Postgraduate Course: MIGSAA Advanced PDE 2 (MATH12005)
|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
|Summary||The course will cover the basic techniques and methods needed for a rigorous understanding of Hyperbolic, Schrodinger and Hamiltonian-Jacobi equations.
i. Heat and Schrodinger equations: Initial value problem and
generalised solutions. Nonlinear Schrodinger Equation and
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)
||Other requirements|| None
Course Delivery Information
|Academic year 2017/18, Not available to visiting students (SS1)
|Learning and Teaching activities (Further Info)
Lecture Hours 20,
Programme Level Learning and Teaching Hours 3,
Directed Learning and Independent Learning Hours
|Assessment (Further Info)
|Additional Information (Assessment)
|No Exam Information
| 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
|Graduate Attributes and Skills
||*Only students of the MIGSAA CDT may take this course*
|Course organiser||Prof Jim Wright
Tel: (0131 6)50 8570
|Course secretary||Ms Isabelle Hanlon
Tel: (0131 6)50 5955