64636 ADVANCED ENGINEERING MATHEMATICS A

Year	No.	Offer	Mode	Description			Cred. Pts
99	64636 	S2  	X 	ADV ENGINEERING MATHS A   	1.00

Contents

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

STAFFING:

PRE-REQUISITE(S)

64001+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
forecasting,  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. The  modules  are  as
follows:

1. the numerical solution of partial differential equations;

2. stochastic process modelling;

3. linear operators and functional analysis;

4. time series analysis and forecasting;

5. 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 synthesise 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

RECOMMENDED REFERENCE MATERIALS:

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

Greenberg, M.D., 1998, Advanced Engineering Mathematics, Prentice
Hall.

Jain, P.K., Ahuja, O.P. and Ahmed, K., 1995, Functional Analysis,
John Wiley & Sons.

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

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

Mehdi, J., 1994, Stochastic Processes, John Wiley & Sons.

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.

Solomon, F., 1987, Probability & Stochastic Processes, Prentice
Hall.

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 WWW
1   S              27/08/99  ASSIGNMENT 1                              10.00     Y   N
2   S              03/09/99  ASSIGNMENT 2                              10.00     Y   N
3   S              29/10/99  ASSIGNMENT 3                              10.00     Y   N
4   S              26/10/99  ASSIGNMENT 4                              10.00     Y   N
5   S              END S2    3 HOUR OPEN EXAMINATION                   60.00     N   N

OTHER REQUIREMENTS:

1    To   obtain   a   pass  in  the  unit,  students   must   perform
     satisfactorily in all aspects of assessment.
2    In  accordance  with  University's  Assignment  Extension  Policy
     (Regulation  5.9), the examiner of a unit may grant an  extension
     of  the  due  date of an assignment in extenuating circumstances.
     This  policy  may  be  found in the USQ  Handbook,  the  Distance
     Education  Study  Guide and the Faculty of Sciences'  Orientation
     Handbook for new on-campus students. All students are advised  to
     study and follow the guidelines associated with this policy.
3    Open   Examination:  an  open  examination  indicates  that   the
     candidate  may have access to any material during the examination
     except  the  following: electronic communication  devices,  bulky
     material,  devices requiring mains power and material  likely  to
     disturb other students.