Related Course/s:

A unit of study in the Bachelor of Engineering (Mechanical Engineering), Bachelor of Engineering (Mechanical) / Bachelor of Commerce, Bachelor of Engineering (Robotics and Mechatronics), Bachelor of Engineering (Robotics and Mechatronics)/ Bachelor of Commerce and Bachelor of Engineering (Robotics and Mechatronics)/ Bachelor of Science (Computer Science and Software Engineering)

Aims & Objectives:

This unit aims to: 

• Introduce students to the computer package Mathematica
• Provide students with mathematical and statistical knowledge and skills to support their concurrent and subsequent engineering studies

• Obtain Fourier series for simple periodic functions
• Calculate Laplace transforms and inverse Laplace transforms and use them to solve differential equations
• Understand the concept of analytic functions of a complex variable
• Determine the images of curves under simple complex mappings
• Apply Mathematica in all of the above fields
• 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 discrete and continuous probability distributions
• Calculate and interpret measures of location and dispersion for populations
• Use a particular kind of graphics calculator and a particular statistics package to assist with the above objectives

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 fundamentals
• Ability to communicate effectively, not only with engineers but also with the community at large
• Ability to undertake problem identification, formulation and solution

Content:

• Introduction to Mathematica.
  
• Fourier series: Fourier series expansion, functions defined over a finite interval, differentiation and integration of Fourier series, engineering application.
  
• Functions of a complex variable: Complex functions and mappings, complex differentiation, complex series, singularities, zeros and residues, contour integration, engineering application.
  
• Laplace transforms: The Laplace transform, properties of the Laplace transform, solution of differential equations, step and impulse functions, transfer functions, engineering application.
  
• Applied probability and statistics: Probabilities of random events, random variables, the Central Limit Theorem, important practical distributions, estimating parameters, control charts, Poisson processes and simple queues, engineering application.

Textbooks:

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