Course Title: Advanced Mathematics for Engineers

Part A: Course Overview

Course Title: Advanced Mathematics for Engineers

Credit Points: 12.00


Course Code




Learning Mode

Teaching Period(s)


City Campus


171H School of Science


Sem 1 2021

Course Coordinator: Dr. Michael Nyblom

Course Coordinator Phone: +61 3 9925 2189

Course Coordinator Email:

Course Coordinator Location: 15.04.18

Course Coordinator Availability: By appointment, by email

Pre-requisite Courses and Assumed Knowledge and Capabilities


Or equivalent first year university mathematics courses. 

Course Description

Advanced Mathematics for Engineering is a single semester course consisting of five main mathematics topics namely, Transforms (Laplace/Fourier), Vector Calculus, Matrices, Power Series and Numerical Analysis. The course content has been selected, in consultation with Engineering, to provide the necessary mathematical training that will assist and expand your learning experience. 

Objectives/Learning Outcomes/Capability Development

This course contributes to the following Program Learning Outcomes:

1.1 Comprehensive, theory-based understanding of the underpinning natural and physical sciences and the engineering fundamentals applicable to the engineering discipline;

1.2 Conceptual understanding of the, mathematics, numerical analysis, which underpin the engineering discipline;

1.3 In-depth understanding of specialist bodies of knowledge within the engineering discipline;

2.1 Application of established engineering methods to complex engineering problem solving;

2.2 Fluent application of engineering techniques, tools and resources;

2.3 Application of systematic engineering synthesis and design processes; and

3.2 Effective oral and written communication in professional and lay domains. 

On successful completion of this course, you would be expected to be able to:

CLO 1. Manipulate Laplace transforms and their inverses, effectively use tables of Laplace transforms and operational formulae and solve appropriate initial value problems.

CLO 2. Solve non-linear equations using various numerical methods and implement using a computer.

CLO 3. Estimate the solution of systems of ordinary differential equations or high order ordinary differential equations using various numerical methods and implement using a computer.

CLO 4. Manipulate Fourier transforms and their inverses, effectively use tables of Fourier transforms and operational formulae and solve appropriate differential equations using Fourier transforms.

CLO 5. Manipulate matrices, solve systems of linear equations, determine Eigen Vectors of square matrices.

CLO 6. Manipulate power series, determine radius of convergence.

CLO 7. Utilise Vector Calculus in the solution of engineering problems, effectively calculate line integrals, determine the derivative and integral of Vector valued functions and apply to calculating arc length. In addition, determine Grad, Div and Curl of vector valued functions. 

Overview of Learning Activities

Primarily face to face. However  an online course site will be used to disseminate course materials through lecture videos, and to provide you access to self-assessment exercises, a Weblearn assignment and written assignments.

The WebLearn assignment, for Laplace Transforms is designed to provide instant feedback and can be attempted repeatedly until proficiency in the learning objectives is achieved. Some WebLearn questions require answers to be entered using a specific syntax. Examples of this syntax are given in the Guide to WebLearn syntax, available from the course site. It is your responsibility to master the syntax before attempting the corresponding WebLearn assignment. Answers marked as incorrect, due to syntax errors, will not be remarked. In addition, there will be three written assignments, which will test your understanding of the remaining content of the course.

Exercises, with answers, are available to help you obtain proficiency in the course content 

Overview of Learning Resources

The Canvas site is where you will find: 

  • Teaching schedule and suggested reading
  • Assessment guide and assessment schedule.
  • Guide to WebLearn syntax.
  • Lecture recordings Recommended references.
  • Tables and formula sheets.
  • Exercises and answers. 

Overview of Assessment

Note: This course has no hurdle requirements.


Assessment Task 1: WebLearn Test (Laplace Transform)

Weighting 20%

This assessment task supports CLOs 1 


Assessment Task 2:  Interim In-class discipline assessment (Fourier and Vector Calculus)

Weighting 20%

This assessment task supports CLOs,4 & 7 


Assessment Task 3:  Interim In-class discipline assessment (Matrices and Power Series)

Weighting 20%

This assessment task supports CLO 5 & 6 


Assessment 4:  Authentic In-Class Practical Assessment (Week 12)

Weighting 40%   

This assessment supports CLO 1-7