Postgraduate Course: MIGS: Advanced PDE 1 (MATH12027)

Course Outline
School	School of Mathematics	College	College of Science and Engineering
Credit level (Normal year taken)	SCQF Level 12 (Postgraduate)	Availability	Not available to visiting students
SCQF Credits	15	ECTS Credits	7.5
Summary	The course will cover the basic techniques and methods needed for a rigorous understanding of Elliptic and Parabolic Equations. Furthermore we will study the basic functions space needed for the analysis of partial differential equations.
Course description	i. Holder and Lp spaces, Arzela-Ascoli, Divergence Theorem and Gronwall's inequality. ii. Laplaces equation, Harmonic functions and basic properties, Fundamental solutions. iii. Sobolev Spaces and their properties, Schwartz space and the Fourier Transform. iv. Elliptic equations: Dirichlet problem, Lax-Milgram, Fredholm Alternative, Interior and boundary regularity. v. Parabolic equations: Heat equation, general second order equations and weak solutions. Galerkin approximation.

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

Course Delivery Information

Academic year 2023/24, Not available to visiting students (SS1)		Quota: None
Course Start	Semester 1
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 foundational function spaces used in the study of basic partial differential equations. Demonstrate familiarity with Elliptic and Parabolic Partial Differential Equations and their properties. Demonstrate a concrete understanding of basic concepts and tools needed to analyse Elliptic and Parabolic Differential Equations rigorously.