Last Updated S022020

DEng 603

Unit Name Applied Mathematical Modelling and Simulation
Unit Code DENG603
Unit Duration 12 weeks


Doctor of Engineering

Duration 3 years
Year Level One
Unit Creator / Reviewer Dr Ali Marzoughi / Dr Milind Siddhpura



Core/Sub-Discipline: Core
Pre/Co-requisites N/A 
Credit Points




Total Program Credit Points 120
Mode of Delivery Online or on-campus. 
Unit Workload

10 hours per week:

Lecture - 1 hour

Tutorial - 1 hour

Assessments / Practical / Lab - 1 hour (where applicable)

Personal Study recommended - 7 hours (guided and unguided)

Unit Description and General Aims

This unit is a graduate level foundation unit for any engineering discipline.  The unit aims to apply mathematical modelling and simulation as well as a multidisciplinary approach to analysing engineering problems. 

A systems approach is thus the identification of inherent relationships and building a useful model to analyse engineering systems. Systems thinking is a way of thinking about, and a language for describing and understanding, the forces and interrelationships that shape the behaviour of systems. This helps us to see how to change systems more effectively, and to act more in tune with the processes of the natural and economic world. (ref: ). 


Advanced studies in Engineering will focus on characterising systems and the application of relevant mathematical methods to bring forth underlying relationships.


Learning Outcomes


On successful completion of this Unit, students are expected to be able to:

  1. Design and identify systems

Bloom’s Level 6

  1. Produce a structured thought process to engineering solutions

Bloom’s Level 6

  1. Recommend relevant mathematical methods towards systems’ definition

Bloom’s Level 5

  1. Evaluate and apply relevant software tools

Bloom’s Level 5

  1. Hypothesise, consolidate, present and apply models and simulations

Bloom’s Level 6

Bloom’s Taxonomy

The cognitive domain levels of Bloom’s Taxonomy:

Bloom's level Bloom's category Description
1 Remember Retrieve relevant knowledge from long-term memory by recognising, identifying, recalling and retrieving
2 Understand Construct meaning from instructional messages by interpreting, classifying, summarising, inferring, comparing, contrasting, mapping and explaining.
3 Apply Carrying out or using a procedure in a given situation by executing, implementing, operating, developing, illustrating, practicing and demonstrating.
4 Analyse Deconstruct material and determine how the parts relate to one another and to an overall structure or purpose by differentiating, organising and attributing.
5 Evaluate Make judgments based on criteria and standards by checking, coordinating, evaluating, recommending, validating, testing, critiquing and judging.
6 Create Put elements together to form a coherent pattern or functional whole by generating, hypothesising, designing, planning, producing and constructing.

Student assessment

Assessment Type When assessed Weighting (% of total unit marks) Learning Outcomes Assessed

Assessment 1

Type: System Definition

Word length: 1000 to 2000

Consider an engineering system – for example a saucepan containing water at room temperature.  This water is to be heated to 90oC.  What are the various processes occurring that describe the system completely?  Complement your answer with a mind map (free tools are available on the net).  What are the mathematical equations?  What assumptions have been built in and what are the system boundaries? Consider both steady and dynamic states.

After topic 4 20% 1, 2,3

Assessment 2


Type: Engineering Application (Mid-project) + Presentation

Word length: 2000 + code + working program

Consider a complex engineering problem in consultation with your facilitator. In your report detail the development of the equations. What were the underlying assumptions, how did you identify the system boundaries?  How did you solve your equations? Provide numerical details as well as code that can be run in an available software package.  What conclusions can you draw and what are the limitations of what you have done?
Due after Topic 8 30% 3,4,5

Assessment 3


Type: Engineering Application (Final Project)

Word length: 2500 + code + working program

In consultation with your facilitator consider a sufficiently complex engineering or other problem where deterministic relationships are not that evident.  Using some of the stochastic methods discussed identify underlying relationships.  Compare and contrast the deterministic versus stochastic approach and identify where you would use one over the other
Final week  50% 3,4

Prescribed and Recommended Readings

Required Textbook(s)

KLUEVER, C. A., Dynamic systems: modelling, simulation, and control, 2nd Edition, 2019, Wiley, ISBN 978-1-119-60186-7.  


