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 2017/18, 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.
|
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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