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A contour map is a map illustrated with contour lines, for example a topographic map, which thus shows valleys and hills, and the steepness or gentleness of slopes. [4] The contour interval of a contour map is the difference in elevation between successive contour lines. [5] The gradient of the function is always perpendicular to the contour ...
On topographic maps, stream gradient can be easily approximated if the scale of the map and the contour intervals are known. Contour lines form a V-shape on the map, pointing upstream. By counting the number of lines that cross a certain segment of a stream, multiplying this by the contour interval, and dividing that quantity by the length of ...
The gradient is defined from Riesz representation theorem, and inner products in complex analysis involve conjugacy (the gradient of a function at some would be ′ ¯, and the complex inner product would attribute twice a conjugate to ′ in the vector field definition of a line integral).
The blue curves are the contour lines, that is, the regions on which the value of is constant. A red arrow originating at a point shows the direction of the negative gradient at that point. Note that the (negative) gradient at a point is orthogonal to the contour line going through that
Sergeant Chris D. Washington checking his Topographic map during a morning deer hunt in Kilgore, Texas A topographic map of Stowe, Vermont with contour lines Part of the same map in a perspective shaded relief view illustrating how the contour lines follow the terrain Sheet #535 (2013 version; second digital edition) of MTN50 Spanish National Topographic map series, covering Algete town (near ...
The gradient theorem states that if the vector field F is the gradient of some scalar-valued function (i.e., if F is conservative), then F is a path-independent vector field (i.e., the integral of F over some piecewise-differentiable curve is dependent only on end points). This theorem has a powerful converse:
Contour integration is closely related to the calculus of residues, [4] a method of complex analysis. One use for contour integrals is the evaluation of integrals along the real line that are not readily found by using only real variable methods. [5] Contour integration methods include:
Cant gradient is the amount by which cant is increased or decreased in a given length of track. The change in cant is required in order to connect a tangent track (no cant) to a curved track (with cant) through a transition curve. The rate of change of cant is used to determine the suitable cant gradient for a given design speed.