THE UNIVERSITY of EDINBURGH

DEGREE REGULATIONS & PROGRAMMES OF STUDY 2023/2024

Timetable information in the Course Catalogue may be subject to change.

University Homepage
DRPS Homepage
DRPS Search
DRPS Contact
DRPS : Course Catalogue : School of Mathematics : Mathematics

Postgraduate Course: MIGSAA Advanced PDE 2 (MATH12005)

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 Hyperbolic, Schrodinger and Hamiltonian-Jacobi equations.
Course description i. Heat and Schrodinger equations: Initial value problem and
generalised solutions. Nonlinear Schrodinger Equation and
Strictarz estimates.
ii. Hyperbolic Equations: Continuity and existence of weak solutions,
iii. Variational techinques: Euler-Lagrange equations, existence of
minimisers and critical points.
iv. Nonvarational techiniques: Monotonicity methods, Fix point methods, Gradient flows.
v. Hamiltonion-Jacobi Equations: Definition and uniqueness of
viscosity solutions, control theory and the Hopf-Lax formula.
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 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) Coursework: 100%
Feedback Not entered
No Exam Information
Learning Outcomes
On completion of this course, the student will be able to:
  1. Thoroughly understand the basic properties of Hyperbolic Partial Differential Equations.
  2. Demonstrate familiarity with Schrodinger Equations and Streictarz inqualities
  3. Demonstrate concrete understanding of basic concepts and tools needed to analyse Hyperbolic, Schrodinger and Hamiltonian-Jacobi 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
Navigation
Help & Information
Home
Introduction
Glossary
Search DPTs and Courses
Regulations
Regulations
Degree Programmes
Introduction
Browse DPTs
Courses
Introduction
Humanities and Social Science
Science and Engineering
Medicine and Veterinary Medicine
Other Information
Combined Course Timetable
Prospectuses
Important Information