MAU34216 Advanced partial differential equations

Module Code	MAU34216
Module Title	Advanced partial differential equations
Semester taught	Semester 2
ECTS Credits	5
Module Lecturer	Prof. Paschalis Karageorgis
Module Prerequisites	MAU34210 Linear partial differential equations OR MAU34215 Introduction to partial differential equations

This module is examined in a 2-hour examination at the end of Semester 2.
Continuous assessment contributes 10% towards the overall mark.
The module is passed if the overall mark for the module is 40% or more. If the overall mark for the module is less than 40% and there is no possibility of compensation, the module will be reassessed as follows:
1) A failed exam in combination with passed continuous assessment will be reassessed by an exam in the supplemental session;
2) The combination of a failed exam and failed continuous assessment is reassessed by the supplemental exam;
3) A failed continuous assessment in combination with a passed exam will be reassessed by one or more summer assignments in advance of the supplemental session.
Capping of reassessments applies to Theoretical Physics (TR035) students enrolled in this module. See full text at https://www.tcd.ie/teaching-learning/academic-affairs/ug-prog-award-regs/derogations/by-school.php Select the year and scroll to the School of Physics.

11 weeks of teaching with 3 lectures per week.

Calculus of variations: functional, variation, extremals, Euler-Lagrange equation, Beltrami identity, brachistochrone, catenary, natural boundary conditions, isoperimetric constraints.
Conservation laws: transport equation, Burgers' equation, method of characteristics, weak solutions, Rankine-Hugoniot jump condition, Oleinik entropy condition.
Wave equation: Spherical means, Euler-Poisson-Darboux equation, Kirchhoff's formula in 3 dimensions, Poisson's formula in 2 dimensions, energy method, finite speed of propagation, domain of dependence.