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...Mathematics wy dierentiable manifolds spring instructor prof michael thaddeus classroom oce lectures m w hours th am noon or by appointment home page www math columbia edu html text spivak calculus on westview press readings and much of the assign ments will be drawn from this it has been placed reserve in library course outline great nineteenth century theorems green gauss stokes line surface integrals were generalized twentieth to arbitrary dimensions domain integration is then a manifold while integrand dierential form we dene explore these concepts prove s theorem subsuming extending classical other words study multivariable higher may follow book fairly closely if time permits how forms are used that two not dierentiably equivalent computing their de rham cohomology groups prerequisites linear algebra v either topology modern analysis i students lacking must seek my explicit permission contacting me e mail at hthaddeus edui preferably telephone even more knock door any teaching as...