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Partial differential equations (PDEs): Existence and uniqueness, regularity, boundary conditions, linear and non-linear operators, stability, soliton theory, integrable PDEs, conservation laws, qualitative dynamics.
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Green's formula for nonorientable manifolds
Usually in differential geometry one proves the Stokes theorem and then obtains divergence theorem and Green's formulas as corollaries. However, divergence theorem is also valid for nonorientable riem …