WebIn many respects, real analysis is a subject that has to deal with pathological issues: things like spaces that are path-connected but not connected, functions that are continuous everywhere but differentiable nowhere, metric spaces that are not complete, etc. This often makes it hard to visualize some of the concepts. WebJan 15, 2015 · To put it simply: I have seen many problem books in real analysis (also on this website), but the exercises they propose seem quite standardized. ... This is a very …
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WebIn a recent post I asked about an epsilon delta proof for an Analysis question. Before posting it I searched for similar questions and their proofs on google but all I found were computational style problems. If anybody is aware of a good resource for problems and solutions of upper-undergraduate level real Analysis problems it would be greatly … WebSep 11, 2008 · Complex analysis is the study of holomorphic functions. Exercise: If f:U-->R2 is a differentiable function at p, with (R-linear) derivative L, where z=x+iy, then ∂f/∂x and ∂f/∂y are both defined at p, and L is the linear function with matrix [ ∂f/∂x ∂f/∂y ], where both entries are regarded as column vectors. WebFeb 25, 2016 · Introductory real analysis quite often explores how badly behaved a function can be, and such pathological functions are often unfamiliar and counterintuitive. For example: Thomae's function is continuous at precisely the irrational numbers; there are … knowledgeworks innovative