The Engineering Handbook - Section 198 - Vector Algebra And Calculus.pdf

Cain, G. “Vector Algebra and Calculus”

The Engineering Handbook.

Ed. Richard C. Dorf
Boca Raton: CRC Press LLC, 2000



















































© 1998 by CRC PRESS LLC
198


Vector Algebra and Calculus



Basic Definitions
Coordinate Systems
Vector Functions
Gradient, Curl, and Divergence

Integration
Integral Theorems


e Cain
ia Institute of Technology



Basic Definitions

A vector is a directed line segment, with two vectors being equal if they have the same length and
the same direction. More precisely, a vector is an equivalence class of directed line segments,
where two directed segments are equivalent if they have the same length and the same direction.
The length of a vector is mon length of its directed segments, and the angle between

vectors is the angle between any of their segments. The length of a vector u is denoted u . There is
j j
defined a distinguished vector having zero length, which is usually denoted 0. It is frequently
useful to visualize a directed segment as an arrow; we then speak of the nose and the tail of the
u v
segment. The sum + of two vectors u and v is defined by taking directed segments from u and
v and placing