The module provides an introduction to real analysis. It develops a rigorous approach to mathematical reason and proof and provides a strong underpinning to the knowledge and skills developed throughout the programme.
Sequences: Definition of a limit of a sequence; upper and lower bounds, supremum/infinum; properties of convergent sequences (e.g. uniqueness, linearity, product of sequences); monotone convergence theorem; subsequences; Bolzano-Weierstrass theorem.
Series: partial sums; convergence of a series; comparison test; absolute convergence; ratio test; alternating series test. Examples of common convergent and divergent series.
Continuity: functions; definition of continuity; properties of continuity (e.g. linearity, continuous preserve convergence); intermediate value theorem; continuous functions on bounded intervals.
Differentiation: differentiability; properties (e.g. linearity; product rule); chain rule; extreme value theorem; Rolle’s theorem; mean value theorem; continuous differentiability.
Lectures supported by tutorials and/or laboratory sessions including use of mathematical software
| Module Content & Assessment | |
|---|---|
| Assessment Breakdown | % |
| Formal Examination | 70 |
| Other Assessment(s) | 30 |