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DRPS : Course Catalogue : School of Engineering : School (School of Engineering)

Undergraduate Course: Partial Differential Equations 3 (SCEE09004)

Course Outline
SchoolSchool of Engineering CollegeCollege of Science and Engineering
Credit level (Normal year taken)SCQF Level 9 (Year 3 Undergraduate) AvailabilityAvailable to all students
SCQF Credits10 ECTS Credits5
SummaryMost physical problems in science and engineering depend on changes in multiple dimensions and these problems are described by Partial Differential Equations (PDE). These equations contain 2 or more partial derivatives, for example a time and a space dimension or multiple space dimensions.This course introduces first and second order PDEs and the solution properties for different classes of PDEs. Based on these different solution properties, we will develop analytical and numerical solution methods for the different classes of PDEs.
Course description The course will consist of 20 lectures and 10 tutorial/lab sessions.

1.Introduction to and classification of partial differential equations (PDEs) [2 lectures]
2.Analytical solution of the Laplace, heat and wave equation: separation of variables, Laplace transform method, d'Alembert and characteristics [8 lectures]
3.Introduction to numerical methods for PDEs [2 lectures]
4.Application of the finite difference method to the different types of PDEs: boundary value problems for stationary PDEs, initial-boundary value problems for transient PDEs, handling of different boundary conditions, accuracy and stability of the solutions [8 lectures]
Entry Requirements (not applicable to Visiting Students)
Pre-requisites Students MUST have passed: Engineering Mathematics 2A (SCEE08009) AND Engineering Mathematics 2B (SCEE08010) AND Engineering Mathematics 1a (MATH08074) AND Engineering Mathematics 1b (MATH08075)
Prohibited Combinations Other requirements None
Information for Visiting Students
High Demand Course? Yes
Course Delivery Information
Academic year 2024/25, Available to all students (SV1) Quota:  None
Course Start Semester 2
Timetable Timetable
Learning and Teaching activities (Further Info) Total Hours: 100 ( Lecture Hours 44, Programme Level Learning and Teaching Hours 2, Directed Learning and Independent Learning Hours 54 )
Assessment (Further Info) Written Exam 70 %, Coursework 30 %, Practical Exam 0 %
Additional Information (Assessment) Written Exam %: 70
Practical Exam %: 0
Coursework %: 30
Feedback The tutorial/lab sessions provide opportunities for formative feedback and the two coursework assignments will provide summative feedback.
Exam Information
Exam Diet Paper Name Hours & Minutes
Main Exam Diet S2 (April/May)2:00
Resit Exam Diet (August)2:00
Learning Outcomes
On completion of this course, the student will be able to:
  1. Distinguish between the three different types of second order partial differential equations; this includes their properties and general solution behaviour
  2. Calculate the analytical solution of engineering problems described by the three types of linear, constant coefficient second order partial differential equations 
  3. Use Python to simulate the numerical solution of engineering problems described by second order partial differential equations
  4. Evaluate the performance and suitability of the numerical methods for the three different types of partial differential equations
Reading List
Applied partial differential equations

Glyn James: Advanced Modern Engineering Mathematics, Chapter 9, required from Engineering Mathematics 2

Svein Linge, Hans Petter Langtangen: Programming for Computations - Python A Gentle Introduction to Numerical Simulations with Python 3.6, Springer, 2020

Randall J. LeVeque: Finite difference methods for ordinary and partial differential equations steady-state and time-dependent problems, SIAM, 2007, available online

Herve Le Dret, Brigitte Lucquin: Partial Differential Equations: Modeling, Analysis and Numerical Approximation, Springer, 2016, available online

S.C. Chapra, R.P Canale: Numerical Methods for Engineers, 6th edition, McGraw-Hill, 2010

Andrew R. Mitchell, David F. Griffiths: The finite difference method in partial differential equations, Wiley, 1980

Leon Lapidus, George F. Pinder: Numerical Solution of Partial Differential Equations in Science and Engineering

Joel Chaskalovic: Mathematical and Numerical Methods for Partial Differential Equations

Mathematical theory of partial differential equations

Qing Han, A Basic Course in Partial Differential Equations

Lawrence C. Evans: Partial Differential Equations

Numerical methods

William H. Press:Numerical Recipes in C: The Art of Scientific Computing
Additional Information
Graduate Attributes and Skills Not entered
KeywordsPartial Differential Equations,Mathematical Modelling,Mathematical Methods,Mechanical Engineering
Course organiserDr Martin Sweatman
Tel: (0131 6)51 3573
Course secretaryMr Tom Lawford-Groves
Tel: (0131 6)50 5687
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