64636 ADVANCED ENGINEERING MATHEMATICS A

Year	No.	Offer	Mode	Description			Cred. Pts
97	64636 	S2  	X 	ADV ENGINEERING MATHS A   	1.00

Contents

• Staffing
• Pre-requisite(s)
• Rationale
• Synopsis
• Objectives
• Topics
• Texts
• Recommended References
• Student Workload
• Assessment Details
• Other Requirements

STAFFING:

PRE-REQUISITE(S)

75002/64001 + 75623/64623

RATIONALE:

Engineers and practising mathematicians who are involved in model
construction and analysis require a wide range of mathematical skills.
Of fundamental importance to engineering and science, are the elements
of stochastic processes, linear operators, time series analysis and
fore-casting, and the numerical solution of partial differential
equations (including finite difference and finite element techniques).

SYNOPSIS:

This unit comprises five modules.  Each student must complete
modules, 1,2, and 4, and one of module 3 or module 5.
  (i) the numerical solution of partial differential equations;
 (ii) stochastic process modelling;
(iii) time series analysis and forecasting;
 (iv) linear operators and functional analysis;
  (v) advanced numerical methods (multigrid and finite element methods).

OBJECTIVES:

According to the choice of modules, upon completion of this
unit, students should be able to:

1. demonstrate the ability to synthesize the range of
   mathematical ideas presented in this unit;
   
2. demonstrate the ability to apply these mathematical techniques
   to engineering problems;
   
3. demonstrate the ability to form discrete formulations of
   elliptic, parabolic and hyperbolic partial differential
   equations and to solve them computationally;
   
4. apply numerical techniques to the modelling and solution of
   flow and potential problems in engineering;
   
5. show understanding of numerical techniques for finite element
   methods;
   
6. demonstrate understanding of random processes of various types
   including aspects of generating functions, discrete time
   Markov chains, the Poisson process and birth/death process;
   
7. apply Markov queue techniques to traffic flow problems and
   other applications in engineering;
   
8. apply the concepts linear vector space, and linear operator,
   to engineering problems;
   
9. use Fourier and Laplace transforms to solve a variety of
   problems;
   
10. determine approximate solutions of such problems by selecting
    a dominant pole;
    
11. determine the optimal filter for estimating a signal in the
    presence of noise.
    
12. demonstrate understanding and application of various time
    series and forecasting techniques;
    
13. apply forecasting techniques to univariate and bi-variate
    data.
    

TOPICS:

 Description                                                    Weighting(%)

Students will study Topics 1, 2 and 4 and one of Topics 3
and 5.

Numerical Partial Differential Equations                              25.00
- finite difference operators
- laplace's equation
- heat flow problems
- the Poisson equation
- boundary conditions
- parabolic and hyperbolic systems
- performance of iterative methods
- introduction to multigrids
- applications

Stochastic Processes                                                  25.00
- generating functions
- discrete time Markov chains
- the Poisson process
- birth and death processes
- Markov queues
- applications to traffic flow etc

Linear Operators and Functional Analysis                              25.00
- linear spaces
- linear operators
- transforms (Fourier, z, Laplace)
- estimation of signals

Time Series and Forecasting                                           25.00
- linear filters
- nonstationary models (ARIMA)
- model identification
- box Jenkins forecasting methods
- applications

Advanced Numerical Methods                                            25.00
- multigrid methods for PDE's
- finite element methods
- convergence acceleration

TEXT and MATERIALS to be PURCHASED:

RECOMMENDED REFERENCE MATERIALS:

Box & Jenkins, Time Series Analysis Forecasting and Control, Holden
Day.

Kreyszig, E. 1993, Advanced Engineering Mathematics, 7th edn, Wiley.

Makridakis, S., Wheelwright, S.C. & McGee V.E. 1983, Forecasting,
Wiley.

Naylor, A.W. & Sell, G.R. 1971, Linear Operator Theory in Engineering
and Science, Holt, Rinehart and Winston.

Oden, J.K. 1979, Applied Functional Analysis, Prentice Hall.

Papoulis, A. 1991, Probability, Random Variables and Stochastic
Processes, McGraw Hill.

STUDENT WORKLOAD REQUIREMENTS:

	ACTIVITY				HOURS
Directed Study                                	84
Private Study                                 	66
Examinations                                  	3
Assessments                                   	16

ASSESSMENT DETAILS:

No  *F/S Marks     Due        Description                              Wtg(%)    LBL
1   S              25/08/97  ASSIGNMENT 1                              10.00     Y
2   S              01/09/97  ASSIGNMENT 2                              10.00     Y
3   S              20/10/97  ASSIGNMENT 3                              10.00     Y
4   S              27/10/97  ASSIGNMENT 4                              10.00     Y
5   S              END S2    3 HOUR OPEN BOOK EXAMINATION              60.00     N

OTHER REQUIREMENTS:

1    To   obtain   a   pass  in  the  unit,  students   must   perform
     satisfactorily in all aspects of assessment.
2    The  due date for assessments is the date by which a student must
     despatch an assignment to the USQ. The onus is on the student  to
     provide proof of the despatch date, if requested by the Examiner.
3    Students  MUST  retain a copy of all assignments  which  must  be
     produced if and when required by the Examiner.
4    Extensions   for  assignment  submission  may   be   granted   in
     extenuating  circumstances. The decision to grant  or  refuse  an
     extension is made by the Examiner. Students should be aware  that
     an  application  for  an  extension does not  guarantee  that  an
     extension will be granted.
5    Students  apply for extension by either applying at the  time  of
     submitting  an  assignment  or  applying  in  writing  prior   to
     submitting  an  assignment.  All  relevant  documentation  should
     accompany the application.
6    If  assignments are submitted after the due date and no extension
     is  granted,  then  a  penalty up to a  maximum  of  20%  of  the
     assignment mark for each working day late may apply.
7    No  further assignments will be accepted for assessment  purposes
     after  assignments or model solutions have been released,  except
     in extenuating circumstances.