The University of Sydney - Engineering

Unit:	BMET9960: Biomedical Engineering Mathematical Modelling (6 CP)
Mode:	Normal-Day
On Offer:	Yes
Level:	Postgraduate
Faculty/School:	School of Biomedical Engineering
Unit Coordinator/s:	Dr Kyme, Andre
Session options:	Semester 1
Versions for this Unit:	2021 - Semester 1 Go

Campus:	Camperdown/Darlington
Pre-Requisites:	None.
Prohibitions:	BMET2960 OR AMME2960
Brief Handbook Description:	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 course 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!
Assumed Knowledge:	Undergraduate mathematics (1000-level) and an appreciation of the biomedical engineering process

Lecturer/s:	Dr Thornber, Ben Dr Kyme, Andre
Tutor/s:	Matilda Longfield, Mahdieh Dashtbani, Christine Poon, David Henry, Jack Geoghegan, Aditya Vishwanathan, Yuxi Liu
Timetable:	BMET9960 Timetable
Time Commitment:	# Activity Name Hours per Week Sessions per Week Weeks per Semester 1 Lecture 2.00 2 13 2 Tutorial 2.00 1 12 3 Independent Study 5.00 1 13
T&L Activities:	2 hours of lectures per week in 2 separate 1 hour lecture blocks. A total of 26 hours of lectures. The tutorials will take place in a weekly 2 hour block. Tutorials address the lecture content with a physically based problem solving approach, facilitated by tutors.

Attributes listed here represent the key course goals (see Course Map tab) designated for this unit. The list below describes how these attributes are developed through practice in the unit. See Learning Outcomes and Assessment tabs for details of how these attributes are assessed.

Attribute Development Method	Attribute Developed
Lectures, tutorials and assignments: Students develop proficiency in a structured approach to engineering problem identification, modelling and solution. Students learn a range of foundational mathematical techniques to solve partial differential equations analytically and numerically. The relationship between the analytical and numerical approaches is explored and also the relevance of this for real-life engineering.	(1) Maths/ Science Methods and Tools (Level 3)
Assignments, tutorials and quizzes: Students apply mathematical techniques to specific biomedical problems and explore the dependencies of their solutions. Tutorials: Students learn how to frame a problem in computer code, implement and debug their code, and visualise and present the results. Assignments: Students practice presenting concise engineering reports.	(2) Engineering/ IT Specialisation (Level 2)
Assignments and tutorials: Students must think creatively about the solutions for the tutorials and assignments, which focus on real-life engineering problems.	(3) Problem Solving and Inventiveness (Level 2)
Lectures, tutorials and assignments: Because much of the content of this unit is shared with AMME2000, students will many examples of how the same mathematical techniques can be applied across mechanical, aero and biomedical applications.	(5) Interdisciplinary, Inclusiveness, Influence (Level 2)

For explanation of attributes and levels see Engineering & IT Graduate Outcomes Table 2018.

Learning outcomes are the key abilities and knowledge that will be assessed in this unit. They are listed according to the course goal supported by each. See Assessment Tab for details how each outcome is assessed.

(5) Interdisciplinary, Inclusiveness, Influence (Level 2)
(3) Problem Solving and Inventiveness (Level 2)
(2) Engineering/ IT Specialisation (Level 2)
(1) Maths/ Science Methods and Tools (Level 3)

Assessment Methods:	# Name Group Weight Due Week Outcomes 1 Assignment 1 No 10.00 Week 4 1, 2, 3, 4, 2 Assignment 2 No 10.00 Week 8 1, 2, 3, 4, 3 Assignment 3 No 10.00 Week 12 1, 2, 3, 4, 4 Quiz No 10.00 Week 10 1, 2, 4, 5 Final exam No 45.00 Exam Period 1, 4, 6 Tutorial Question - Total for all tuts Yes 10.00 Multiple Weeks 1, 2, 3, 4, 7 Weekly pre-work No 5.00 Multiple Weeks 1, 2, 4,
Assessment Description:	Assignment 1: Analytical and numerical solution to the heat diffusion equation. Assignment 2: Analytical and numerical solution to the wave equation. Assignment 3: Finite element solution to an engineering problem. Quiz: Analytical solutions to the heat and wave equations, integrals and transforms. Weekly pre-work: This mark is based on a short quiz, based on the pre-work for that week, and to be completed prior to the lectures that week. Tutorial assessment: 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%. Late assignments will be penalised at a rate of 5% per day (a mark of 0 will be awarded beyond 10 days late). All assignments must be handed in as a soft copy via Turnitin. There may be statistically defensible moderation when combining the marks from each component to ensure consistency of marking between markers, and alignment of final grades with unit outcomes.
Assessment Feedback:	Marked assessments and feedback from lecturer/tutors.
Grading:	Grade Type Description Standards Based Assessment Final grades in this unit are awarded at levels of HD for High Distinction, DI (previously D) for Distinction, CR for Credit, PS (previously P) for Pass and FA (previously F) for Fail as defined by University of Sydney Assessment Policy. Details of the Assessment Policy are available on the Policies website at http://sydney.edu.au/policies . Standards for grades in individual assessment tasks and the summative method for obtaining a final mark in the unit will be set out in a marking guide supplied by the unit coordinator.
Policies & Procedures:	See the policies page of the faculty website at http://sydney.edu.au/engineering/student-policies/ for information regarding university policies and local provisions and procedures within the Faculty of Engineering and Information Technologies.

