Analysis I
Math 554, Spring 1996

Professor Robert Sharpley
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
    Lectures last modified: 1 May. 1996