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Establishment of New Special Deductions from Gauss Divergence Theorem in a Vector Field

Ikenna Kamalu, S.O. Opebiyi, P. Oghome

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Abstract

Stokes proved that it is possible to express a surface integral in terms of a line integral round the boundary curve.Just as Green employed Stokes theorem in a vector field to establish another theorem (deduction), Gauss divergence theorem is employed herein to establish new special deductions i.e. equations (10), (12) and (13). The equations are tested with real live problems and the responses are positive.

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Stokes proved that it is possible to express a surface integral in terms of a line integral round the boundary curve.Just as Green employed Stokes theorem in a vector field to establish another theorem (deduction), Gauss divergence theorem is employed herein to establish new special deductions i.e. equations (10), (12) and (13). The equations are tested with real live problems and the responses are positive.

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Available abstract

Stokes proved that it is possible to express a surface integral in terms of a line integral round the boundary curve.Just as Green employed Stokes theorem in a vector field to establish another theorem (deduction), Gauss divergence theorem is employed herein to establish new special deductions i.e. equations (10), (12) and (13). The equations are tested with real live problems and the responses are positive.

Key concepts: Divergence theorem, Kelvin–Stokes theorem, Green's theorem, Mathematics, Surface integral, Line integral, Gauss, Mathematical analysis

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