Ordinary Integrals and Vector Calculus Concepts

Ordinary Integral

Indefinite integral of vector R(u) with respect to u.

Indefinite Integral

Integral without specified limits, includes constant vector.

Definite Integral

Integral with specific limits, evaluates to S(b) - S(a).

Line Integral

Integral of vector function along a curve C.

Position Vector

Vector r(u) representing points (x,y,z) in space.

Tangential Component

Component of vector A along curve C's direction.

Work Done

Line integral of force F along path C.

Circulation

Integral around closed curve C in fluid mechanics.

Conservative Vector Field

Vector field A where A.dr is path-independent.

Scalar Potential

Function c such that A = ∇c in conservative fields.

Exact Differential

Integral of A.dr equals total differential of a function.

Surface Integral

Integral of vector field A over surface S.

Flux of A

Surface integral representing flow through surface S.

Unit Normal Vector

Vector perpendicular to surface, indicating direction.

Projected Area

Area of surface S projected onto coordinate planes.

Volume Integral

Integral over a volume V enclosed by a surface.

Differential Area Element

dS represents an infinitesimal area on surface S.

Continuous Derivative

Derivative exists and is continuous over specified interval.

Closed Curve

Curve that does not intersect itself, forms a loop.

Limits of Sums

Definition of integrals based on Riemann sums.

Arbitrary Constant Vector

Constant vector c independent of variable u.

Integration Notation

Symbolic representation of integrals, e.g., ∫.