By James R. Munkres
From the preface:
"This ebook is meant as a textual content for a direction in research, on the senior or first-year graduate level.
A year-long path in actual research is a vital a part of the practise of any strength mathematician. For the 1st half one of these path, there's massive contract as to what the syllabus can be. usual issues contain: series and sequence, the topology of metric areas, and the by-product and the Riemannian indispensable for capabilities of a unmarried variable. there are various very good texts for the sort of path, together with books by means of Apostol, Rudin, Goldberg, and Royden, between others.
There isn't any such common contract as to what the syllabus of the second one 1/2 this type of direction might be. a part of the matter is that there are just too many issues that belong in this kind of direction for one with the intention to deal with all of them in the confines of a unmarried semester, at greater than a superficial level.
At M.I.T., we've got handled the matter by way of delivering self sustaining second-term classes in research. this sort of offers with the by-product and the Riemannian critical for features of numerous variables, via a remedy of differential varieties and an explanation of Stokes' theorem for manifolds in euclidean house. the current ebook has resulted from my years of training this direction. the opposite offers with the Lebesque vital in euclidean house and its purposes to Fourier analysis."
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Extra info for Analysis on Manifolds
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