Undergraduate Course: Introduction to Partial Differential Equations (MATH10100)
|School||School of Mathematics
||College||College of Science and Engineering
|Credit level (Normal year taken)||SCQF Level 10 (Year 4 Undergraduate)
||Availability||Available to all students
|Summary||A rigorous introduction covering the basics of elliptic, hyperbolic, parabolic and dispersive PDEs. This is a pure maths course.
In academic year 2022-23 and later, MATH10101 Metric spaces is recommended for this course.
From Newton's laws of motion, to Maxwell's equations of electrodynamics and Einstein's equations of relativity, Partial Differential Equations (PDEs) provide a mathematical language to describe the physical world. It is perhaps less known that PDEs have been the driving force behind a large part of Analysis. The theory of Fourier series was first developed in an attempt to solve the wave and heat equations. A large part of the modern theory of Integration was developed in order to make rigorous sense of the integrals that appear in the formulas defining the Fourier coefficients. More recently, a stunning success of geometric PDEs was Perelman's proof of the Poincare conjecture, a long-standing problem in Topology, using the Ricci flow.
This course is a rigorous introduction to the wave, heat, and Laplace equations. These are the prototypes of hyperbolic, parabolic and elliptic equations, the three main types of PDEs. We'll investigate under what conditions solutions exist and whether or not they are unique. We'll also study some of the basic properties of solutions such as finite speed of propagation, the Huygens principle and conservation of energy. These properties originate in Physics but have powerful mathematical expressions that allow us to develop rigorously a large part of the theory of PDEs.
Entry Requirements (not applicable to Visiting Students)
|| Students MUST have passed:
Honours Analysis (MATH10068)
||Other requirements|| In academic year 2022-23 and later, MATH10101 Metric spaces is recommended for this course.
Information for Visiting Students
|High Demand Course?
Course Delivery Information
|Academic year 2020/21, Available to all students (SV1)
|Learning and Teaching activities (Further Info)
Lecture Hours 22,
Seminar/Tutorial Hours 5,
Summative Assessment Hours 2,
Programme Level Learning and Teaching Hours 2,
Directed Learning and Independent Learning Hours
|Assessment (Further Info)
|Additional Information (Assessment)
||Hours & Minutes
|Main Exam Diet S1 (December)||2:00|
On completion of this course, the student will be able to:
- Demonstrate an understanding of rigorous PDEs by proving unseen results using the methods of the course.
- Correctly state the main definitions and theorems in the course.
- Produce examples and counterexamples illustrating the mathematical concepts presented in the course
- Explain their reasoning about rigorous PDEs clearly and precisely, using appropriate technical language.
|1. Walter Strauss: Partial Differential Equations.|
2. Laurence Evans: Partial Differential Equations.
|Graduate Attributes and Skills
|Keywords||PDE,Partial Differential Equations
|Course organiser||Dr Aram Karakhanyan
Tel: (0131 6)50 5056
|Course secretary||Mrs Alison Fairgrieve
Tel: (0131 6)50 5045