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Lecture

Green's Theorem: Demonstration and Applications

In course

MATH-203(b): Analysis III

Le cours étudie les concepts fondamentaux de l'analyse vectorielle et l'analyse de Fourier en vue de leur utilisation pour résoudre des problèmes pluridisciplinaires d'ingénierie scientifique. ...

Description

This lecture covers the demonstration of Green's Theorem, showing how each pig leaves the domain positively or negatively traversed, and how the theorem is oriented. The instructor explains the route of each pig, the orientation of the theorem, and provides examples and exercises to illustrate the applications of Green's Theorem.

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Instructors (2)

David Valentin Strütt

Maria Colombo

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Related concepts (30)

Green's theorem

In vector calculus, Green's theorem relates a line integral around a simple closed curve C to a double integral over the plane region D bounded by C. It is the two-dimensional special case of Stokes' theorem. Let C be a positively oriented, piecewise smooth, simple closed curve in a plane, and let D be the region bounded by C. If L and M are functions of (x, y) defined on an open region containing D and have continuous partial derivatives there, then where the path of integration along C is anticlockwise.

Stokes' theorem

Stokes' theorem, also known as the Kelvin–Stokes theorem after Lord Kelvin and George Stokes, the fundamental theorem for curls or simply the curl theorem, is a theorem in vector calculus on . Given a vector field, the theorem relates the integral of the curl of the vector field over some surface, to the line integral of the vector field around the boundary of the surface. The classical theorem of Stokes can be stated in one sentence: The line integral of a vector field over a loop is equal to the flux of its curl through the enclosed surface.

Divergence theorem

In vector calculus, the divergence theorem, also known as Gauss's theorem or Ostrogradsky's theorem, is a theorem which relates the flux of a vector field through a closed surface to the divergence of the field in the volume enclosed. More precisely, the divergence theorem states that the surface integral of a vector field over a closed surface, which is called the "flux" through the surface, is equal to the volume integral of the divergence over the region inside the surface.

Green's function

In mathematics, a Green's function is the impulse response of an inhomogeneous linear differential operator defined on a domain with specified initial conditions or boundary conditions. This means that if is the linear differential operator, then the Green's function is the solution of the equation , where is Dirac's delta function; the solution of the initial-value problem is the convolution ().

2016 St. Louis Cardinals season

The St. Louis Cardinals 2016 season was the 135th for the Major League Baseball (MLB) franchise in St. Louis, Missouri, the 125th season in the National League (NL), and the 11th at Busch Stadium III. They entered the season having won a major-league best 100 games, as three-time defending NL Central division champions, and with five consecutive playoff appearances. Forbes magazine estimated the value of the club to be $1.6 billion in 2016, making it the seventh-most valuable franchise in MLB.

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