Course Title: Design complex algorithms using mathematical and scientific principles

Part B: Course Detail

Teaching Period: Term1 2008

Course Code: MATH7039

Course Title: Design complex algorithms using mathematical and scientific principles

School: 155T Vocational Health and Sciences

Campus: City Campus

Program: C6068 - Advanced Diploma of Computer Science

Course Contact: Raymond Rozen

Course Contact Phone: +61 3 9925 4699

Course Contact Email:

Name and Contact Details of All Other Relevant Staff

Nominal Hours: 60

Regardless of the mode of delivery, represent a guide to the relative teaching time and student effort required to successfully achieve a particular competency/module. This may include not only scheduled classes or workplace visits but also the amount of effort required to undertake, evaluate and complete all assessment requirements, including any non-classroom activities.

Pre-requisites and Co-requisites

MATH 7012C

Course Description

A selection of topics including,
Matrices and Simultaneous Equations
Integral Calculus
Numerical Methods
Laboratory Techniques
Differential Equations

National Codes, Titles, Elements and Performance Criteria

National Element Code & Title:

VBP029 Design complex algorithms using mathematical and scientific principles


Apply mathematical/scientific method to the process

Performance Criteria:



Identify the process for applying mathematical/scientific principles

Performance Criteria:



Select appropriate mathematical/scientific method

Performance Criteria:



Verify and interpret results

Performance Criteria:


Learning Outcomes

Apply mathematical/scientific method to the process
Identify the process for applying mathematical/scientific principles
Select appropriate mathematical/scientific method
Verify and interpret results

Details of Learning Activities

Lecturer Inputs:
All course content will be presented by the lecturer with worked examples of solutions to mathematical problems. The lecturer will provide assistance during class to assist students in their problem solving tasks.

Student Input: Students are required to:
attend all classes,
to complete assigned mathematical problems outside classes in order to improve their problem solving ability,
to complete all assessment tasks.

Teaching Schedule

Topic A Matrices and Simultaneous Equations

Topics Exercises
Definition of matrices,special matrices,addition and subtraction,scalar multiplication,multiplication of matrices, the transpose of a matrix,        Week1
Set 1
Solving 2x2 simultaneous equations,algebraic,graphical methods, 2x2 determinants,and inverse of a 2x2 matrix                                                     Week 2
Set 2
3x3 matrices,determinants of 3x3,simultaneous equations in three unknowns, deducing the inverse matrix                                                              Week 3
Set 3,4
Gaussian elimination,solution of three equations in three unknowns,what happens when the determinant is zero, explanation of solutions.    Week 4
Set 5
Finding inverses of 3x3 matrices, using Maple and calculators                                                                                                                                              Week 5
Set 6                                                                                         

Topic B Vectors

Topics Exercises
To understand the differences between scalars and vectors, to be able to represent vectors as directed line segments, to be able to add and subtract
 vectors diagrammatically, to understand the concept of the zero vector, to understand scalar multiplications of vectors. To be able to solve vector problems
using the sine and cosine rule.                                                                                                                                                                                                     Week 6
To use the unit vectors to represent vectors in three dimensions, to use direction cosines, to find angles between vectors and the coordinates axes, to be able to resolve a vector parallel to the x and y axes, to solve vector problems using resolution of vectors.

Topic C Integral Calculus

Topics Exercises
To understand the basic rules for antidifferentiation. To integrate polynomial functions,  To be able to determine the constant of integration
To evaluate definite integrals                                                                                                                                                                                                           Week 7
Set 1, 2 3
To find the area bounded by a curve and the x axis, To determine areas between two curves                                                                                          Week 8
To integrate basic trigonometric functions, To integrate basic exponential functions,                                                                                                         Week 9
Set 5, 6
To integrate functions involving logarithms, Integration by recognition                                                                                                                                   Week 10
Set 7,8
To use non-linear substitutions to determine integrals,  To evaluate definite integrals when using substitutions, To use the substitution
method or change of variable rule in integration.                                                                                                                                                                         Week 11
Set 9, 10, 12
To use numerical methods such as the left and right, hand rule, the midpoint rule and trapezoidal rule, to approximate areas.
To use linear substitutions to determine integrals                                                                                                                                                                      Week 12
Set 11
To determine volumes of solids of revolution, and find arc length of plane curves.                                                                                                              Week 13

Topic D Differential Equations

Introduction to differential equations, solving de’s classification, general and particular solutions, integrating factor, first order homogeneous types                                                                                                                                                                                                                                                                                                               Week 14

Applications of first-order differential equations, electrical problems, growth and decay, acceleration and velocity problems                                   Week 15

Topic E Numerical Methods

Topics Exercises
Solving non-linear equations, the fixed point or simple iteration method, the Newton-Raphson method, Set 1
Numerical integration, left, right, mid-point, trapziodal, Simpon’s rule, Set 2
Numerical solutions to differential equations, Euler’s method Set 3

Topic E Laboratory Techniques ( Including Numerical Methods )

Topics Exercises
Review of Excel spreadsheets, Using Excel to sketch graphs of cubics and trigonometric functions. Introduction to maple, using maple to sketch graphs. Lab 1
Using Excel to do basic statistics, find the mean and standard deviation of both grouped and ungrouped data, constructing histograms and pie-charts, simulation techniques, coin tossing and dice throwing. Lab 2
Using excel to sketch graphs of parametric equations and polar graphs. Lab 3
Using Excel to find determinants, using matrices to solve simultaneous equations in 3x3 , 4x4 and 5x5 cases.
Using maple to solve matrix equations and simultaneous equations. Lab 4
Numerical methods, using Excel to solve non-linear equations, using the fixed point or simple iteration method, the Newton-Raphson method. Lab 5
Numerical methods using Excel to find definite integrals, Numerical integration, left, right, mid-point, trapezoidal, Simpson’s rule. Using Maple to evaluate definite integrals, including left, right and mid-point numerical methods. Lab 6
Numerical solutions to differential equations, Euler’s method. Using Maple to solve first order differential equations, including integrating factor and homogeneous types. Lab 7

Learning Resources

Prescribed Texts


Other Resources

Prescribed text: While there are no prescribed text for this course, a set of notes, problem sheets and booklets will be handed out to students.
Recommended texts
Any first year text, or Specialist Mathematics Year 12 text, covering matrices, vectors and calculus.
Thomas & Finney Calculus and Analytic Geometry Stewart J. Calculus

Overview of Assessment

The student must demonstrate an understanding of all elements of a particular competency to be deemed competent.
Assessment will incorporate a variety of methods including written tests. There will be a Module Assignment, Laboratory Work and Final Theory Exam.

Assessment Tasks

Assessment for this course, includes
1 x 3 hour End of Semester exam on topics A, B and C below 70%
Laboratory Work 20%
Two assignments worth 5% each.
You have to obtain a satisfactory standard on each aspect of the course to pass the entire course.

Assessment Matrix

Course Overview: Access Course Overview