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Monthly Archives: December 2012
Basic Analysis: Uniform Convergence
Once again, let be a subset. Suppose we now have a sequence of functions , where n = 1, 2, 3, … , such that for each x in D, the sequence converges to some real value. We’ll denote this value by f(x), thus … Continue reading
Posted in Notes
Tagged advanced, analysis, continuity, convergence, pointwise convergence, series, uniform convergence
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Basic Analysis: Differentiation (2)
Finding Extremum Points One of the most common applications of differentiation is in finding all local maximum and minimum points. Definition. We say f(x) has a local maximum (resp. minimum) at x=a, if there is an open interval (b, c) containing a, such … Continue reading
Posted in Notes
Tagged advanced, analysis, compact sets, differentiation, mean value theorem, rolle's theorem
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