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DEGREE REGULATIONS & PROGRAMMES OF STUDY 2023/2024

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DRPS : Course Catalogue : School of Mathematics : Mathematics

Postgraduate Course: MIGSAA Advanced PDE 1 (MATH12006)

Course Outline
SchoolSchool of Mathematics CollegeCollege of Science and Engineering
Credit level (Normal year taken)SCQF Level 12 (Postgraduate) AvailabilityNot available to visiting students
SCQF Credits15 ECTS Credits7.5
SummaryThe 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) Coursework: 100%
Feedback Not entered
No Exam Information
Learning Outcomes
On completion of this course, the student will be able to:
  1. Thoroughly understand foundational function spaces used in the study of basic partial differential equations.
  2. Demonstrate familiarity with Elliptic and Parabolic Partial Differential Equations and their properties.
  3. Demonstrate a concrete understanding of basic concepts and tools needed to analyse Elliptic and Parabolic Differential Equations rigorously.
Reading List
None
Additional Information
Graduate Attributes and Skills Not entered
Special Arrangements *Only students of the MIGSAA CDT may take this course*
KeywordsNot entered
Contacts
Course organiserProf Jim Wright
Tel: (0131 6)50 8570
Email: J.R.Wright@ed.ac.uk
Course secretaryMs Isabelle Hanlon
Tel: (0131 6)50 5955
Email: i.hanlon@ed.ac.uk
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