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DRPS : Course Catalogue : School of Mathematics : Mathematics

Undergraduate Course: Introduction to Partial Differential Equations (MATH10100)

Course Outline
SchoolSchool of Mathematics CollegeCollege of Science and Engineering
Credit level (Normal year taken)SCQF Level 10 (Year 4 Undergraduate) AvailabilityAvailable to all students
SCQF Credits10 ECTS Credits5
SummaryA rigorous introduction covering the basics of elliptic, hyperbolic, parabolic and dispersive PDEs. This is a pure maths course.
Course description 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)
Pre-requisites Students MUST have passed: Honours Analysis (MATH10068)
It is RECOMMENDED that students have passed Metric Spaces (MATH10101)
Prohibited Combinations Other requirements None
Information for Visiting Students
High Demand Course? Yes
Course Delivery Information
Academic year 2023/24, Available to all students (SV1) Quota:  None
Course Start Semester 1
Timetable Timetable
Learning and Teaching activities (Further Info) Total Hours: 100 ( Lecture Hours 22, Seminar/Tutorial Hours 5, Summative Assessment Hours 2, Programme Level Learning and Teaching Hours 2, Directed Learning and Independent Learning Hours 69 )
Assessment (Further Info) Written Exam 80 %, Coursework 20 %, Practical Exam 0 %
Additional Information (Assessment) Coursework: 20%
Exam 80%
Feedback Not entered
Exam Information
Exam Diet Paper Name Hours & Minutes
Main Exam Diet S1 (December)2:00
Learning Outcomes
On completion of this course, the student will be able to:
  1. Demonstrate an understanding of rigorous PDEs by proving unseen results using the methods of the course.
  2. Correctly state the main definitions and theorems in the course.
  3. Produce examples and counterexamples illustrating the mathematical concepts presented in the course
  4. Explain their reasoning about rigorous PDEs clearly and precisely, using appropriate technical language.
Reading List
1. Walter Strauss: Partial Differential Equations.
2. Laurence Evans: Partial Differential Equations.
Additional Information
Graduate Attributes and Skills Not entered
KeywordsPDE,Partial Differential Equations
Course organiserDr Aram Karakhanyan
Tel: (0131 6)50 5056
Course secretaryMrs Alison Fairgrieve
Tel: (0131 6)50 5045
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