Mathematics

Analysis 1

Module code: G5085
Level 4
15 credits in spring teaching
Teaching method: Lecture, Workshop
Assessment modes: Coursework, Unseen examination

In this module, the topics you will cover will include:

  • Sequences; convergence, Cauchy sequences, subsequences
  • Series; proof and application of convergence/divergence criteria
  • Limits of functions; definitions, examples and properties
  • Continuity; intermediate value theorem, uniform continuity
  • Differentiability; definition, proofs of mean value theorems.

Module learning outcomes

  • Demonstrate knowledge of the definitions and the elementary properties of continuous and differentiable functions of one real variable.
  • Appreciate rigorous arguments in calculus and be able to deploy them in solving problems in analysis.
  • Understand the main theorems and their proofs on continuous and differentiable functions on the real line.
  • Understand the concepts and definitions of convergent sequences and series, provide and explain examples and counterexamples.