Related Course/s:

A unit of study in the Bachelor of Engineering (Electrical and Electronic Engineering), Bachelor of Engineering (Electrical and Electronic Engineering) / Bachelor of Commerce, Bachelor of Engineering (Electronics and Computer Systems), Bachelor of Engineering (Electronics and Computer Systems)/ Bachelor of Science (Computer Science and Software Engineering), Bachelor of Engineering (Electronics and Computer Systems)/ Bachelor of Commerce, Bachelor of Engineering (Electronics and Computer Systems)/ Bachelor of Science (Biomedical Sciences), Bachelor of Engineering (Telecommunication and Network Engineering), Bachelor of Engineering (Telecommunication and Network Engineering)/ Bachelor of Science (Computer Science and Software Engineering).

Aims & Objectives:

After successfully completing this unit, you should be able to:

• Produce and interpret various graphical representations and summary statistics of datasets.
• Understand and apply basic concepts of probability, including calculating and interpreting unconditional and conditional probabilities.
• Recognise and use general and standard discrete and continuous probability distributions
• Calculate and interpret measures of location and dispersion for populations
• Understand and interpret quantile-quantile plots
• Understand the basic concepts of statistical inference, including confidence interval, sample size and hypothesis testing.
• Apply the basic concepts of statistical inference in various contexts e.g. inference on the mean, inference on proportion, investigating independence in two-way contingency tables, simple linear regression
• Understand and apply concepts in correlation and regression, including fitting, interpreting and applying simple linear regression models
• Understand and apply basic principles of statistical control theory
• Use a particular kind of graphics calculator and a particular statistics package to assist with the above objectives
• Operate with complex numbers
• Understand the concepts of function of a complex variable and analytic functions
• Find the images of curves and regions under complex mappings
• Evaluate simple z-transforms and their inverses
• Calculate by hand the eigenvalues and eigenvectors of a 2x2 and 3x3 matrix
• Classify a quadratic form and find its canonical form
• Calculate some simple matrix functions using the Cayley-Hamilton theorem
• Use a particular kind of graphics calculator and a particular mathematical computer package to assist with these and other mathematical objectives, including calculating the eigenvalues and eigenvectors of any square matrix

Teaching Methods:

Lectures (36 hrs), Tutorials (12 hrs), Computer Laboratories (12 hrs)

Assessment:

Tests/Assignments (30-45%), Examination (55-70%)

Generic Skills Outcomes:

• Ability to apply knowledge of basic science and engineering fundamental
• Ability to communicate effectively, not only with engineers but also with the community at large
• Ability to undertake problem identification, formulation and solution

Content:

• Matrix Analysis: The eigenvalue problem, numerical methods, reduction to canonical form, functions of a matrix, engineering application
• Functions of a Complex Variable: Complex functions and mappings, complex differentiation, complex series, singularities, zeros and residues, contour integration, z-transform: properties and uses, engineering application
• Applied Probability and Statistics: Exploratory data analysis, probability, random variables and probability distributions, important practical distributions, quantile-quantile plots, estimating parameters, hypothesis testing, correlation and regression, goodness-of-fit tests, statistical quality control

Note: A Statistics package and a Mathematics package will be used in this unit. Students will be expected to have access to a particular kind of graphics calculator.

References: