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DEGREE REGULATIONS & PROGRAMMES OF STUDY 2015/2016

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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 2015/16, 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
i. Thorough understanding of the basic properties of Hyperbolic
Partial Differential Equations.
ii. Familiarity with Schrodinger Equations and Strictarz inequalities
iii. Concrete understanding of basic concepts and tools needed to
analysis 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:
Course secretaryMiss Keira Farrell
Tel: (0131 6)51 5987
Email:
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