>>12574472Some mexican mathematician gives analysis courses at my uni and she had a detailed guide in her web page, it goes covers pretty much most of undergrad analysis.
>Metric spaces (normed spaces, function spaces, metric subspaces & isometries)>Continuity (open and closed sets, sequences and the likes)>Compacity (compact sets, heine-borel theorem, semicontinuity, uniform continuity)>Completeness (complete metric spaces, complete function spaces, series in banach spaces)>Banach's fixed point theorem ( Banach's theorem, Integral equations,...)>Compacity in function spaces (totally bounded sets, Arzela-Ascoli theorem, existence of the surve of minimum length)>Approximation theorems ( Weierstrass's theorem, the Stone-Weierstrass theorem)>Derivability ( the derivative, mean value theorem, differentiability criteria, diffyQs, partial diffiQs, higher order diffyQs, linear homeomorfisms, the implicit function theorem)>Integral of a continuous function with compact support ( unicity, invariance, substitution theorem)>Lebesgue integration (integral of a semicontinuous function, measure of a set, integrable sets)>Integration theorems (Fubini, convergence, radial functions)>Lebesgue spaces ( Measureability, Lp() spaces, nulity and compacity crriteria)>Hilbert spaces >Sobolev spaces>Sobolev embeddingsIs the material any good is is it dubious?
