Mathematics

Analysis 2

Module code: G5095
Level 5
15 credits in autumn teaching
Teaching method: Lecture, Workshop
Assessment modes: Coursework, Unseen examination

Topics covered:

  • Power series, radius of convergence, Taylor series and Taylor's
    formula, applications and examples.
  • Upper and lower sums, the Riemann integral, basic properties of the Riemann
    integral, primitive; fundamental theorem of calculus, integration by parts and
    change of variabl, applications and examples.
  • Pointwise and uniform convergence of sequences and series of functions,
    interchange of differentiation or integration and limit for sequences and series,
    differentiation and integration of power series term by term, applications and
    examples.

Module learning outcomes

  • understand the theory of Riemann integral and apply this to examples;
  • understand and apply the concept of uniform convergence for sequences and series of functions;
  • understand and apply fundamental theorem of calculus, integration by parts, and change of variable