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3rd part of 3-semester course on Calculus and Real Analysis: A detailed introduction to abstract measure theory is followed by the study of abstract integration of real- and complex-valued measurable maps. Noteworthy theorems include dominated convergence, Fubini, and change of variables. L^p spaces are studied, including an introduction to convolution and Fourier transform. An introductory section on the integration over submanifolds of R^n culminates in the Gauss-Green Theorem.
Course Notes and Supplementary Material (PDF format)
|Course notes||v3 PDF (1.4M)||10/21/21|