Module Catalogues, Xi'an Jiaotong-Liverpool University   
Module Code: MTH210
Module Title: Partial Differential Equations
Module Level: Level 2
Module Credits: 5.00
Academic Year: 2019/20
Semester: SEM2
Originating Department: Mathematical Sciences
Pre-requisites: MTH106
To familiarize students with basic properties of partial differential equations of the first and second order.

To illustrate the breadth of applications of PDEs and fundamental importance of related concepts.
Learning outcomes 
A. Use elementary techniques for the solution of certain first order PDEs.

B. Classify second order PDEs.

C. Solve canonical linear PDEs of first and second order in one dimension.

D. Solve elementary boundary and initial value problems.

Method of teaching and learning 
This module will be delivered by a combination of formal lectures and tutorials.
Introduction, Important PDEs.

Integral curves and surfaces of vector fields.

Quasi-linear and linear equations of first order. Characteristics.

Second order linear PDEs: classification and canonical forms, well-posed problems.

Laplace’s equation: harmonic functions, Dirichlet problem, Green’s function.

The wave equation: initial value problem, domain of dependence, Kirchhoff’s formula, Huygens’ principle.

The heat equation: initial-boundary value problem, maximum-minimum principle, solution of the initial-boundary value problem in one dimension.
Delivery Hours  
Lectures Seminars Tutorials Lab/Prcaticals Fieldwork / Placement Other(Private study) Total
Hours/Semester 39    13      98  150 


Sequence Method % of Final Mark
1 Final Exam 80.00
2 Class Test 1 10.00
3 Class Test 2 10.00

Module Catalogue generated from SITS CUT-OFF: 12/9/2019 11:57:31 PM