Module Catalogues, Xi'an Jiaotong-Liverpool University

Module Code: MTH210
Module Title: Partial Differential Equations
Module Level: Level 2
Module Credits: 5.00
Semester: SEM2
Originating Department: Mathematical Sciences
Pre-requisites: MTH106

 Aims 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.
 Syllabus 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

## Assessment

 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: 6/4/2020 6:41:15 AM