Analysis I
Math 554/703 I

Professor Robert Sharpley
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 

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