Dr Travis Mitchell
Course overview
- Study period
- Semester 2, 2024 (22/07/2024 - 18/11/2024)
- Study level
- Undergraduate
- Location
- St Lucia
- Attendance mode
- In Person
- Units
- 2
- Administrative campus
- St Lucia
- Coordinating unit
- Mech & Mine Engineering School
This course provides an introduction to the development and application of numerical methods to resolve common challenges faced in mechanical engineering. It builds an important foundation of knowledge in programming, numerical algorithms, and simulation techniques that is essential for modern day engineers. The course starts with numerical approaches for interpolation, differentiation and quadrature before introducing direct and iterative approaches to solve linear systems. Solution techniques for ordinary differential equations (ODEs) and non-linear equations are formulated and techniques for data fitting and optimisation (inc. least-squares approaches) are developed and applied to engineering problems. The final module of the course formulates computational techniques to solve partial differential equations (parabolic, hyperbolic, and elliptic) with numerous applications involving heat transfer, convection-diffusion, and wave propagation. Completion of this course will provide students with the necessary skills to develop computational approaches to address a wide range of engineering problems.
Course requirements
Assumed background
First-year mathematics; basic mechanics; Python programming.
Prerequisites
You'll need to complete the following courses before enrolling in this one:
(ENGG1001 or CSSE1001) and (MATH1051 or MATH1071)
Recommended prerequisites
We recommend completing the following courses before enrolling in this one:
(MATH1052 or MATH1072)
Course staff
Course coordinator
Lecturer
Dr Travis Mitchell
Dr Nick Gibbons
Professor Vincent Wheatley
Timetable
The timetable for this course is available on the UQ Public Timetable.
Additional timetable information
Content delivery in MECH2700 is via a 2 hour lecture. The 3rd hour of content per week is a contact where we work through the complete engineering problem solving process using numerical methods. You will then put this learning into practice in weekly two hour computer laboratory sessions. You need attend only one computer laboratory (I01..I06) session per week.ﾠ Note these lab sessions will start in Week 2.
ﾠ
Aims and outcomes
The aim of this course is to continue the development of the student's capability in the mathematical formulation of mechanical engineering problems, the application of computers to the numerical analysis of these mathematical models, and the interpretation and reporting of that analysis.
Learning outcomes
After successfully completing this course you should be able to:
LO1.
Formulate mathematical models of systems encountered in mechanical engineering - Understand which types of mathematical model are appropriate for different systems.
LO2.
Formulate mathematical models of systems encountered in mechanical engineering - Model systems using algebraic equations, ordinary differential equations, partial differential equations, systems of linear equations, interpolating functions, approximating functions and integral equations.
LO3.
Formulate mathematical models of systems encountered in mechanical engineering - Construct system models based on rough descriptions of mechanical engineering situations or problems.
LO4.
Select or develop numerical methods to analyse the behaviour of system models - Compute solutions to nonlinear algebraic equations using the bisection method, Newtons method, secant method, shadow position method and fixed point iteration comparing their convergence, efficiency and robustness.
LO5.
Select or develop numerical methods to analyse the behaviour of system models - Compute solutions to ordinary differential equations using the Euler, modified Euler and Runge-Kutta methods, and analyse their order of accuracy using Taylor series.
LO6.
Select or develop numerical methods to analyse the behaviour of system models - Compute solutions to integration problems using Newton-Cotes methods, Gauss quadrature and composite quadrature methods.
LO7.
Select or develop numerical methods to analyse the behaviour of system models - Approximate derivatives of function using finite differences and analyse their order of accuracy.
LO8.
Select or develop numerical methods to analyse the behaviour of system models - Compute solutions to partial differential equations using a spectrum of numerical methods.
LO9.
Select or develop numerical methods to analyse the behaviour of system models - Compute solutions to one-dimensional optimisation problems using the Golden search algorithm.
LO10.
Select or develop numerical methods to analyse engineering data - Generate continuous approximations of engineering data using monomial and Lagrange interpolation and least-squares fitting for general basis functions.
LO11.
Select or develop numerical methods to analyse engineering data - Approximate integrals of engineering data using quadrature methods.
LO12.
Select or develop numerical methods to analyse engineering data - Approximate derivatives from engineering data using finite differences and analyse their order of accuracy.
LO13.
Select or develop numerical methods to analyse engineering data - Visualize engineering data using a variety of approaches.
LO14.
Compose computer programs to implement numerical methods - Construct functional programs in the Python language that systematically initialize required variables, execute a numerical method and output the variables of interest.
LO15.
Compose computer programs to implement numerical methods - Construct functional programs in the Python language that systematically read in, analyse and visualise engineering data.
LO16.
Interpret, evaluate and report on the results of numerical analysis - Interpret the results of numerical analysis in terms of the behaviour of the physical system it models.
LO17.
Interpret, evaluate and report on the results of numerical analysis - Evaluate the performance of numerical analysis in terms of convergence and efficiency.
LO18.
Interpret, evaluate and report on the results of numerical analysis - Report on the results of numerical analysis in written and graphical format.
LO19.
