Analysis I
Math 554/703 I

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

Table of Contents

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 (updated)   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. 

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

Lecture Set 9a Upper and Lower Riemann Sums & Integrals, and Riemann integrability 

Lecture Set 9b  Intermediate Value Thm for Integrals, Fundamental Theorems of Calculus 

This page maintained by Robert Sharpley (sharpley@math.sc.edu) and last updated Nov. 2, 2003.  This page ©2003-2004, The Board of Trustees of the University of South Carolina.  URL: http://www.,math.sc.edu/~sharpley/math554