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...C multivariate calculus michael d alder november contents introduction optimisation the second derivative test constrained lagrangian multipliers fields and forms denitions galore integrating vector elds over curves independence of parametrisation conservative exact closed loops conservatism green s theorem motivation functions as transformations change variables in integration spin classical version dierential exterior for pure mathematicians return to relatively mundane more on stretching again stokes modern divergence fourier theory various kinds spaces function applications fiddly things odd even series dierentiation several partial equations diusion equation intuitive saying it algebra laplace...