Chapter 8 Vector Algebra and Analytic Geometry of Space1
Chapter 9 The multivariable differential calculus and
Chapter 10 Multiple Integrals104
Chapter 11 Line and Surface Integrals146
Chapter 12 Infinite Series188
Some of the things we measure are determined simply by their magnitudes. To record mass, length or time, for example, we need only write down a number and name an appropriate unit of measure. We need more information to describe a force, displacement, or velocity. To describe a force, we need to record the direction in which it acts as well as how large it is. To describe a body's displacement, we have to say in what direction it moved as well as how far. To describe a body's velocity, we have to know where the body is headed as well as how fast it is going.
A quantity that has both magnitude and direction, such as force, displacement, or velocity, is called a vector. A vector is usually represented by a line segment with an arrow, a directed line segment. The length of the directed line segment represents the magnitude of the vector and the arrow points in the direction of the vector. The vector represented by the directed line segment from the initial point A to the terminal point B is denoted by AB(Figure 8-1)。