Remarks on Multiple Variable Calculus Fundamental Theorem and Stokes Formula
Yuwen Luo
Abstract
Yuwen Luo
Abstract
In this paper,the author stated fundamental theorem of multiple variable calculus.On the plane,the fundamental theorem is Green formula;on the space,fundamental theorem of calculus is Gauss formula;and on surface,it is Stokes formula which we have studied.Furthermore,after the concept exterior differentiation be introduced,these three formulas can be expressed as one formula,that is,generalized Stokes formula.Then it will help readers to understand more deeply the fundamental theorem of calculus in textbook.
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In this paper,the author stated fundamental theorem of multiple variable calculus.On the plane,the fundamental theorem is Green formula;on the space,fundamental theorem of calculus is Gauss formula;and on surface,it is Stokes formula which we have studied.Furthermore,after the concept exterior differentiation be introduced,these three formulas can be expressed as one formula,that is,generalized Stokes formula.Then it will help readers to understand more deeply the fundamental theorem of calculus in textbook.
Key concepts: Mathematics, Divergence theorem, Fundamental theorem of calculus, Fundamental theorem, Calculus (dental), Gauss, Variable (mathematics), Time-scale calculus