Postgraduate Course: MIGSAA Advanced PDE 1 (MATH12006)
|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 Elliptic and Parabolic Equations. Furthermore we will study the basic functions space needed for the analysis of partial differential equations.
i. Holder and Lp spaces, Arzela-Ascoli, Divergence Theorem and Gronwall's inequality.
ii. Laplaces equation, Harmonic functions and basic properties, Fundamental solutions.
iii. Sobolev Spaces and their properties, Schwartz space and the Fourier Transform.
iv. Elliptic equations: Dirichlet problem, Lax-Milgram, Fredholm Alternative, Interior and boundary regularity.
v. Parabolic equations: Heat equation, general second order
equations and weak solutions. Galerkin approximation.
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 foundational function spaces used in
the study of basic partial differential equations.
ii. Familiarity with Elliptic and Parabolic Partial Differential
Equations and their properties.
iii. Concrete understanding of basic concepts and tools needed to analyse Elliptic and Parabolic Differential Equations rigorously.
|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