131B. Analysis. (4) Lecture, three hours; discussion, one hour. P/NP or letter grading. Requisites: courses 33B, 115A, 131A. Derivatives, Riemann integral, sequences and series of functions, power series, Fourier series.
The following schedule, with textbook sections and topics, is based on 26 lectures. The remaining classroom meetings are for leeway, reviews, and midterm exams. These are scheduled by the individual instructor. Often there are midterm exams about the beginning of fourth and eighth weeks of instruction, plus reviews for the final exam.
Section 14.8 is the proof of the Weierstrass Approximation Theorem. This should probably be left for the Honors Section.
This is rather difficult, but it introduces summation by parts. Using summation by parts to prove Dirichlet's Test (and hence the Alternating Series Test) is an alternative to Abel's Theorem.
This is a lot, but Sections 17.1 is just a review of linear transformations and 17.2 and 17.3 contain only one theorem.