Prescribed Text/s:	Note: Students are expected to have a personal copy of all books listed. Advanced Engineering Mathematics Title: Advanced Engineering Mathematics Author/s: Kreyszig Edition: 10th edition Publish Location: Wiley Link: http://www.wileydirect.com.au/buy/advanced-engineering-mathematics-10th-edition/
Note on Resources:	Lecture notes will be provided. The prescribed text is Advanced Engineering Mathematics, 10th ed. (Kreyszig).

Note that the "Weeks" referred to in this Schedule are those of the official university semester calendar https://web.timetable.usyd.edu.au/calendar.jsp

Week	Description
Week 1	Introduction to the UoS Introduction to numerical methods Discretisation Interpolation Least squares Cubic Splines Taylor Series Finite Differences
Week 2	What is a PDE? Generic PDE introduction inc. classification Derivation of the Heat Diffusion Equation Exact Solution of the Heat Diffusion Equation (Fourier Series) Solution of Heat Equation via separation of variables Heat equation with non-homogeneous boundary conditions.
Week 3	Initial Value Problems, Boundary Value Problems, initial conditions, boundary conditions, well posed problems Accuracy, stability, consistency Linear Algebra Forward time centred space solution of the heat diffusion equation.
Week 4	Introduction to and Derivation of the Wave Equation Classification of wave-like equations Approximate solution using Fourier Series
	Assessment Due: Assignment 1
Week 5	Separation of variables solution to the wave equation Eigenvalues and Eigenfunctions Numerical Solution of the wave equation
Week 6	Fourier Integrals and transforms Fourier Integral solutions to infinite problems
Week 7	FFT and signal processing
Week 8	Laplace Transforms Solution of the semi-infinite wave equation using Laplace Transforms
	Assessment Due: Assignment 2
Week 9	Introduction to Finite elements Piecewise linear basis functions Method of weighted residuals
Week 10	Foundations of Stress Analysis Axially Loaded Bar Numerical Solution
	Assessment Due: Quiz
Week 11	Introduction and derivation of the Laplace and Poisson equation Applications Exact solution based on Fourier Series
Week 12	Numerical discretization of the 2D Laplace equation Solution using iterative methods
	Revision
	Assessment Due: Assignment 3
Week 13	Understanding PDEs Tools to determine behaviour Summary
Exam Period	Assessment Due: Final exam

Course Relations

The following is a list of courses which have added this Unit to their structure.

Course	Year(s) Offered
Master of Professional Engineering (Biomedical)	2021, 2022, 2018, 2019, 2020
Master of Engineering	2019, 2020, 2021, 2022
Master of Professional Engineering (Accelerated) (Biomedical)	2019, 2020

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Course Goals

This unit contributes to the achievement of the following course goals:

Attribute	Practiced	Assessed
(5) Interdisciplinary, Inclusiveness, Influence (Level 2)	Yes	34.25%
(3) Problem Solving and Inventiveness (Level 2)	Yes	11.75%
(2) Engineering/ IT Specialisation (Level 2)	Yes	16%
(1) Maths/ Science Methods and Tools (Level 3)	Yes	38%

These goals are selected from Engineering & IT Graduate Outcomes Table 2018 which defines overall goals for courses where this unit is primarily offered. See Engineering & IT Graduate Outcomes Table 2018 for details of the attributes and levels to be developed in the course as a whole. Percentage figures alongside each course goal provide a rough indication of their relative weighting in assessment for this unit. Note that not all goals are necessarily part of assessment. Some may be more about practice activity. See Learning outcomes for details of what is assessed in relation to each goal and Assessment for details of how the outcome is assessed. See Attributes for details of practice provided for each goal.