Tensor Analysis and the Calculus of Moving Surfaces: Lesson 2 - The Two Definitions of the Gradient Flashcards
evaluates to the same number in all coordinate systems
invariant
an increase or decrease in the magnitude of a property
gradient
a coordinate system that specifies each point uniquely in a plane by a pair of numerical coordinates, which are the signed distances to the point from two fixed perpendicular directed lines, measured in the same unit of length.
Cartesian coordinate system
a coordinate system on an affine space where each coordinate is an affine map to the number line
affine coordinate system
a coordinate system that uses straight lines
orthogonal affine coordinate system
affine non-orthogonal coordinate system (parallelogram)
helsinki coordinate system
an expression that works in all coordinate systems
a geometric expression! (tensor calculus)
