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Introduction to Real Analysis Spring 2014 Lecture Notes

Introduction to real AnalysisSpring 2014 Lecture NotesVern I. PaulsenApril 22, 20142 Contents1 Sequences and Series of Behavior of Riemann Integrals with Limits .. Uniform Convergence and Continuity .. Uniform Convergence and Derivatives .. Series of Functions .. An Increasing Function with a Dense Set of Discontinuities . A Space Filling Curve .. Power Series .. Operations on Power Series .. Taylor Series .. Polynomial Approximation .. The Stone-Weierstrass Theorem .. Fourier Series .. Orthonormal Sets of Functions .. Fourier Series, Continued .. Equicontinuity and the Arzela-Ascoli Theorem .. 532 Multivariable Differential The Total Derivative.

Chapter 1 Sequences and Series of Functions In this chapter we introduce di erent notions of convergence for sequence and series of functions and then examine how integrals and derivatives be-

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