Recommended Textbook(s):

Kreyszig, E., Advanced Engineering Mathematics, 10th Edition, August 2011, Wiley, ISBN 978-1-118-26670-0

Polya, G., How to Solve It: A new aspect of mathematical method, Second Edition, Princeton University press, ISBN 9780691164076  


Reference Materials

As advised during the class.  

Software Reference Material

Mendeley or EndNoteTM software for constructing reference lists, bibliography (, (



Microsoft Excel

Other tools as advised


Unit Content

Topic 1 

Introduction to dynamic systems

This topic focuses on systems definition and analysis through problem solving process. To assist in the understanding, relatively simple but fundamental systems will be chosen to discuss following key concepts:

  1. Different types of engineering systems: Distributed, Lumped, Continues, Discrete-time, Time varying, Time invariant and Nonlinear systems.
  2. How to model dynamic systems (Mechanical Systems). In this topic, students learn the fundamental engineering mathematical model of some practical mechanical systems. They will learn how to use mathematical model of simple mechanical systems to solve the complex systems in practice.

Topic 2

How to model dynamic systems

  1. Mathematical modelling of Electrical and Electromechanical systems. 
  2. Mathematical modelling of Fluid and Thermal systems.
  3. Mathematical modelling for fundamental engineering systems such as electrical and electromechanical, fluid and hydraulic systems will be continued in this section. This is essential for the engineers at this level to know how to model different types of equipment which is used in the industry.


Topic 3

Standard mathematical models for dynamic systems

  1. State-Space representation
  2. Linearization
  3. Transfer function and block diagrams
  4. Standard I/O functions

Topic 4

On linear dynamic systems and their analytical solutions

  1. Ordinary Differential Equations. 
  2. First-order, Second order, and Higher-order systems.
  3. Eigenvalues and State-space representation. 
  4. Simplified model.


Topic 5

Dynamic system analysis

  1. Laplace transformation
  2. Inverse Laplace transformation
  3. Application of Laplace Transformation on Analysis Dynamic Systems

Topic 6 

System Response

  1. Transient Response and steady-state response for first-order and second-order systems. 
  2. Frequency response 
  3. Analytical solution of the state equation.
  4. Response to non-linear systems


Topic 7

Introduction to control systems

  1. Feedback control systems and type of controllers
  2. Time-domain performance specifications
  3. Frequency-domain performance specifications
  4. System identification based on transfer function


Topic 8

Mathematical model and control of physical systems (Case Study1)

  1. Vibration Isolation System for a Commercial Vehicle

Topic 9

Mathematical model and control of physical systems (Case Study2)

  1. Mathematical model and feedback control design for a hydraulic servomechanism control


Topic 10

Mathematical model and control of physical systems (Case Study3)

  1. Armature controlled DC motor


Topics 11 and 12

These remaining topics will revisit the software tools and address any pending concerns. Key areas to be addressed during this period:

  1. An example of a non-deterministic simulation technique (e.g., Mont Carlo Simulation, ...)
  2. The use of tools such as MATLAB/SIMULINK


Engineers Australia

The Australian Engineering Stage 1 Competency Standards for the Professional Engineer, approved as of 2013. This table is referenced in the mapping of graduate attributes to learning outcomes and via the learning outcomes to student assessment.

Stage 1 Competencies and Elements Competency
1. Knowledge and Skill Base
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, statistics, and computer and information sciences which underpin the engineering discipline.
1.3 In-depth understanding of specialist bodies of knowledge within the engineering discipline.
1.4 Discernment of knowledge development and research directions within the engineering discipline.
1.5 Knowledge of engineering design practice and contextual factors impacting the engineering discipline.
1.6 Understanding of the scope, principles, norms, accountabilities and bounds of sustainable engineering practice in the specific discipline.
2. Engineering Application Ability
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.
2.4 Application of systematic approaches to the conduct and management of engineering projects.
3. Professional and Personal Attributes
3.1 Ethical conduct and professional accountability.
3.2 Effective oral and written communication in professional and lay domains.
3.3 Creative, innovative and pro-active demeanor.
3.4 Professional use and management of information.
3.5 Orderly management of self and professional conduct.
3.6 Effective team membership and team leadership.

Software/Hardware Used


  • Software: MATLAB, SIMULINK
  • Version: N/A
  • Instructions: N/A 
  • Additional resources or files: N/A


  • N/A