Study Guide for Real Analysis I

1.  Definitions of upper and lower bounds, sup and inf; the limit of a sequence and the limit of a function; continuity; Riemann integral.

2.  The ideas in major theorems and properties:  Completeness Axiom, Bolzano-Weirstrass theorem, the relationship between sequence limits and function limits, relationship between differentiability and continuity, the Easy Integrability theorem and why it is "easy", the Fundamental theorem of Calculus – real analysis version.

3.  Be able to use the definition of limit of a sequence and limit of a function to prove limits using an epsilon proof. 

4.  Be able to read a simple analysis proof involving limits and explain what is happening.  Examples include the Squeeze theorem for sequences or functions, the sum or product limit theorems for sequences or functions.