圆坐标
The Cartesian coordinate system is a very convenient tool to use when describing the displacements and velocities of objects and the forces acting on ...
球坐标
Spherical coordinate systems are preferred over Cartesian, polar, or cylindrical coordinates for systems with spherical symmetry. For example, to describe ...
向量代数:图形方法
Vectors can be multiplied by scalars, added to other vectors, or subtracted from other vectors. The vector sum of two (or more) vectors is called the ...
向量代数:分量法
It is cumbersome to find the magnitudes of vectors using the parallelogram rule or using the graphical method to perform mathematical operations like ...
标量积 （点积）
The scalar multiplication of two vectors is known as the scalar or dot product. As the name indicates, the scalar product of two vectors results in a ...
向量积（叉积）
Vector multiplication of two vectors yields a vector product, with the magnitude equal to the product of the individual vectors multiplied by the sine of ...
标量和矢量三元乘积
Two vectors can be multiplied using a scalar product or a vector product. The resultant of a scalar product is scalar, while with vector products, the ...
Gradient 和 Del 运算符
In mathematics and physics, the gradient and del operator are fundamental concepts used to describe the behavior of functions and fields in space. The ...
发散和旋度
The divergence of a vector field at a point is the net outward flow of the flux out of a small volume through a closed surface enclosing the volume, as ...
二阶导数和拉普拉斯算子
The first order operators using the del operator include the gradient, divergence and curl. Certain combinations of first order operators on a scalar or ...
线积分、曲面积分和体积积分
A line integral for a vector field is defined as the integral of the dot product of a vector function with an infinitesimal displacement vector along a ...
散度和斯托克斯定理
The divergence and Stokes' theorems are a variation of Green's theorem in a higher dimension. They are also a generalization of the fundamental ...
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