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MA20218: Analysis 2A

Follow this link for further information on academic years Academic Year: 2016/7
Further information on owning departmentsOwning Department/School: Department of Mathematical Sciences
Further information on credits Credits: 6      [equivalent to 12 CATS credits]
Further information on notional study hours Notional Study Hours: 120
Further information on unit levels Level: Intermediate (FHEQ level 5)
Further information on teaching periods Period:
Semester 1
Further information on unit assessment Assessment Summary: EX 100%
Further information on unit assessment Assessment Detail:
  • Examination (EX 100%)
Further information on supplementary assessment Supplementary Assessment:
MA20218 Mandatory extra work (where allowed by programme regulations)
Further information on requisites Requisites:
Before taking this module you must take MA10207 AND take MA10209 AND take MA10210
Further information on descriptions Description: Aims:
To extend the notions of continuity and limit from R to Rn, normed spaces and metric spaces, and develop some topology in these spaces. To study sequences of functions and their relation with integration and power series.

Learning Outcomes:
After taking this unit students should be able to:
* state definitions and theorems in real analysis and present proofs of the main theorems
* construct their own proofs of simple unseen results and of simple propositions
* present mathematical arguments in a precise, lucid and grammatical fashion
* apply definitions and theorems to simple examples
* carry out computations with integrals and power series
* manipulate sequences and limits in Rn, normed spaces and metric spaces.

Skills:
Numeracy T/F A
Problem Solving T/F A
Spoken and Written Communication F (in tutorials and on problem sheets).

Content:
Sequences of functions, uniform convergence. Integrals and limits, differentiating under the integral.
Complex differentiation, real and complex power series, Weierstrass M-test, differentiation and integration of power series, exp, log and trig functions, Euler's formula.
Real and complex normed vector spaces, L2 and uniform norm, operator norm
Metric spaces, sequences, convergence, completeness. Open, closed and bounded sets, neighbourhoods; limits and continuity, characterisations via sequences and open sets.
Topology on Rn: Bolzano-Weierstrass, Heine-Borel, and Weierstrass theorems. Decreasing sets, Lipschitz maps and uniform continuity, Contraction mapping theorem.
Further information on programme availabilityProgramme availability:

MA20218 is Compulsory on the following programmes:

Department of Computer Science
  • USCM-AFB20 : BSc(Hons) Computer Science and Mathematics (Year 2)
  • USCM-AAB20 : BSc(Hons) Computer Science and Mathematics with Study year abroad (Year 2)
  • USCM-AKB20 : BSc(Hons) Computer Science and Mathematics with Year long work placement (Year 2)
  • USCM-AFM14 : MComp(Hons) Computer Science and Mathematics (Year 2)
  • USCM-AAM14 : MComp(Hons) Computer Science and Mathematics with Study year abroad (Year 2)
  • USCM-AKM14 : MComp(Hons) Computer Science and Mathematics with Year long work placement (Year 2)
Department of Mathematical Sciences Department of Physics

MA20218 is Optional on the following programmes:

Department of Economics

Notes: