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Part IV The Integral Theorems of Vector Calculus

In this chapter we introduce the main integral theorems in vector calculus, namely the theorems of Green, Gauss and Stokes. They have many applications within and outside mathematics. In particular they appear, possibly in a generalised form, in every “field theory” such as for instance gravitation or electro-magnetism (Maxwell equations). They can also be used to derive many other equations including the transport equation, the heat equation and the wave equation.