Boundary Value Problems/Vector Field and Flow

Return Boundary Value Problems

Vector Analysis: Basics

edit

We are interested in operations on sets in a multidimensional space. The focus is on physical problems so think about three spatial dimensions,  , and the dimension of time  . For notation, I will use   ,  and  . This is easily scaled to   - dimensions for larger spaces. So   corresponds to   for most of the time, or less.

Two types of fields

edit

Scalar Field

edit

A scalar x is a real number, this is denoted as  . A vector in 3-D   is a "3-tuple" of real numbers   where   for  . Example:  

Vector Field

edit