Outline

Overview

BMET2960 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 mathematical tools covered in the lectures include: 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. There is a strong emphasis in both the lectures and tutorials on applying these mathematical methods to real biomedical engineering problems involving electrical, mechanical, thermal and chemical mechanisms in the human body. Specific examples include heat regulation, vibrations in biological systems, and the analysis of physiological signals such as ECG and EEG.

Unit details and rules

Academic unit	Biomedical Engineering
Credit points	6
Prerequisites ?	(MATH1001 OR MATH1021 OR MATH1901 OR MATH1921) AND (MATH1002 OR MATH1902) AND (MATH1003 OR MATH1023 OR MATH1903 OR MATH1923)
Corequisites ?	None
Prohibitions ?	AMME2960
Assumed knowledge ?	(AMME1960 OR BMET1960) AND (AMME1961 OR BMET1961)
Available to study abroad and exchange students	Yes

Teaching staff

Coordinator	Andre Kyme, andre.kyme@sydney.edu.au

Type	Description	Weight	Due	Length
Final exam	Final exam n/a	45%	Formal exam period	2 hours
Outcomes assessed:
Assignment	Weekly Pre-Lecture Quiz Weekly online quiz	5%	Multiple weeks	n/a
Outcomes assessed:
Assignment	Tutorials Assessment Weekly online tutorial assessment	10%	Multiple weeks	n/a
Outcomes assessed:
Small test	Mid-Semester Quiz 1 In-class quiz	10%	Week 04 Due date: 19 Mar 2020 at 12:00	50 min
Outcomes assessed:
Assignment	Assignment 1 Assignment 1	10%	Week 06	n/a
Outcomes assessed:
Small test	Mid-Semester Quiz 2 In-class quiz	10%	Week 10 Due date: 07 May 2020 at 12:00	50 min
Outcomes assessed:
Assignment	Assignment 2 Assignment 2	10%	Week 12	n/a
Outcomes assessed:

Assessment summary

Assignment 1 (10%): Analytical and numerical solution of the heat diffusion or wave equation.
Assignment 2 (10%): Analytical and numerical solution of the Laplace equation.
Quiz 1 (10%): Material is Sections 1 and 2 of the lecture notes.
Quiz 2 (10%): Analytical solutions to the heat, wave, Laplace/Poisson equations, integrals and transforms.
Weekly pre-lecture quizzes (5%): A short, weekly, online quiz based on the pre-lecture work for the week and to be completed prior to the lectures that week.
Tutorial assessment (10%): 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%.
Final exam (45%): 2-hour written exam.

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.

For more information see guide to grades.

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.

This unit has an exception to the standard University policy or supplementary information has been provided by the unit coordinator. This information is displayed below:

5% per day

Academic integrity

The Current Student website provides information on academic integrity 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 integrity breaches seriously.

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

Use of generative artificial intelligence (AI) and automated writing tools

You may only use generative AI and automated writing tools in assessment tasks if you are permitted to by your unit coordinator. If you do use these tools, you must acknowledge this in your work, either in a footnote or an acknowledgement section. The assessment instructions or unit outline will give guidance of the types of tools that are permitted and how the tools should be used.

Your final submitted work must be your own, original work. You must acknowledge any use of generative AI tools that have been used in the assessment, and any material that forms part of your submission must be appropriately referenced. For guidance on how to acknowledge the use of AI, please refer to the AI in Education Canvas site.

The unapproved use of these tools or unacknowledged use will be considered a breach of the Academic Integrity Policy and penalties may apply.

Studiosity is permitted unless otherwise indicated by the unit coordinator. The use of this service must be acknowledged in your submission as detailed on the Learning Hub’s Canvas page.

Outside assessment tasks, generative AI tools may be used to support your learning. The AI in Education Canvas site contains a number of productive ways that students are using AI to improve their learning.

Learning support

Simple extensions

If you encounter a problem submitting your work on time, you may be able to apply for an extension of five calendar days through a simple extension.  The application process will be different depending on the type of assessment and extensions cannot be granted for some assessment types like exams.

Special consideration

If exceptional circumstances mean you can’t complete an assessment, you need consideration for a longer period of time, or if you have essential commitments which impact your performance in an assessment, you may be eligible for special consideration or special arrangements.

Special consideration applications will not be affected by a simple extension application.

Using AI responsibly

Co-created with students, AI in Education includes lots of helpful examples of how students use generative AI tools to support their learning. It explains how generative AI works, the different tools available and how to use them responsibly and productively.

Weekly schedule

WK	Topic	Learning activity
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	1. Forward-in-time centred-in-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 wavelike 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 11	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.

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.

Outcomes
Graduate qualities

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 applications
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

Graduate qualities

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.

Outcome map

Learning outcomes	Graduate qualities
Learning outcomes

Responding to student feedback

This section outlines changes made to this unit following staff and student reviews.

Bringing the Laplace equation forward so that students understand better the connections and differences in solutions with heat/wave using Fourier Series. Including a new video lecture on the characteristic equation and how it results in different solutions An analytical practice problem will be covered in the tutorial each week Moving from 3 assignments and 1 quiz, to 2 quizzes and 2 assignments to ensure that key material presented early is bedded in for the rest of the UoS. Provide a forum to go over assignment solutions following marking Make assignment rubric available before submission Consolidated FEA materials The catch-up tutorial is now at 5pm instead of 6pm

Disclaimer

The University reserves the right to amend units of study or no longer offer certain units, including where there are low enrolment numbers.

To help you understand common terms that we use at the University, we offer an online glossary.

Current students

Overview

Overview

Unit details and rules

Teaching staff

Assessment

Assessment

Assessment summary

Assessment criteria

Late submission

Academic integrity

Learning support

Learning support

Simple extensions

Special consideration

Using AI responsibly

Weekly schedule

Weekly schedule

Study commitment

Learning outcomes

Learning outcomes

Graduate qualities

Outcome map

Responding to student feedback

Responding to student feedback

Disclaimer

On this page

Useful links

Media

Student links

About us

Connect

Current students

BMET2960: Biomedical Engineering 2

Semester 1, 2020 [Normal day] - Camperdown/Darlington, Sydney

Overview

Overview

Unit details and rules

Teaching staff

Assessment

Assessment

Assessment summary

Assessment criteria

Late submission

Academic integrity

Learning support

Learning support

Simple extensions

Special consideration

Using AI responsibly

Weekly schedule

Weekly schedule

Study commitment

Learning outcomes

Learning outcomes

Graduate qualities

Outcome map

Responding to student feedback

Responding to student feedback

Disclaimer

On this page

Useful links

Media

Student links

About us

Connect