Postgraduate Course: MIGS: Advanced PDE 2 (MATH12026)
|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 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)
||Other requirements|| None
Course Delivery Information
|Academic year 2021/22, 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
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.
|Graduate Attributes and Skills
|Course organiser||Prof Benedict Leimkuhler
|Course secretary||Mrs Katy Cameron
Tel: (0131 6)50 5085