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Why should curve integral and surface integral be separated by multiple integral in Mathematical Analysis (third edition) (second volume) edited by East China Normal University?
In order to better connect before and after, the curve integral is converted into double integral to calculate, which leads to a Green's formula, that is, the closed curve integral is converted into double integral in the region, and the surface integral is converted into triple integral to calculate, which leads to a Gaussian formula, that is, the closed curve region is divided into triple integral in the volume, and the double integral and the triple integral are related. Triple integral can be transformed into the product of successive (repeated) single integral and double integral. In fact, Chen Shengshen, a master of differential geometry, is definitely a great task master. Chen Lao discussed in detail what is the basic problem of calculus and why. The four formulas of Leiden-Leibniz, Green, Gauss and Stokes are actually a formula expressed by external differential, and the essence is the same.