Calculus on Manifolds

Thus the Divergence Theorem states that, under the given conditions, the flux of F across the boundary surface of E is equal to the triple integral of the divergence of F over

The idea of the above proof can be applied to the proof of Stoke’s Theorem for general cases... One can show that the Stoke’s theorem holds for any k-form and for any k-chains on R

The motivation to study the fundamental theorem is probably to compute inte- gration?. We have the following properties that follows directly from definition of

As in the proof of Green’s Theorem, we prove the Divergence Theorem for more general regions by pasting smaller regions together along common faces... Thus, when we add the

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Topics include Inverse Function Theorem, Implicit Function Theorem, Integrable Functions, Fubini’s Theorem, Partitions of Unity, Change of Variable, Fields and Forms,

參考書目 Elementary Topics in Differential Geometry (Undergraduate Texts in Mathematics), J. Foundations of Differentiable Manifolds and Lie Groups (Graduate Texts in

spaces, smooth manifolds, syplectic forms on smooth manifolds and Hamiltonian actions.. 教學目標 Provide a