REAL ANALYSIS (4 Credits)

Learning Outcomes:

On successful completion of this course, student will be able to: explain the properties of real numbers, supremum, infimum and continuous functions; calculate limit of sequences and functions ,differential and Riemann Integral; apply theorems and convergence test of sequences and series; analyze if subsets of a metric space are open, closed, connected, bounded.

Topics:

1. Preliminaries;
2. The Real Numbers;
3. Sequences;
4. Limits;
5. Continuous Functions;
6. Differentiation;
7. The Riemann Integral;
8. Sequences of Functions;
9. Infinite Series;
10. Topology.