Stoke's Theorem: The value of the line integral along a simple, closed, piecewise-smooth, positively oriented curve C, is related to the area of the surface C encloses. F must have continuous partial derivatives on a region in ℝ³. Stoke's theorem can be used to find the magnetic field strength a given distance from a straight wire (Ampere's law). C would represent the circumference of an imaginary circle at a constant distance around the wire, and the right side of the equation would be…
Green's Theorem: The value of the integral along a simple, closed, positively oriented, and piecewise-smooth curve C is related to the area it encloses by this equation. For this to be true, P and Q must also have continuous partial derivatives. Green's Theorem is a special case of Stoke's Theorem and can be used to calculate the areas of complicated shapes i.e. lakes, bacteria cultures,... Planimeters are devices that engineers frequently use to find areas and they are built using the…
Online Calculation on STATISTICS Basic and advanced Statistics Mathematics
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