Analysis I
Math 554, Spring 1996

Professor Robert Sharpley
`sharpley@math.sc.edu`Department of Mathematics
University of South Carolina

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Table of Contents

Math554 Info and Syllabus for Spring 1996

Lecture Set 1 (The Real Number System)

Lecture Set 2 (Induction, Sequences and Limits)

Lecture Set 3 (Properties of Limits, Cauchy sequences)

Lecture Set 4 (Open and Closed Sets)

Lecture Set 5 (Limits of Functions and Continuity)

Lecture Set 6 (Compactness, Heine-Borel, Extreme Value Thm, Uniform Continuity,... )

Lecture Set 7 (Connectedness, Intermediate Value Thm, Fixed Pt. Thm.; Compactness II)

Lecture Set 8 (Differentiation, Rolle's Thm., Mean Value Thm.)

Lecture Set 9 (The Riemann Integral and its properties, Intermediate Value Thm for Integrals, Fundamental Theorems of Calculus)

If you have any questions, please send e-mail to sharpley@math.sc.eduLectures last modified: 1 May. 1996