Real Analysis I

Catalog description

The core components of the course are sets and the real line, metric spaces, sequences and series of functions and the theory of differentiation and integration. After completing this course, students should be able to: (1) Explain and restate theorems and definitions in different contexts and as they apply to special cases in each of the four core components of the course. (2)Identify which theorems and definitions apply to various situations in each of the four core components of the course (3) Construct proofs in each of the four core components of the course. Use the theorems and techniques to solve problems in each of the four core components of the course. (4)Use the theorems and techniques to solve problems in each of the four core components of the course. The course is intended to provide students with a fuller understanding of the calculus, as well as prepare them for graduate school in mathematics and other disciplines requiring analytical and numerical solution of equations arising from mathematical modeling.