# DEGREE REGULATIONS & PROGRAMMES OF STUDY 2021/2022

### Information in the Degree Programme Tables may still be subject to change in response to Covid-19

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DRPS : Course Catalogue : School of Mathematics : Mathematics

# 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 SCQF Credits 10 ECTS Credits 5 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. 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.
 Pre-requisites Students MUST have passed: Honours Analysis (MATH10068) Co-requisites Prohibited Combinations Other requirements In academic year 2022-23 and later, MATH10101 Metric spaces is recommended for this course.
 Pre-requisites None High Demand Course? Yes
 Academic year 2021/22, 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
 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 courseExplain 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 Not entered Keywords PDE,Partial Differential Equations
 Course organiser Dr Aram Karakhanyan Tel: (0131 6)50 5056 Email: aram.karakhanyan@ed.ac.uk Course secretary Mrs Alison Fairgrieve Tel: (0131 6)50 5045 Email: Alison.Fairgrieve@ed.ac.uk
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