Undergraduate Course: Introduction to Partial Differential Equations (MATH10100)
Course Outline
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.

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 longstanding 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)
Prerequisites 
Students MUST have passed:
Honours Analysis (MATH10068)

Corequisites  
Prohibited Combinations  
Other requirements  It is RECOMMENDED that students have passed Metric Spaces (MATH10101) 
Information for Visiting Students
Prerequisites  Visiting students are advised to check that they have studied the material covered in the syllabus of each prerequisite course before enrolling. 
High Demand Course? 
Yes 
Course Delivery Information

Academic year 2024/25, 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)  Introduction to Partial Differential Equations (MATH10100)  2:120  
Learning Outcomes
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.

Reading List
1. Walter Strauss: Partial Differential Equations.
2. Laurence Evans: Partial Differential Equations.

Additional Information
Graduate Attributes and Skills 
Not entered 
Keywords  PDE,Partial Differential Equations 
Contacts
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 

