Unit of study_

# AMME2000: Engineering Analysis

## Overview

This course is designed to provide students with the necessary tools for mathematically modelling and solving problems in engineering. Engineering methods will be considered for a range of canonical problems including; Conduction heat transfer in one and two dimensions, vibration, stress and deflection analysis, convection and stability problems. The focus will be on real problems, deriving analytical solutions via separation of variables; Fourier series and Fourier transforms; Laplace transforms; scaling and solving numerically using finite differences, finite element and finite volume approaches.

### Details

Academic unit Aerospace, Mechanical and Mechatronic AMME2000 Engineering Analysis Semester 1, 2020 Normal day Camperdown/Darlington, Sydney 6

### Enrolment rules

 Prohibitions ? None (MATH1001 OR MATH1021 OR MATH1901 OR MATH1921 OR MATH1906 OR MATH1931) AND (MATH1002 OR MATH1902) AND (MATH1003 OR MATH1023 OR MATH1903 OR MATH1923 OR MATH1907 OR MATH1933) AND (ENGG1801 OR INFO1103 OR INFO1903 OR INFO1110 OR INFO1910 OR DATA1002 OR DATA1902) None Yes

### Teaching staff and contact details

Coordinator Ben Thornber, ben.thornber@sydney.edu.au

## Assessment

Type Description Weight Due Length
Assignment Weekly pre-work
5% - n/a
Outcomes assessed:
Final exam Exam
Delivered online through Canvas
45% Formal exam period 2 hours
Outcomes assessed:
Assignment Tutorial question - total for all tuts
10% Multiple weeks n/a
Outcomes assessed:
Tutorial quiz Quiz 1
Delivered online using Canvas in Thursday Week 4, 12-1pm
10% Week 04 1 hour
Outcomes assessed:
Assignment Assignment 1
10% Week 06 n/a
Outcomes assessed:
Tutorial quiz Quiz 2
Delivered online using Canvas in Thursday Week 10, 12-1pm.
10% Week 10 1hr
Outcomes assessed:
Assignment Assignment 2
10% Week 12 n/a
Outcomes assessed:
• Assignment 1: Analytical and numerical solution of the heat or wave diffusion equation.
• Assignment 2: Analytical and numerical solution of the Laplace Equation
• Quiz 1: Material in Sections 1 and 2 of the lecture notes
• Quiz 2: Analytical solutions to the heat, wave, Laplace/Poisson equations, integrals and transforms.
• Tutorial question: One exercise from each tutorial must be completed by 9 am Tuesday of the following week. A student completing all exercises successfully will gain 10%.
• Weekly pre-work: This mark is based on a short exercise or quiz, based on the pre-work, to be completed prior to the lectures that week.
Detailed information for each assessment can be found on Canvas.

### Assessment criteria

The University awards common result grades, set out in the Coursework Policy 2014 (Schedule 1).

As a general guide, a high distinction indicates work of an exceptional standard, a distinction a very high standard, a credit a good standard, and a pass an acceptable standard.

Result name

Mark range

Description

High distinction

85 - 100

Distinction

75 - 84

Credit

65 - 74

Pass

50 - 64

Fail

0 - 49

When you don’t meet the learning outcomes of the unit to a satisfactory standard.

### Late submission

In accordance with University policy, these penalties apply when written work is submitted after 11:59pm on the due date:

• Deduction of 5% of the maximum mark for each calendar day after the due date.
• After ten calendar days late, a mark of zero will be awarded.

### Special consideration

If you experience short-term circumstances beyond your control, such as illness, injury or misadventure or if you have essential commitments which impact your preparation or performance in an assessment, you may be eligible for special consideration or special arrangements.

The Current Student website provides information on academic honesty, academic dishonesty, and the resources available to all students.

The University expects students and staff to act ethically and honestly and will treat all allegations of academic dishonesty or plagiarism seriously.

We use similarity detection software to detect potential instances of plagiarism or other forms of academic dishonesty. If such matches indicate evidence of plagiarism or other forms of dishonesty, your teacher is required to report your work for further investigation.

