Postgraduate Course: MIGSAA Advanced PDE 2 (MATH12005)

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 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: Thoroughly understand the basic properties of Hyperbolic Partial Differential Equations. Demonstrate familiarity with Schrodinger Equations and Streictarz inqualities Demonstrate concrete understanding of basic concepts and tools needed to analyse Hyperbolic, Schrodinger and Hamiltonian-Jacobi Equations rigorously.