Sajang Yang: Vector Analysis

Wednesday, January 12, 2011

Vector Analysis

The purpose of vector analysis is to acquire a thorough understanding of the mathematical methods required to deal with fields.

Mathematically, a field is a function that describes a physical quantity at all points in space. In scalar fields this physical quantity is completely specified by a single number for each point. For vector fields both a number and a direction are required.

A vector can be specified by its components:

$A = A_x\bold{i}+A_y\bold{j}+A_z\bold{k}$

scalar (or dot) product:

$\bold{A}\cdot \bold{B}=ABcos(\varphi - \theta )$

$\bold{A}\cdot \bold{B}=ABcos(\varphi - \theta )= ABcos\varphi cos\theta + ABsin\varphi sin\theta = A_xB_x + A_yB_y$

vector (or cross) product:

2 comments:

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