Postgraduate Course: MIGS: Advanced PDE 1 (MATH12027)
|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 2020/21, 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 foundational function spaces used in the study of basic partial differential equations.
- Demonstrate familiarity with Elliptic and Parabolic Partial Differential Equations and their properties.
- Demonstrate a concrete understanding of basic concepts and tools needed to analyse Elliptic and Parabolic Differential Equations rigorously.
|Graduate Attributes and Skills
|Course organiser||Prof Benedict Leimkuhler
|Course secretary||Mrs Katy Cameron
Tel: (0131 6)50 5085