ALGEBRA AND CALCULUS II

Year	No.	Offer	Mode	Description			Cred. Pts
96	64613 	S2  	D 	ALGEBRA AND CALCULUS II   	1.00

Contents

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

STAFFING:

PRE-REQUISITE(S)

64612/75612

RATIONALE:

This unit continues on from Algebra and Calculus I, providing students with the basic tools of linear algebra and calculus for the analysis of problems in science and engineering.

SYNOPSIS:

The unit introduces the basic techniques of multi-variable calculus
with particular emphasis on functions of two or three variables.
Differential calculus is extended to cover gradients and directional
derivatives, the determination of extrema, and the divergence and curl
of vector fields.  Integral calculus is extended to double and triple
integrals, line integrals and Green's theorem.  Single variable
calculus is developed to cover series approximations and differentiation
of integrals.  Vector spaces are introduced with discussions of linear
independence, bases, the Gram-Schmidt process, the eigenvalue problem
and the theory of equations.

OBJECTIVES:

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

1. solve ordinary first and second order differential equations;
2. find the partial derivatives of a function of several variables;
3. find the Taylor series for functions of one and two variables;
4. find the rank of a matrix and bases for its column and null spaces;
5. determine the linear dependence or independence of a set of vectors and construct orthogonal bases;
6. determine eigenvalues and eigenvectors of matrices;
7. solve systems of first order differential equations with constant coefficients;
8. calculate gradients and directional derivates for functions of several variables;
9. solve extrema problems for functions of two variables;
10. calculate the divergence and curl of vector fields;
11. calculate line and work integrals;
12. evaluate double integrals and apply Green's Theorem;
13. evaluate volume integrals with the appropriate choice of variables;

TOPICS:

 Description                                                    Weighting(%)

Differential Equations, including first and second order              25.00
equations and systems of first order equations.

Multiple Integrals, including the use of polar coordinates            25.00
and applications to volumes, centres of mass, and moments
of inertia.  Line integrals and Green's Theorem.

Curves and surfaces, partial differentiation, directional             25.00
derivatives, div, grad, curl; extrema.

Eigenvalues and eigenvectors, linear transformations, power           25.00
of a matrix, symmetric matrices, linear dependence, bases,
projections, Gram-Schmidt Process, column space, rank and
the theory of equations.

TEXT and MATERIALS to be PURCHASED:

Larson,R.E., Hostetler, R.P., Edwards, B.H, "Calculus",
4th edition, D C Heath and Co. 1990.

RECOMMENDED REFERENCE MATERIALS:

Grossman, S, 'Calculus', 5th edn, Academic Press, 1992.

Grobe, E M & Grobe, C A, 'Student Solutions Manual to accompany Elementary
Linear Algebra Applications version, 6th edn, John Wiley, New York, 1991.

Kreyszig, E, 'Advanced Engineering Mathematics', John Wiley, New York, 1988.

Roberts, A W, 'Elementary Linear Algebra', 2nd edn, Addison-Wesley, Reading,
Mass, 1981.

Thomas, G & Finney, R, 'Calculus and Analytic Geometry', 8th edn, Addison
Wesley, 1992. (World Student Series Edition).

STUDENT WORKLOAD REQUIREMENTS:

	ACTIVITY				HOURS
Lectures                                      	56
Tutorials/Workshops                           	28
Private Study                                 	72
Examinations                                  	3
Assessments                                   	16

ASSESSMENT DETAILS:

No	*F/S	Marks		Due		Description					Wtg(%)		LBL
1 	S 	50.00   	16/08/96	ASSIGNMENT 1                            	10.00   	Y
2 	S 	50.00   	06/09/96	ASSIGNMENT 2                            	10.00   	Y
3 	S 	50.00   	25/10/96	ASSIGNMENT 3                            	10.00   	Y
4 	S 	100.00  	END S2  	3 HOUR CLOSED BOOK EXAMINATION          	70.00   	N

OTHER REQUIREMENTS:

1    Students must complete 80% of tutorial exercises and/or mid-
     semester assessments to the satisfaction of the Examiner to pass
     the unit.
2    To obtain a pass in the unit, students must perform satisfactorily
     in all aspects of assessment.
3    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.
4    Students MUST  retain a  copy of  all assignments  which  must  be
     produced if and when required by the Examiner.
5    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.
6    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.
7    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.
8    No  further assignments will  be accepted for  assessment purposes
     after assignments or model solutions have been released, except in
     extenuating circumstances.