BMET9960: Biomedical Engineering Mathematical Modelling (2021 - Semester 1)

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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:
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)
1. Apply mathematical techniques to solve problems across a range of biomedical and mechanical examples.
(3) Problem Solving and Inventiveness (Level 2)
2. Practice thinking creatively about the solutions to assignment problems, which focus on real-life engineering applications.
(2) Engineering/ IT Specialisation (Level 2)
3. Develop 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.
(1) Maths/ Science Methods and Tools (Level 3)
4. Understand and apply the physical relations and mathematical modelling of the basic problems in engineering structures, fluid mechanics and heat and mass transfer.
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.
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 . 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 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.
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

Week Description
Week 1 Introduction to the UoS

Introduction to numerical methods



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


Exact solution based on Fourier Series
Week 12 Numerical discretization of the 2D Laplace equation

Solution using iterative methods
Assessment Due: Assignment 3
Week 13 Understanding PDEs

Tools to determine behaviour

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, 2018, 2019, 2020
Master of Engineering 2019, 2020, 2021
Master of Professional Engineering (Accelerated) (Biomedical) 2019, 2020

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.