Boundary Value Problems/Vector Field and Flow

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Return Boundary Value Problems

Vector Analysis: Basics[edit | edit source]

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 | edit source]

Scalar Field[edit | edit source]

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 | edit source]