Postgraduate Course: MIGS: Elliptic and Parabolic PDEs (MATH11210)

Course Outline
School	School of Mathematics	College	College of Science and Engineering
Credit level (Normal year taken)	SCQF Level 11 (Postgraduate)	Availability	Not available to visiting students
SCQF Credits	15	ECTS Credits	7.5
Summary	This course covers parabolic and elliptic equations. Useful methods to study solutions such as travelling wave and similarity solutions are developed and nonexistence and multiplicity results for solutions of nonlinear elliptic problems are studied by a variety of methods. Different concepts and tools are developed such as maximum principles, blow up and comparison theorems. One striking result that will be proved is that positive solutions of autonomous semilinear elliptic problems on a ball must be radially symmetric. The remaining lectures are on variational formulation of elliptic PDEs. The material includes an introduction to the Sobolev function spaces, Sobolev embedding and trace theorems. - Analysis of parabolic and elliptic PDEs (including existence, uniqueness, maximum principles, energy estimates, monotone iteration, regularity, eigenfunctions) - Variational theory of PDEs - Sobolev embeddings and trace theorems
Course description	The aim is to learn new things to get a broad education in the area as a basis for a wide range of PhD projects and for post-PhD employment. Unless otherwise noted, the details of the content of these courses can be found on the Scottish Mathematical Sciences Training Centre web site www.smstc.ac.uk

Entry Requirements (not applicable to Visiting Students)
Pre-requisites		Co-requisites
Prohibited Combinations		Other requirements	None

Course Delivery Information

Academic year 2022/23, Not available to visiting students (SS1)		Quota: None
Course Start	Semester 2
Timetable	Timetable
Learning and Teaching activities (Further Info)	Total Hours: 150 ( Lecture Hours 20, Programme Level Learning and Teaching Hours 3, Directed Learning and Independent Learning Hours 127 )
Assessment (Further Info)	Written Exam 0 %, Coursework 100 %, Practical Exam 0 %
Additional Information (Assessment)	100% coursework
Feedback	Not entered
No Exam Information

Learning Outcomes
On completion of this course, the student will be able to: Thoroughly understand the analytical concepts and methods developed in the uniqueness and existence theorems for solutions of PDEs. Apply finite element approximations to solve PDEs.