BMET9960: Biomedical Engineering Mathematical Modelling (2021  Semester 1)
Unit:  BMET9960: Biomedical Engineering Mathematical Modelling (6 CP) 
Mode:  NormalDay 
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 
PreRequisites:  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 examplebased 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 wellequipped with useful tools for your future engineering career. We hope you enjoy it! 
Assumed Knowledge:  Undergraduate mathematics (1000level) 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: 


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 reallife 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 reallife 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)Assessment Methods: 


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 prework: This mark is based on a short quiz, based on the prework 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: 


Policies & Procedures:  See the policies page of the faculty website at http://sydney.edu.au/engineering/studentpolicies/ 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 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 nonhomogeneous 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 wavelike 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 semiinfinite 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 
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.