DCU Home | Our Courses | Loop | Registry | Library | Search DCU

Module Specifications..

Current Academic Year 2023 - 2024

Please note that this information is subject to change.

Module Title Analysis 2
Module Code MS231
School School of Mathematical Sciences
Module Co-ordinatorSemester 1: Martin Friesen
Semester 2: Martin Friesen
Autumn: Martin Friesen
Module TeachersJacobus Sanders
Martin Friesen
NFQ level 8 Credit Rating 7.5
Pre-requisite None
Co-requisite None
Compatibles None
Incompatibles None
Repeat examination

This module covers the essential parts of classical and modern Analysis as required for future courses on Probability and Statistics, Differential Equations, and Partial Differential Equations. The topics covered by this course include but are not restricted to: Metric spaces, Continuous functions, Convolutions, and Fourier Analysis

Learning Outcomes

1. Learn important mathematical concepts as used in subsequent courses in Probability Theory, Stochastic Processes, Differential Equations, and Partial Differential Equations
2. Apply theoretical concepts to particular modelling and computational problems related with real-world applications

Workload Full-time hours per semester
Type Hours Description
Lecture36Students will attend lectures where new material will be presented and explained. Also attention will be drawn to various supporting material and tutorials as the course progresses.
Tutorial12Students will show their solutions to homework questions and will receive help with and feed-back on these solutions.
Independent Study78Corresponding to each lecture students will devote approximately one additional hour of independent study to the material discussed in that lecture or to work on support material when attention is drawn to such in lectures. Before each tutorial students will devote approximately three and a half hours to solving homework problems which are to be discussed in that tutorial.
Total Workload: 126

All module information is indicative and subject to change. For further information,students are advised to refer to the University's Marks and Standards and Programme Specific Regulations at: http://www.dcu.ie/registry/examinations/index.shtml

Indicative Content and Learning Activities

Metric and Normed spaces
metrics, norms, inner products, convergence, completeness, open and closed sets, compactness

Continuous functions
completeness, pointwise and uniform convergence, Arzela-Ascoli Theorem, Hoelder and Lipschitz continuity, Banachs fixed-point theorem, applications

elementary properties, Dirac approximation and mollifiers, (applications)

Harmonic Analysis
periodic functions, Fourier coefficients, representation by Fourier series, Plancherel identity, abstract Fourier decomposition in Hilbert spaces

Integration theory
Riemann-Stieltjes integration, integration of distribution functions, Young integral

Assessment Breakdown
Continuous Assessment20% Examination Weight80%
Course Work Breakdown
TypeDescription% of totalAssessment Date
Written Examn/a20%n/a
Reassessment Requirement Type
Resit arrangements are explained by the following categories;
1 = A resit is available for all components of the module
2 = No resit is available for 100% continuous assessment module
3 = No resit is available for the continuous assessment component
This module is category 3
Indicative Reading List

    Other Resources

    Programme or List of Programmes
    ACMBSc in Actuarial Mathematics
    BSSAStudy Abroad (DCU Business School)
    BSSAOStudy Abroad (DCU Business School)
    CAFMCommon Entry, Actuarial, Financial Maths
    HMSAStudy Abroad (Humanities & Soc Science)
    HMSAOStudy Abroad (Humanities & Soc Science)
    IESAStudy Abroad (Institute of Education)
    IESAOStudy Abroad (Institute of Education)
    SHSAStudy Abroad (Science & Health)
    SHSAOStudy Abroad (Science & Health)

    My DCU | Loop | Disclaimer | Privacy Statement