Module Specifications..
Current Academic Year 2023  2024
Please note that this information is subject to change.
 
Repeat examination 

Description 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 realworld applications  
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, ArzelaAscoli Theorem, Hoelder and Lipschitz continuity, Banachs fixedpoint theorem, applications Convolutions 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 RiemannStieltjes integration, integration of distribution functions, Young integral  
 
Indicative Reading List  
Other Resources None  
Programme or List of Programmes  
Archives: 
