 Beautiful Equations Explained… Green’s Theorem

Understanding maths formulas can be difficult, and when it comes to calculus this is definitely the rule rather than the exception. We want you to appreciate and enjoy all our equations, and so here is all you need to know about one of the most daunting of equations: Green’s theorem.

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This equation represents the relationship between a line integral around a simple closed curve C and a double integral over the plane D bounded by C. It is known as Green’s theorem.

This theorem is used to evaluate line integrals of functions of (x,y), such as L and M in the above equation, when defined over D, the region enclosed by the simple closed curve with anti-clockwise orientation C. As well as being helpful in proving other mathematical concepts, its applications in physics are broad, for example in modelling the flow of fluids and electromagnetism.

George Green was a self-taught English mathematical physicist who was one of the first physicists to use mathematical theory in the research of electricity and magnetism. While it was Reimann who provided the first proof of this theorem, an essay Green wrote in 1828 introduced, among other things, a similar theorem as well as the still widely used Green’s functions. Many find his humble beginnings inspiring, the son of a baker who received just one year of formal education; his work formed the foundation for many of the famous scientists, such as James Maxwell, who followed.