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...Calculus on manifolds introduction to multivariable functions dierentiation directional deriva tives implicit and inverse function theorems review of integration partition unity lectures change variables applications dieomorphisms in n dimensional space explaining the determinant volume a parallelopiped integrating scalar multilinear algebra alternating tensors wedge product tangent vectors dierential forms operator grad curl div pullback over parametrized orientability orientable stokes theorem classical versions proofs above...