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MA270 Analysis 3

Lecturer: Jose Rodrigo

Term(s): Term 1

Status for Mathematics students: Core for Maths

Commitment: 30 one-hour lectures plus assignments

Assessment: 85% by 2-hour examination, 15% coursework

Formal registration prerequisites: None

Assumed knowledge: Notions of convergence, and basic results for sequences, series, differentiation and integration from introductory analysis modules like MA141 Analysis 1 and MA139 Analysis 2; knowledge of vector spaces from MA150 Algebra 2

Useful background: Basic results about curves, surfaces and vector fields from MA144 Methods of Mathematical Modelling 2

Synergies: MA250 Introduction to Partial Differential Equations

Leads to: The following modules have this module listed as assumed knowledge or useful background:


  • Continuous Vector-Valued Functions
  • Some Linear Algebra
  • Differentiable Functions
  • Uniform convergence and applications
  • Convergence of sequences and series of functions
  • Introduction to complex valued functions

Objectives: By the end of the module the students should be able to:

  • Understand uniform and pointwise convergence of functions together with properties of the limit function
  • Study the continuity, differentiability and integral of the limit of a uniformly convergent sequence of functions
  • Study complex differentiability (Cauchy-Riemann equations) and complex power series
  • Study contour integrals: Cauchy's integral formulas and applications.

Books: There is no recommended textbook for the course. A complete set of lecture notes will be provided.


Additional Resources