Course Title: Design complex algorithms using mathematical and scientific principles

Part B: Course Detail

Teaching Period: Term1 2009

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:

OH&S requirements for carrying out the work are followed.
Model of the process is created.
Appropriate computations are performed.
If appropriate, relevant computer appliication software is used to aid solution.
Decisions for dealing with unexpected situations are made from discussions with appropriate personnel, job specifications and enterprise procedures.
Methods for dealing with unexpected situations are selected on the basis of safety and specified work outcomes.


Identify the process for applying mathematical/scientific principles

Performance Criteria:

OH&S and environmental requirements for a given work area are obtained and understood.
The process is determined through analysis of a real-life or laboratory situation.
The requests, design briefs or equivalent are clarified with the appropriate personnel.
Where appropriate, expert advice is sought with respect to the process and according to enterprise procedures.


Select appropriate mathematical/scientific method

Performance Criteria:

OH&S requirements for carrying out the work are followed.
Industry codes, regulations and technical documentation relevant to the process are interpreted and understood.
Where appropriate, tables, graphs and software packages are used to obtain computational data.
The appropriate assumptions underlying the solution are made and recorded.
Resources required are identified, obtained and checked as fit for purpose.
The most appropriate method of modeling is selected and can be justified.


Verify and interpret results

Performance Criteria:

OH&S requirements for completing the work are followed.
Results are verified, interpreted and discussed with appropriate personnel.
Results are documented, graphed or charted.

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 7,8  . Set 1, 2 3
To find the area bounded by a curve and the x axis, To determine areas between two curves, Week 9, Set  4
To integrate basic trigonometric functions, To integrate basic exponential functions, Week 10, Set 5, 6
To integrate functions involving logarithms, Integration by recognition, Week 11, 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 12  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 13, Set 11
To determine volumes of solids of revolution, and find arc length of plane curves, Week 14
Topic D Differential Equations
Introduction to differential equations, solving de’s classification, general and particular solutions, integrating factor, first order homogeneous types ,Week 15
Applications of first-order differential equations, electrical problems, growth and decay, acceleration and velocity problems,Week 16
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 2 hour Mid-Semester Exam Topics A and B 30%     1 x 2 hour End of Semester exam Topics C and D  30%
Laboratory Work 20%
Two assignments worth 10% 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