Convergence of sequence of real numbers, real valued functions of real variables, differentiability, Taylor's theorem; Functions of several variables - limit, continuity, partial and directional derivatives, differentiability, chain rule, Taylor's theorem, inverse function theorem, implicit function theorem, maxima and minima, multiple integral, change of variables, Fubini's theorem; Metrics and norms - metric spaces, convergence in metric spaces, completeness, compactness, contraction mapping, Banach fixed point theorem; Sequences and series of functions, uniform convergence, equicontinuity, Ascoli's theorem, Weierstrass approximation theorem.
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