math247 calculus iii advanced level felix zhou winter 2019 university of waterloo notes written from henry shum s lectures 1 contents 1 euclidean space 7 1 1 denitions 7 1 ...
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...Math calculus iii advanced level felix zhou winter university of waterloo notes written from henry shum s lectures contents euclidean space denitions inequalities sequences n denition and convergence in r cauchy completeness bounded closed open sets examples more properties subsets compact nonexamples example heine borel theorem other compactness connected covers subcovers topological connectedness limits functions the limit a function continuity continuous on some combining polynomials compositions norm extreme value domains path convex uniform uniformly lipschitz derivatives single variable dierentiation directional partial results dierentiability conditions for an alternative view dierentiable sucient combinations are not necessary computing rules dierentiating mean gradients linear approximation higher order mixed taylor continuously critical points poynomials...