COURSE OUTLINE
MATH3101/5305
Computational Mathematics
Semester 1, 2017
Cricos Provider Code: 00098G Copyright 2016 -School of Mathematics and Statistics, UNSW Australia
DRAFT VERSION
Information about the course
Course Authority: A/Prof. William McLean RC-2085.
Consultation: See my timetable on the course home page.
Credit: This course counts for 6 Units of Credit (6UOC).
Prerequisites: Students taking MATH3101 must have previously passed 12 units
of credit in Level 2 Math courses including
MATH2011 or MATH2111, and
MATH2120 or MATH2130 or MATH2121 or MATH2221.
The alternative prerequisites for Engineering students are either MATH2019(DN)
and MATH2089, or else both MATH2069(CR) and MATH2099.
In addition to these formal prerequisites, students must have some prior
experience with simple computer programming. Although the computing
component of the course aims to be reasonably self-contained, the presentation of
topics assumes that students are already familiar with key concepts of procedural programming, including input/output statements, for-loops, if-statements and
function calls.
The graduate course MATH5305 assumes prior study equivalent to the above.
Exclusions: MATH3301.
Classes: Students in Math3101 and Math5305 attend the same classes. In each of
weeks 112 you will attend two lectures, and in each of weeks 213, you will attend
one tutorial and one computing class, as shown below.
Class type
Weeks
Day
Time
Room
Lecture
112
Wednesday
911 AM
Red Centre 4082
Tutorial
213
Tuesday
1011 AM
Colombo LG02
BYOD Computing
213
Tuesday
45 PM
Goldstein G09
Computing
213
Tuesday
56 PM
Red Centre G12A
You have a choice for the computing class: either bring you own laptop to the earlier
class in Goldstein G09, or else go to the later class in the G12A computer lab.
TELT: All course materials will be available on the course home page, which is
accessed by logging on to
http://moodle.telt.unsw.edu.au/my/.
You should check regularly for new materials.
Course aims
MATH3101/5305 introduces finite difference methods for computing approximate
solutions to partial differential equations. The theoretical component of the course
treats fundamental concepts including stability and convergence, as well as some
necessary topics in numerical linear algebra. The practical component of the course
addresses the computer implementation of finite difference methods. In this way,
students can develop a solid foundation for employment or further study in a wide
range of scientific and engineering fields that rely on numerical modelling.
Relation to other mathematics courses
MATH3101 is an elective third-year course that is a natural sequel to the secondyear course MATH2301 Mathematical Computing. MATH3311/5335 Computational Methods for Finance has similar aims to MATH3101/5305 but with a focus
on applications in finance. In some years, the School of Mathematics and Statistics
offers an honours course on Finite Element and Quasi-Monte Carlo Methods.
Student Learning Outcomes
The theoretical component of the course will enable you to
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formulate a finite difference approximation to a partial differential equation;
employ Taylor expansions to estimate the local truncation error and the order
of consistency of a finite difference scheme;
determine when a scheme is stable;
decide whether explicit or implicit time stepping is appropriate for a given
problem;
assess a scheme for its numerical dissipation and dispersion;
exploit sparsity and other matrix structure to solve a system of linear equations
efficiently.
Assessment
The course has three assessment tasks:
Computing exercise Weeks 34
Class Test
Week 6
Lab Test
Week 10
Assignment
Week 12
Final Exam
November
5%
15%
15%
15%
50%
Refer to the course home page for further details, such as the topics covered in the
class test.
If you are absent from a class test, you must provide a medical certificate. A
further test may be offered at the discretion of the lecturer. Otherwise an M will
be recorded and your final mark will be calculated from the other assessment tasks.
Do not apply for special consideration if you are sick for a class test. (Applying for
special consideration is necessary only for an assessment worth 20% or more of your
final mark.)
Reference books
There is no prescribed textbook for the course, but you may find the following texts
useful:
A. Iserles, A First Course in the Numerical Analysis of Differential Equations,
Cambridge University Press, 1996, P515.35/8
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K. W. Morton and D. F. Mayers, Numerical Solution of Partial Differential
Equations, Cambridge University Press, 1994, P517.383/298
Granville Sewell, The Numerical Solution of Ordinary and Partial Differential
Equations, Academic Press, 1988, P517.382/205
The content of the course will be defined by the lectures, Moodle resources, the
tutorial problems and the lab exercises.
Syllabus
Boundary-value problems in 1D
Linear two-point boundary-value problems
Finite difference approximation
Error analysis
Tridiagonal linear systems
Diffusion equations in 1D
Separation of variables
Spatial discretisation
Explicit Euler method
Implicit Euler method
CrandNicolson and BDF2 methods
Conservation laws in 1D
Characteristics
Linear advection equation
Explicit upwind scheme
CFL conditions
LaxWendroff and box schemes
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Dissipation and dispersion
Finite volume methods
Elliptic problems in 2D
Five-point scheme for the Poisson equation
Discrete maximum principle
Matrix structure
Computing
The computing component of the course accounts for around 40% of the assessment.
You will learn to use the Julia programming language to implement numerical methods for solving partial differential equations. Information about Julia is available
at
http://julialang.org/
The computing component also includes an introduction to some topics that are
useful for scientific computing on a Linux platform.
If you attend the BYOD computing class then you will need to install Julia and a
number of supporting packages on your laptop. Advice about how to do this will
be provided in the Week 1 lectures and on Moodle. You will need to use only free
software in this course.
School Rules and Regulations
Details of the general rules regarding attendance, release of marks, special consideration etc are available via the School of Mathematics and Statistics Web site:
http://www.maths.unsw.edu.au/currentstudents/assessment-policies
In particular, for the additional assessment policies see
http://www.maths.unsw.edu.au/currentstudents/additional-assessment
The dates for the additional assessment exams are available from the online Student
Noticeboard.
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