Last Updated S022020

DEng 603

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

 

Doctor of Engineering

Duration 3 years
Year Level One
Unit Creator / Reviewer Dr. Srinivas Shastri Sitharamarao
Core/Sub-Discipline: Core
Pre/Co-requisites N/A 
Credit Points

 

4

 

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: http://www.thwink.org/sustain/glossary/SystemsThinking.htm ). 

 

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)

Polya, G., How to Solve It: A new aspect of mathematical method, Second Edition, Princeton University press, ISBN 9780691164076  (Useful reference book for entire course). 

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

Reference Materials

As advised during the class.  

Software Reference Material

EndNoteTM software for constructing reference lists, bibliography (www.endnote.com)

MATLAB

SIMULINK

Microsoft Excel

Other tools as advised

 

Unit Content

Topic 1 

Introduction to Problem Solving

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

  1. Defining an engineering system: Deterministic and complex systems
  2. Generality: What is the unknown; what are the data; what is / are the condition(s).
  3. Common sense: What is this and how can it be applied?
  4. Critical questioning
  5. Four phases of problem solving: Understand the problem; how are the various items connected (unknown linked to the data?), using this information to formulate a plan; verify and validate the solution (looking back).

A key challenge is to know where to start, and then asking the question of what can one do?  These questions lead to a question – research methodology and the need to break down into manageable steps. 

 

Topic 2

Problem solving examples

  1. Revision of topic 1: The application of concepts discussed previously through a number of examples. These are thought problems but require depth of analysis. Ask critical questions and fall back on the concepts discussed in Topic 1.
  2. Problem solving Examples: Specifically, students are expected to come prepared with problems starting on page 234 will be explored. This topic discusses design questions in engineering projects / applications as per the book by Polya.

Topic 3

Revision of mathematical modelling and simulation

  1. Revision of mathematical modelling
  2. Revision of Simulation
  3. Development of mathematical models: This topic will consider the development of mathematical models. A higher engineering mathematics textbook will be used for the , development of mathematical models from first principles. Simulation of the mathematical models: A paper by Anu Maria (Introduction to Modeling and Simulation) will be used to understand the concepts of modelling and simulation.  Throughout each topic, the principles of Polya are referenced and reinforced to build mathematical models. Systems will be discussed and a model will be developed.

 

Topic 4

Revision of Mathematical methods

  1. Ordinary Differential Equations
  2. Linear Algebra and Vector Calculus, Fourier Analysis, Partial Differential Equations
  3. Complex Analysis
  4. Numeric Analysis
  5. Example/s

 

Topic 5

Mathematical model development Problem 1

  1. Problem statement
  2. Develop mathematical model

 

Topic 6 

Mathematical model development Problem 2

  1. Problem statement
  2. Develop mathematical model

 

Topic 7

Mathematical model development Problem 3

  1. Problem statement
  2. Develop mathematical model

 

Topic 8

Mathematical model development Problem 4

  1. Problem statement
  2. Develop mathematical model

 

Topic 9

Complex systems

  1. Identification of system (Deterministic or complex)
  2. Nature of data, quality and quantity of data required.
  3. Data analysis and Probability theory
  4. Optimisation
  5. Mathematical statistics

 

Topic 10

Complex system Problem/s

  1. Problem statement
  2. Solve complex system

 

Topic 11 and 12

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

  1. The use of tools such as MATLAB/SIMULINK
  2. Use of spread sheeting software

 

 

Software/Hardware Used

Software

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

Hardware

  • N/A