The n-dimensional Euclidean space RN, real valued functions on RN: limits, continuity and differentiability, the chain rule and the directional derivative, the gradient and its properties, implicit functions and inverse mappings, extremal problems and Lagrange multipliers, multiple integration: definition, applications and techniques, the Jacobian and change of variables. Vector analysis: line integrals and surface integrals, GREEN's, stokes' and Gauss' formulas.

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