Integral Geometry and Fields: Theorematic Proofs and Numerical Models

This work is divided into Divergence Theorem at Manifold, Green Theorem at Manifold (Difference, corresponding to traditional Green Theorem) and Curl Theorem at Manifold (Difference, corresponding to traditional Stokes Theorem) three parts; From different perspectives of three new typical integral theorems, this work demonstrates that base on individualized geometric object (Manifold)coordinates, through matrixing operations, realize new formular conjunctions between different typical integrals; and provides corresponding numerical models; New integral formular demonstrations and numerical models indicate: Base on individualized geometric object coordinates, through unified standardized_concise_matrixing integral operations, science explorers can obtain analytic integral values or float integral values in discretional precision of discretional complicated geometric objects (Manifold; Especially point irregular, asymmetrical geometric shapes in 2-Dimensional and 3-Dimensional Euclidean space of real world); New typical numerical modelings possess vast mathematical, physical, engineering applicational field, involve that in 2-Dimensional and 3-Dimensional Euclidean space of real world, exact integral calculation of vector field and scalar field about discretional complicated geometric objects and their boundary regions,and then realize direct triple connection between calculus, topology and physical engineering calculation.