Course info

This course provides a gentle but rigorous introduction to real analysis.

Syllabus

- Monotonic and convergent sequences; related results such as sums, products and quotients of convergent sequences.
- Cauchy sequences and the equivalence of the Cauchy property and convergence
- Limits of functions
- Continuous and differentiable functions of one real variable; related results such as sums, products, quotients and compositions (chain rule).
- Boundedness of continuous functions on closed bounded intervals.
- Theorems related to continuous and differentiable functions, such as Rolle's Theorem and the Mean Value Theorem

On completion of the course students should be able to:
- understand principles underlying proofs of basic theorems concerning limits, continuity and differentiability.
- use correctly the quantifiers and other logical notation needed in analysis;
- reproduce elementary epsilon-delta arguments;