## Weekly schedule

WK Topic Learning activity Learning outcomes
Week 01 1. Introduction to the UoS; 2. Introduction to numerical methods; 3. Discretisation; 4. Interpolation; 5. Least squares; 6. Cubic Splines; 7. Taylor series; 8. Finite differences Lecture (2 hr)
Week 02 1. What is a PDE?; 2. Generic PDE introduction inc. classification; 3. Derivation of the heat diffusion equation; 4. Exact solution of the heat diffusion equation (Fourier series); 5. Solution of heat equation via separation of variables; 6. Heat equation with non-homogeneous boundary conditions Lecture (2 hr)
Week 03 1. Initial value problems, boundary value problems, initial conditions, boundary conditions, well posed problems; 2. Accuracy, stability, consistency; 3. Linear algebra; Lecture (2 hr)
Week 04 Forward time centred space solution of the heat diffusion equation. Lecture (2 hr)
Week 05 1. Heat equation with more complex initial and boundary conditions; 2. Introduction to and derivation of the wave equation; 3. Classification of wave-like equations; 4. Approximate solution using Fourier series Lecture (2 hr)
Week 06 1. Wave equation with complex initial conditions; 2. Numerical solution of the wave equation. Lecture (2 hr)
Week 07 1. Introduction and derivation of the Laplace and Poisson equation; 2. Applications; 3. Exact solution based on Fourier series. 4. Numerical discretization of the 2D Laplace equation; 5. Solution using iterative methods; Lecture (2 hr)
Week 08 1. Understanding PDEs - method to determine behaviour. 2. Fourier integrals and transforms; Lecture (2 hr)
Week 09 1. Fourier integral solutions to infinite problems; 2. FFT and Signal Processing; 3. Fourier Transform solutions to PDEs. Lecture (2 hr)
Week 10 1. Laplace transforms; 2. Solution of the semi-infinite wave equation using Laplace transforms Lecture (2 hr)
Week 11 1. Laplace Transform solution to the heat equation; 2. Introduction to finite elements; Lecture (2 hr)
Week 12 1. Piecewise linear basis functions; 2. Method of weighted residuals; 3. Weak formulation of the PDE and solution. Lecture (2 hr)
Week 13 1. Foundations of stress analysis; 2. FEA solution for an axially loaded bar Lecture (2 hr)

### Study commitment

Typically, there is a minimum expectation of 1.5-2 hours of student effort per week per credit point for units of study offered over a full semester. For a 6 credit point unit, this equates to roughly 120-150 hours of student effort in total.

All readings for this unit can be accessed on the Library eReserve link available on Canvas.

• Advanced Engineering Mathematics, E. Kreyszig, 10th Edition, Wiley, 2011.

## Learning outcomes

Learning outcomes are what students know, understand and are able to do on completion of a unit of study. They are aligned with the University’s graduate qualities and are assessed as part of the curriculum.

At the completion of this unit, you should be able to:

• LO1. understand and apply the physical relations and mathematical modelling of fundamental problems in engineering structures, fluid mechanics and heat and mass transfer.
• LO2. creatively solve assignment problems, which focus on real-life engineering challenges
• LO3. have developed proficiency in a structured approach to engineering problem identification, modelling and solution; develop proficiency in translating a written problem into a set of algorithmic steps, and then into computer code to obtain a solution

The graduate qualities are the qualities and skills that all University of Sydney graduates must demonstrate on successful completion of an award course. As a future Sydney graduate, the set of qualities have been designed to equip you for the contemporary world.

 GQ1 Depth of disciplinary expertise Deep disciplinary expertise is the ability to integrate and rigorously apply knowledge, understanding and skills of a recognised discipline defined by scholarly activity, as well as familiarity with evolving practice of the discipline. GQ2 Critical thinking and problem solving Critical thinking and problem solving are the questioning of ideas, evidence and assumptions in order to propose and evaluate hypotheses or alternative arguments before formulating a conclusion or a solution to an identified problem. GQ3 Oral and written communication Effective communication, in both oral and written form, is the clear exchange of meaning in a manner that is appropriate to audience and context. GQ4 Information and digital literacy Information and digital literacy is the ability to locate, interpret, evaluate, manage, adapt, integrate, create and convey information using appropriate resources, tools and strategies. GQ5 Inventiveness Generating novel ideas and solutions. GQ6 Cultural competence Cultural Competence is the ability to actively, ethically, respectfully, and successfully engage across and between cultures. In the Australian context, this includes and celebrates Aboriginal and Torres Strait Islander cultures, knowledge systems, and a mature understanding of contemporary issues. GQ7 Interdisciplinary effectiveness Interdisciplinary effectiveness is the integration and synthesis of multiple viewpoints and practices, working effectively across disciplinary boundaries. GQ8 Integrated professional, ethical, and personal identity An integrated professional, ethical and personal identity is understanding the interaction between one’s personal and professional selves in an ethical context. GQ9 Influence Engaging others in a process, idea or vision.