VECTOR ANALYSIS AND DIFFERENTIAL EQUATIONS

Year	No.	Offer	Mode	Description			Cred. Pts
96	64622 	S1  	D 	VECTOR ANAL & DIFF EQUATNS	1.00

Contents

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

STAFFING:

PRE-REQUISITE(S)

64613/75613

RATIONALE:

This unit provides the mathematical tools required for an understanding of the principles that permeate much of mathematical physics and engineering science.

SYNOPSIS:

1  Organization:  The unit is offered in two concurrent modules.
   Module 1 is concerned with topics in advanced calculus and vector
   analysis and Module 2 with ordinary and partial differential
   equations.

2  Content:  Module 1 - deals with smooth scalar and vector functions
   of scalar or vector variables; in particular with curves and
   surfaces in space and scalar and vector fields.  Line, surface
   and volume integrals and the theorems of Gauss and Stokes lead to
   the development of the fundamental equations of mathematical
   physics and the discussion of conservative fields and potentials.

            Module 2 - deals with the description of linear systems
   through linear differential equations.  Laplace transform techniques
   are developed to analyse the nature of system response to impulses
   and other inputs.  Fourier series and transform techniques are also
   discussed.

OBJECTIVES:

On completion of this unit, students will be able to:

1. determine coordinate vectors for curves and surfaces in space and their tangent lines and tangent planes;
2. evaluate line and surface integrals;
3. apply the integral theorems to calculate flux and work integrals;
4. determine scalar potentials for conservative fields.
5. find Fourier series for given functions;
6. solve partial differential equations by the technique of seperation of variables;
7. find Laplace transforms of given functions;
8. use Laplace transforms to solve constant coefficient differential equations and systems of differential equations;
9. apply Laplace and Fourier transform techniques to the solution of partial differential equations.

TOPICS:

 Description                                                    Weighting(%)

Module 1
Scalar and vector fields; curves and surfaces; tangents               5.00
and normals; directional derivatives; Leibnitz's rule

Line integrals, work and circulation                                  5.00

Surface integrals, flux; divergence and curl of vector                5.00
fields

Volume integrals, change of variables in double and triple            7.00
integrals

Divergence theorem                                                    7.00

Stokes theorem and Green's theorem in the plane                       7.00

Work integrals independent of path; irrotational flows                5.00

Conservative fields, scalar potentials.                               5.00

Fourier series                                                        7.00

Fourier integral, Fourier transforms                                  7.00

Module 2

First order equations isoclines & approximate methods                 5.00

Phase plane analysis of linear systems                                5.00

Non-linear systems                                                    5.00

Laplace transform and its properties                                  7.00

Step and impulse function, Shifting Theorems                          7.00

Convolution, unit impulse response and transfer function              7.00

Laplace's equation, heat flow                                         5.00

Wave equation                                                         5.00

TEXT and MATERIALS to be PURCHASED:

RECOMMENDED REFERENCE MATERIALS:

Greenberg, Michael P, 'Foundations of Applied Mathematics',
Prentice-Hall, NJ, 1978.

Kaplan, W, 'Advanced Mathematics for Engineers', Addison-Wesley,
Reading, Mass, 1981.

Amazigo, J C & Rubenfeld, L A, 'Advanced Calculus', John Wiley,
New York, 1980.

STUDENT WORKLOAD REQUIREMENTS:

	ACTIVITY				HOURS
Lectures                                      	56
Tutorials/Workshops                           	28
Private Study                                 	60
Examinations                                  	4
Assessments                                   	20

ASSESSMENT DETAILS:

No	*F/S	Marks		Due		Description					Wtg(%)		LBL
1 	S 	        	22/03/96	ASSIGNMENT 1.1 (WEEK 5)                 	5.00    	N
2 	S 	        	10/05/96	ASSIGNMENT 1.2 (WEEK 12)                	5.00    	N
3 	S 	        	15/03/96	ASSIGNMENT 2.1 (WEEK 4)                 	5.00    	N
4 	S 	        	26/04/96	ASSIGNMENT 2.2 (WEEK 10)                	5.00    	N
5 	S 	        	END S1  	CLOSED BOOK EXAMINATION - 2 HOURS       	40.00   	N
6 	S 	        	END S1  	CLOSED BOOK EXAMINATION - 2 HOURS       	40.00   	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.
In accordance with University policy and Guidelines,
i     an Examiner may grant an extension of the due date of an
      assignment in extenuating circumstances;
ii    no assignments will be accepted for assessment purposes
      after assignments or model solutions have been released
      except in extenuating circumstances;
iii   assignments submitted after the due date without any
      extenuating circumstances will attract a penalty of at
      most 20% of the assignment mark for each working day
      late;
iv    students who submit an assignment after the due date and
      wish to claim extenuating circumstances, must provide
      documentary evidence with the assignment explaining
      the circumstances;
v     the unit examiner shall consider a claim for extenuating
      circumstances and decide on the outcome;
vi    the decision of the Dean shall be final in any dispute
      that may arise in the implementation of these guidelines.