Plan for the rest of the semester

There are now 5 weeks left of regular lecturing (the plan is to have 2 weeks of recap after that).

The important topics left are the study of Fourier series (ca. 2 weeks) and some differential calculus including especially the inverse function theorem (ca. 2 weeks). I will cover the former based on Riemann integration, which is assumed known from before (as opposed to Lebesgue integration, as in Spaces). I will cover the latter based on an elementary (coordinate based) theory of derivation in Euclidean spaces ie R^n (as opposed to differentiation of functions between general normed vector spaces in which no choice of basis has been made).

Thus the choice is to consolidate known techniques rather than to introduce new abstractions. You will learn Lebesgue measure later, in MAT3400. The coordinate free approach to differentiation (which is really pretty) can be learned as a self study.

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