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.
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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.
|
Additional Information
| Graduate Attributes and Skills |
Not entered |
| Special Arrangements |
*Only students of the MIGSAA CDT may take this course* |
| Keywords | Not entered |
Contacts
| Course organiser | Prof Jim Wright
Tel: (0131 6)50 8570
Email: J.R.Wright@ed.ac.uk |
Course secretary | Ms Isabelle Hanlon
Tel: (0131 6)50 5955
Email: i.hanlon@ed.ac.uk |
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