Requirements/prerequisites: prerequisite: MA342E
Duration: Hilary term, 10 weeks

Number of lectures per week: 3 lectures including tutorials per week

Assessment:

End-of-year Examination: This module will be examined jointly with MA342E in a 3-hour examination in Trinity term, except that those taking just one of the two modules will have a 2 hour examination. However there will be separate results for MA342E and MA342F.

Description: This module will meet at the Dublin Institute for Advanced Studies, 10 Burlington Road, Dublin 4. Most likely the lectures will be scheduled on Tuesday afternoons (and clash with MA4446).

Distributions (or generalised functions). Definition and basic properties. Examples. Antiderivative. Convergence. Regulatisation and approximations of delta. Fourier transform and convolutions. The space S and tempered distributions. Singular solutions of differential equations and Green's functions.

References.
W. Rudin, Functional Analysis, McGraw-Hill (1973) - part II
H. Bremermann, Distributions, complex variables, and Fourier transforms, Addison-Wesley (1965).

Jul 6, 2010