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:

- Design and identify systems

*Bloom’s Level 6*

- Produce a structured thought process to engineering solutions

*Bloom’s Level 6*

- Recommend relevant mathematical methods towards systems’ definition

*Bloom’s Level 5*

- Evaluate and apply relevant software tools

*Bloom’s Level 5*

- 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 |

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 90 |
After topic 4 | 20% | 1, 2,3 |

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 |

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, 10^{th} Edition, August 2011, Wiley, ISBN 978-1-118-26670-0

Reference Materials

As advised during the class.

Software Reference Material

EndNote^{TM} 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:

- Defining an engineering system: Deterministic and complex systems
- Generality: What is the unknown; what are the data; what is / are the condition(s).
- Common sense: What is this and how can it be applied?
- Critical questioning
- 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*

- 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.
- 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*

- Revision of mathematical modelling
- Revision of Simulation
- 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*

- Ordinary Differential Equations
- Linear Algebra and Vector Calculus, Fourier Analysis, Partial Differential Equations
- Complex Analysis
- Numeric Analysis
- Example/s

#### Topic 5

*Mathematical model development Problem 1*

- Problem statement
- Develop mathematical model

#### Topic 6

*Mathematical model development Problem 2*

- Problem statement
- Develop mathematical model

#### Topic 7

*Mathematical model development Problem 3*

- Problem statement
- Develop mathematical model

#### Topic 8

*Mathematical model development Problem 4*

- Problem statement
- Develop mathematical model

#### Topic 9

*Complex systems*

- Identification of system (Deterministic or complex)
- Nature of data, quality and quantity of data required.
- Data analysis and Probability theory
- Optimisation
- Mathematical statistics

#### Topic 10

*Complex system Problem/s*

- Problem statement
- 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:

- The use of tools such as MATLAB/SIMULINK
- 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