BMET9960: Semester 1, 2021

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Units BMET9960 Semester 1 2021 [Normal day]

Unit of study_

BMET9960: Biomedical Engineering Mathematical Modelling

Semester 1, 2021 [Normal day] - Remote

Overview

BMET9960 is designed to equip you with the necessary tools to mathematically model and solve a range of canonical problems in engineering: conduction heat transfer, vibration, stress and deflection analysis, convection and stability. You will learn how to compute analytical and numerical solutions to these problems, and then apply this to relevant and interesting biomedical examples. By the end of this unit you will know how to derive analytical solutions via separation of variables, Fourier series and Fourier transforms and Laplace transforms. You will also know how to solve the same problems numerically using finite difference, finite element and finite volume approaches. The theoretical component of the unit is complemented by tutorials where you will learn how to use Matlab to implement and visualise your solutions. There is plenty of support in the early weeks of the unit to refresh your Matlab knowledge, or to learn Matlab for the first time if you've had no prior experience. Gaining a good working knowledge of Matlab to solve engineering problems and explore the solution space of these problems is one of the key benefits of this unit - it will set you up very well for future units requiring programming expertise! There is a strong emphasis in both the lectures and tutorials on example-based learning - you will see and attempt many different examples involving a wide range of biomedical applications. Applications include electrical, mechanical, thermal and chemical mechanisms in the human body and specific examples include heat regulation, vibrations of biological systems, and analysis of physiological signals such as ECG and EEG. This is a challenging but very rewarding unit and you'll come away feeling well-equipped with useful tools for your future engineering career. We hope you enjoy it!

Unit details and rules

Unit code	BMET9960
Academic unit	Biomedical Engineering
Credit points	6
Prohibitions ?	BMET2960 or AMME2960
Prerequisites ?	None
Corequisites ?	None
Assumed knowledge ?	Undergraduate mathematics (1000-level) and an appreciation of the biomedical engineering process
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 (Open book)	Final exam Type C	40%	Formal exam period	2 hours
Outcomes assessed:
Small test	Mid-Semester Quiz 1 In-class quiz	10%	Week 04 Due date: 25 Mar 2021 at 12:00	60 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: 13 May 2021 at 12:00	60 min
Outcomes assessed:
Assignment	Assignment 2 Assignment 2	15%	Week 12	n/a
Outcomes assessed:
Online task	Wekly Pre-Lecture Quiz Weekly online quiz	5%	Weekly	n/a
Outcomes assessed:
Assignment	Tutorials Assessment Weekly online tutorial assessment	10%	Weekly	n/a
Outcomes assessed:
= Type C final exam ?

Assessment summary

Assignment 1 (10%): Analytical and numerical solution of the heat diffusion equation.
Assignment 2 (15%): Analytical and numerical solution of the Laplace equation.
Quiz 1 (10%): Students will be advised what is examinable.
Quiz 2 (10%): Students will be advised what is examinable.
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 (40%): 2-hour written exam.

Detailed information for each assessment can be found on Canvas.

Assessment criteria

See Canvas for details

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.

You may only use artificial intelligence and writing assistance tools in assessment tasks if you are permitted to by your unit coordinator, and if you do use them, you must also acknowledge this in your work, either in a footnote or an acknowledgement section.

Studiosity is permitted for postgraduate units unless otherwise indicated by the unit coordinator. The use of this service must be acknowledged in your submission.

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 01	Introduction to Matlab	Tutorial (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 02	Numerical methods, Taylor series, PDEs and interpolation	Tutorial (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 03	Analytical solution to heat equation	Tutorial (2 hr)
Week 04	1. Forward-in-time centred-in-space solution of the heat diffusion equation.	Lecture (2 hr)
Week 04	Numerical solution to heat equation	Tutorial (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 05	Solution to heat equation with more complex BCs	Tutorial (2 hr)
Week 06	1. Wave equation with complex initial conditions; 2. Numerical solution of the wave equation.	Lecture (2 hr)
Week 06	Analytical solution to wave equation	Tutorial (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 07	Numerical solution to wave equation	Tutorial (2 hr)
Week 08	1. Understanding PDEs - method to determine behaviour. 2. Fourier integrals and transforms.	Lecture (2 hr)
Week 08	Analytical solution to Laplace equation	Tutorial (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 09	Fourier integral solution to the heat equation	Tutorial (2 hr)
Week 10	1. Laplace transforms; 2. Solution of the semi-infinite wave equation using Laplace transforms.	Lecture (2 hr)
Week 10	Fourier transform	Tutorial (2 hr)
Week 11	1. Laplace Transform solution to the heat equation; 2. Introduction to finite elements.	Lecture (2 hr)
Week 11	Laplace transform solution to heat and wave equation	Tutorial (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 12	Implicit numerical methods	Tutorial (2 hr)
Week 13	1. Foundations of stress analysis; 2. FEA solution for an axially loaded bar.	Lecture (2 hr)
Week 13	Finite element analysis	Tutorial (2 hr)
Weekly	Individual learning and problem solving	Independent study (4 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.

This is the first time this unit has been offered.

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

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