Math 522, Analysis II
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Syllabus:[pdf] Schedule 1st week (Sept 8-10) Convergence of functional sequences and series, uniform convergence. 2nd week (Sept 13-17) Properties of uniform convergence (pp. 147-153). 3rd week (Sept 20-25) Power series 4th week (Sept 27-Oct 1) Elementary functions 5th week (Oct 4-Oct 8) Stone-Weierstrass theorem, equicontinuity. 6th week (Oct 11-15) Midterm 1, equicontituity. 7th week (Oct 18-22) Compactness, criteria. 8th week (Oct 25-29) Compactness in C(E), contraction principle and applications. 9th week (Nov 1-5) Contraction principle, Fourier series 10th week (Nov 8-12) Fourier series 11th week (Nov 15-19) Midterm 2, Fourier series 12th week (Nov 22-24) Fourier series, Wiener algebra 13th week (Nov 29- Dec 3) Wiener algebra, multi-variable calculus 14th week (Dec 6-10) Multi-variable calculus, the inverse function theorem 15th week (Dec 13-15) The inverse function theorem, applications |
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