Divergence Theorems and Green's Theorem

Flashcards focusing on key concepts and definitions related to Green's Theorem and the Divergence Theorem in vector calculus.

Green's Theorem

A theorem that relates the circulation of a vector field around a simple closed curve to the double integral of the divergence over the region enclosed by the curve.

Divergence Theorem

A theorem that relates the flow of a vector field through a closed surface to the divergence of the field inside the surface.

Flux

The amount of a quantity passing through a surface per unit time, often represented as the integral of a vector field over a surface.

Simple Solid Region

A region in space that is bounded by a well-defined surface and has no holes or gaps.

Positive Orientation

The direction of a surface normal vector which is outward from the solid region it bounds.

Surface Integral

An integral that sums up the values of a function over a surface.

Bounding Surface

The surface that encloses a volume in three-dimensional space.

Continuous Partial Derivatives

A property of functions indicating that their partial derivatives exist and are continuous, which is important for applying theorems in vector calculus.

Divergence (of a vector field)

A scalar function that measures the extent to which a vector field is expanding or contracting at a given point.

Volume Integral

An integral that sums a quantity over a three-dimensional volume.