64636 ADVANCED ENGINEERING MATHEMATICS A

Year	No.	Offer	Mode	Description			Cred. Pts
00	64636 	S2  	X 	ADV ENGINEERING MATHS A   	1.00

Contents


STAFFING:

Examiner: T. ROBERTS
Moderator: S. SUSLOV
Instructional design: S. REUSHLE

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:

To develop an awareness of the way in which mathematics is
used to solve engineering problems. To gain a proficiency in
applying mathematics to engineering problems. The following
specific objectives relate to individual modules; students
should be able to:

  1. form discrete formulations of elliptic, parabolic and
    hyperbolic partial differential equations and solve them
    computationally; apply numerical techniques to the modelling
    and solution of flow and potential problems in engineering;
  2. understand random processes of various types including
    discrete time Markov chains, the Poisson process and
    birth/death process; apply Markov queue techniques engineering
    problems;
  3. use Fourier and Laplace transforms to solve a variety of
    problems; apply the concepts linear vector space, and linear
    operator, to engineering problems; determine the optimal
    filter for estimating a signal in the presence of noise;
  4. demonstrate understanding and application of various time
    series and forecasting techniques;
  5. understand and use multigrid, finite element and weighted
    residual methods.

TOPICS:

 Description                                                    Weighting(%)
    Students will study Topics 1, 2 and 4 and their own choice of one of Topics 3 and 5: Topic 3 has a lot to offer Civil and Mechanical Engineers; whereas Topic 5 supports the analysis typically needed in Mechatronics and Control.
  1. Numerical Partial Differential Equations 25.00 - finite difference operators and their stability - Laplace's equation - heat flow problems - the Poisson equation - boundary conditions - parabolic and hyperbolic systems - iterative methods - introduction to multigrids - applications

  2. Stochastic Processes 25.00 - discrete time Markov chains - the Poisson process - birth and death processes - Markov queues and applications

  3. Transforms, Linear Operators and Functional Analysis 25.00 - Fourier & Laplace transforms - estimation of signals - linear spaces & operators - orthogonal decomposition

  4. Time Series and Forecasting 25.00 - linear filters - nonstationary models (ARIMA) - model identification - Box Jenkins forecasting methods - z transforms - applications

  5. Advanced Numerical Methods 25.00 - multigrid methods for PDE's - finite element methods - weighted residuals


RECOMMENDED REFERENCE MATERIALS:

Box & Jenkins, 1994, Time Series Analysis Forecasting and Control,
3rd edn, 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. 1999, Advanced Engineering Mathematics, 8th edn, Wiley.

Makridakis, S., Wheelwright, S.C. , 1998, Forecasting, 3rd edn,
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.

Some electronic resources for this unit may be available via its home
page: http://www.sci.usq.edu.au/units/64636


STUDENT WORKLOAD REQUIREMENTS:

	ACTIVITY				HOURS
Private Study                                 	140
Examinations                                  	3
Assessments                                   	25

ASSESSMENT DETAILS:

No  *F/S Marks     Due        Description                              Wtg(%)    LBL WWW
1   S              18/08/00  ASSIGNMENT 1                              10.00     Y   N
2   S              25/08/00  ASSIGNMENT 2                              10.00     Y   N
3   S              20/10/00  ASSIGNMENT 3                              10.00     Y   N
4   S              27/10/00  ASSIGNMENT 4                              10.00     Y   N
5   S              END S2    3 HOUR OPEN EXAMINATION                   60.00     N   N

*F=Formative, S=Summative

OTHER REQUIREMENTS:

1    To   obtain   a   pass  in  the  unit,  students   must   perform
     satisfactorily in all aspects of assessment. a. Students must:  i
     obtain an overall passing mark; ii perform satisfactorily in  the
     examination(s) (ie get at least close to the passing  mark);  iii
     normally attain at least 50% in the assignments as a whole. b. If
     a  student obtains an overall passing mark, but does not  perform
     satisfactorily  in  an  examination,  the  student  may,  at  the
     discretion   of   the  examiner,  be  granted   a   supplementary
     examination to attempt to increase the mark for that part  before
     being  reconsidered for a pass in the unit.  c.  A  student  will
     normally not be granted a deferred examination for an examination
     unless he/she performs satisfactorily in any other examination(s)
     and  in  the  assignments. d. A final grade will be allocated  as
     follows:  raw  marks  for the assessments  will  be  summed  with
     weightings  specified  in  the  Assessment  Details;  performance
     demonstrated  in the examination will be reviewed with  reference
     to  the unit's objectives and a scaling decided; the scaled marks
     then determine the final grade.
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 within ten days if and when required by the Examiner.
4    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.
5    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.

This information is accurate as at 31/10/00