INTRODUCTION TO REAL ANALYSIS

This course is an introduction to the basic techniques of real analysis within the context of single-variable calculus. Topics include a review of the real number system and the completeness axiom, limits of sequences and the algebra of limits; limits of functions and the algebra of limits; continuous functions and their algebraic properties; the intermediate value theorem; differentiable functions and the algebra of differentiation; the mean value theorem and Taylor's theorem; the Riemann integral; and the fundamental theorems of calculus.