## Advanced CalculusSeths and functions; Continuity; Defferentiation; Integration; Series; Uniform convergence; Diferentiation of transformations; Aplications to geometry and analysis; Differential geometry and vector calculus; Numerical methods. |

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3-space absolutely convergent apply approximation assume bounded set choose closed curve compute continuous function converges uniformly coordinate Corollary corresponding critical point defined definition described differential forms direction divergence theorem divergent domain double integral dudv dx dy dxdy dxdydz dydz dzdx equivalent evaluate example Exercise exists finite number formula function F given graph Green's theorem grid illustration improper integral integrand interval inverse iterated integral Jacobian Let f Let f(x lim f(x limit line segment linear transformation mapping matrix maximum mean value theorem neighborhood notion obtain one-to-one open set orientation origin plane point p0 polynomial proof prove real numbers rectangle region sequence set function set of points Show simple smooth curve solution surface tangent tion unbounded uniformly continuous uniformly convergent variables vector write zero