MAU34210 Linear partial differential equations

Module Code	MAU34210
Module Title	Linear partial differential equations
Semester taught	Semester 2
ECTS Credits	5
Module Lecturer	Dr. Nicholas Aidoo
Module Prerequisites	MAU11404 Techniques in theoretical physics OR MAU23205 Ordinary 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.
Any failed components are reassessed, if necessary, by an exam in the reassessment session.
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.

Explicit methods: separation of variables, method of characteristics, quasilinear equations, fully nonlinear equations, second-order PDE.
Wave equation: d'Alembert's formula, conservation of energy, reflection method, uniqueness of solutions, inhomogeneous equation.
Heat equation: heat kernel, maximum principle, uniqueness of bounded solutions, stability of solutions, inhomogeneous equation.
Laplace equation: maximum principle, rotational invariance, Dirichlet problem for rectangles and disks, Poisson formula.