MAT 214E - Mathematics IV

Course Objectives

1. To teach the student the techniques and methods of Mathematical Analysis and to allow the student
to develop a certain level of proficiency in these methods.
2. To allow the student to be able to use these techniques and methods to reinforce an understanding of
learned calculus.

Course Description

Limits of Sequences, Bounded Sequences, Sets of Real Numbers, Bounded Functions, Limits of
Functions, Monotone Functions, Continuity, Properties of Continuous Functions, Uniform Continuity,
Definition of the Integral, Properties of the Integral, Necessary and Sufficient Conditions for Riemann
Integrability, Pointwise and Uniform Convergence, Sets and Functions in Rn, Differentiable Functions,
Implicit- and Inverse Function Theorems.