MATHS 7104 - Numerical Methods

North Terrace Campus - Semester 2 - 2015

To explore complex systems, physicists, engineers, financiers and mathematicians require computational methods since mathematical models are only rarely solvable algebraically. Numerical methods, based upon sound computational mathematics, are the basic algorithms underpinning computer predictions in modern systems science. Such methods include techniques for simple optimisation, interpolation from the known to the unknown, linear algebra underlying systems of equations, ordinary differential equations to simulate systems, and stochastic simulation under random influences. Topics covered are: the mathematical and computational foundations of the numerical approximation and solution of scientific problems; simple optimisation; vectorisation; clustering; polynomial and spline interpolation; pattern recognition; integration and differentiation; solution of large scale systems of linear and nonlinear equations; modelling and solution with sparse equations; explicit schemes to solve ordinary differential equations; random numbers; stochastic system simulation.

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Course Details

Course Code	MATHS 7104
Course	Numerical Methods
Coordinating Unit	Mathematical Sciences
Term	Semester 2
Level	Postgraduate Coursework
Location/s	North Terrace Campus
Units	3
Contact	Up to 3.5 hours per week
Available for Study Abroad and Exchange	Y
Prerequisites	MATHS 1012 and (COMP SCI 1012, 1101, MECH ENG 1100, 1102, 1103, 1104, 1105, C&ENVENG 1012)
Incompatible	MATHS 2104
Assumed Knowledge	MATHS 2102 or MATHS 2201
Assessment	ongoing assessment 50%, exam 50%

Course Staff

Course Coordinator: Dr Trent Mattner

Course Timetable

The full timetable of all activities for this course can be accessed from .

Course Learning Outcomes

1	Demonstrate understanding of common numerical methods and how they are used to obtain approximate solutions to otherwise intractable mathematical problems.
2	Apply numerical methods to obtain approximate solutions to mathematical problems.
3	Derive numerical methods for various mathematical operations and tasks, such as interpolation, differentiation, integration, the solution of linear and nonlinear equations, and the solution of differential equations.
4	Analyse and evaluate the accuracy of common numerical methods.
5	Implement numerical methods in Matlab.
6	Write efficient, well-documented Matlab code and present numerical results in an informative way.

最新糖心Vlog Graduate Attribute	Course Learning Outcome(s)
Knowledge and understanding of the content and techniques of a chosen discipline at advanced levels that are internationally recognised.	1,2,3,4,5
The ability to locate, analyse, evaluate and synthesise information from a wide variety of sources in a planned and timely manner.	2,3,4,5
An ability to apply effective, creative and innovative solutions, both independently and cooperatively, to current and future problems.	2,3,4,5
Skills of a high order in interpersonal understanding, teamwork and communication.	5,6
A proficiency in the appropriate use of contemporary technologies.	5,6
A commitment to continuous learning and the capacity to maintain intellectual curiosity throughout life.	1,2,3,4,5,6

Learning & Teaching Modes

This course uses a variety of methods for delivery of the course material.

Some lecture material is delivered using online screencasts together with interactive Maple TA exercises and quizzes. Other lecture material is delivered in traditional face-to-face lecture format.

Tutorials are held fortnightly. In these classes, you will complete short quizzes and work on tutorial problems that aim to enhance your understanding of the lecture material and ability to solve theoretical problems. You are encouraged to attempt the problems before the tutorial and to complete all the remaining problems afterwards.

Practicals are held fortnightly, alternating with tutorials. In these classes, you will use Matlab to implement numerical algorithms developed in lectures. Practical work must be submitted to show that you have completed the session.

Assignments are set fortnightly. In the assignments, you are usually asked to write a Matlab program to solve a mathematical problem and present your results in a written report. Questions about theoretical aspects of the problem may also be asked.

Workload

The information below is provided as a guide to assist students in engaging appropriately with the course requirements.

Activity	Quantity	Workload hours
Lecture	24	72
Tutorials	5	20
Assignments	5	40
Practicals	6	24
TOTALS		156

Learning Activities Summary

Schedule
Week 1	Matlab revision, vectorisation.
Week 2	Polynomial interpolation.	Practical 1: Matlab and vectorisation.
Week 3	Numerical differentiation and integration.	Tutorial 1: Polynomial interpolation.
Week 4	Linear and cubic splines in one dimension.	Practical 2: Numerical integration and differentiation.
Week 5	Radial basis function splines in multiple dimensions.	Tutorial 2: Numerical integration and differentation.
Week 6	LU and QR factorisation and applications.	Practical 3: Splines.
Week 7	Norms and condition numbers. Jacobi method.	Tutorial 3: LU and QR factorisation.
Week 8	Fixed point iteration, Newton's method.	Practical 4: Numerical linear algebra.
Week 9	Euler's method, Improved Euler method, Initial-value problems.	Tutorial 4: Jacobi method, fixed point iteration and Newton's method.
Week 10	Runge Kutta methods, time-step limitations, Matlab ODE solvers.	Practical 5: Newton's method and ordinary differential equations.
Week 11	Boundary-value problems. Partial differential equations. Monte Carlo methods.	Tutorial 5: Ordinary differential equations.
Week 12	Monte Carlo methods. Review	Practical 6: Test

The 最新糖心Vlog's policy on Assessment for Coursework Programs is based on the following four principles:

Assessment must encourage and reinforce learning.
Assessment must enable robust and fair judgements about student performance.
Assessment practices must be fair and equitable to students and give them the opportunity to demonstrate what they have learned.
Assessment must maintain academic standards.

Assessment Summary

Component	Weighting	Objective Assessed
Exam	50%	All
Practical test	15%	All
Assignments	25%	All
Quizzes/MapleTA	10%	All

Assessment Related Requirements

In order to pass the course, you must obtain:

an aggregate mark of at least 50%, AND
at least 45% on the exam.

Assessment Detail

Assessment Item	Distributed	Due Date	Weighting
Assignment 1	Week 2	Week4	5%
Assignment 2	Week 4	Week 6	5%
Assignment 3	Week 6	Week 8	5%
Assignment 4	Week 8	Week 10	5%
Assignment 5	Week 10	Week 12	5%

Tutorial quizzes and MapleTA exercises will be set throughout the course. They are of equal weight.

Submission

You will need to submit both electronic and hardcopy components for each assignment. The electronic component must be submitted according to the assignment instructions. It will be marked electronically and the result added to your hardcopy mark. The hardcopy component must be submitted to the designated hand-in boxes within the School of Mathematical Sciences with a signed cover sheet attached.

Late assignments will not be accepted. Students may be excused from an assignment for medical or compassionate reasons. Documentation is required and the lecturer must be notified as soon as possible.

Assignments will have a two week turn-around time for feedback to students.

Course Grading

Grades for your performance in this course will be awarded in accordance with the following scheme:

M10 (Coursework Mark Scheme)
Grade	Mark	Description
FNS		Fail No Submission
F	1-49	Fail
P	50-64	Pass
C	65-74	Credit
D	75-84	Distinction
HD	85-100	High Distinction
CN		Continuing
NFE		No Formal Examination
RP		Result Pending

Further details of the grades/results can be obtained from Examinations.

Grade Descriptors are available which provide a general guide to the standard of work that is expected at each grade level. More information at Assessment for Coursework Programs.

Final results for this course will be made available through .

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Authorised by:	Deputy Vice-Chancellor and Vice-President (Academic)
Maintained by:	Course Outlines Administrator

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