Understand and apply new approaches from the numerical methods literature - Understand the language and structure of the numerical analysis field sufficiently to find and understand new numerical methods from the literature.
LO20.
Understand and apply new approaches from the numerical methods literature - Evaluate the suitability of new numerical analysis techniques for your applications.
LO21.
Understand and apply new approaches from the numerical methods literature - Apply new numerical analysis techniques to engineering applications by implementing them in Python programs.
Assessment
Assessment summary
| Category | Assessment task | Weight | Due date |
|---|---|---|---|
| Computer Code, Tutorial/ Problem Set | Weekly tutorial exercise | 10% |
Due weekly at 4 pm Friday from Week 2 |
| Computer Code, Paper/ Report/ Annotation | Assignment 1 | 15% |
6/09/2024 4:00 pm |
| Computer Code, Paper/ Report/ Annotation | Assignment 2 | 15% |
25/10/2024 4:00 pm |
| Examination |
End of Semester Examination
|
60% |
End of Semester Exam Period 2/11/2024 - 16/11/2024 |
A hurdle is an assessment requirement that must be satisfied in order to receive a specific grade for the course. Check the assessment details for more information about hurdle requirements.
Assessment details
Weekly tutorial exercise
- Mode
- Product/ Artefact/ Multimedia, Written
- Category
- Computer Code, Tutorial/ Problem Set
- Weight
- 10%
- Due date
Due weekly at 4 pm Friday from Week 2
Task description
Short weekly theoretical and/or coding tasks to apply the analysis techniques discussed in lectures to engineering problems. Each weekly task is due at 4pm Friday of the given week.
Submission guidelines
Submission of both theoretical and programming task should be provided in a single pdf to the submission links provided on Blackboard. The theoretical question may be scanned or typeset. The code can be copied into the document along with the output/results.
Deferral or extension
You cannot defer or apply for an extension for this assessment.
To accommodate unforeseen circustances such as illness, the best 10 of 12 submissions are used for this assessment task and timely feedback needs to be provided to students.
Late submission
You will receive a mark of 0 if this assessment is submitted late.
The best 10 of 12 submission are used for this assessment task and timely feedback needs to be provided to students, late submissions will not be accepted.
Assignment 1
- Mode
- Written
- Category
- Computer Code, Paper/ Report/ Annotation
- Weight
- 15%
- Due date
6/09/2024 4:00 pm
Task description
An exercise in modelling and programming that will require submission to be described on Blackboard. You are to do this exercise individually and you are welcome to ask questions in the computer lab (ICT) sessions.
Submission guidelines
Your assignment should be submitted as a single PDF document plus a set of Python source code files that can be run for verification. The source code should include a README file that describes how your code can be executed to produce your submitted results. A link for submission will be provided on BlackBoard.
Deferral or extension
You may be able to apply for an extension.
The maximum extension allowed is 14 days. Extensions are given in multiples of 24 hours.
Feedback is provided to students following 14 calendar days.
A Student Access Plan (SAP) can only be used for a first extension. Extensions based on an SAP may be granted for up to seven (7) days, or the maximum number of days specified in the Electronic Course Profile (ECP), if it is less than seven (7) days. Any further extensions will require additional supporting documentation, such as a medical certificate.
Late submission
A penalty of 10% of the maximum possible mark will be deducted per 24 hours from time submission is due for up to 7 days. After 7 days, you will receive a mark of 0.
Assignment 2
- Mode
- Written
- Category
- Computer Code, Paper/ Report/ Annotation
- Weight
- 15%
- Due date
25/10/2024 4:00 pm
Task description
A larger exercise in modelling and programming that will require submission as to be detailed on Blackboard. You are to do this exercise in pairs (or individually) and you are welcome to ask questions in the computer lab (ICT) sessions.
If, for whatever reason, you find that your group is not functioning effectively, please contact your Course Coordinator for support.
Submission guidelines
Your assignment should be submitted as a single PDF document plus a set of Python source code files that can be run for verification. The source code should include a README file that describes how your code can be executed to produce your submitted results. A link for submission will be provided on BlackBoard.
Deferral or extension
You may be able to apply for an extension.
The maximum extension allowed is 14 days. Extensions are given in multiples of 24 hours.
Feedback is provided to students following 14 calendar days.
A Student Access Plan (SAP) can only be used for a first extension. Extensions based on an SAP may be granted for up to seven (7) days, or the maximum number of days specified in the Electronic Course Profile (ECP), if it is less than seven (7) days. Any further extensions will require additional supporting documentation, such as a medical certificate.
Late submission
A penalty of 10% of the maximum possible mark will be deducted per 24 hours from time submission is due for up to 7 days. After 7 days, you will receive a mark of 0.
End of Semester Examination
- Hurdle
- Identity Verified
- Mode
- Written
- Category
- Examination
- Weight
- 60%
- Due date
End of Semester Exam Period
2/11/2024 - 16/11/2024
Task description
End of semester closed book examination.
Hurdle requirements
Identity verified assessment (IVA)ﾠwill be through obtainingﾠat least 40% of the available marksﾠin the final exam. You need to pass the IVA hurdle to pass the course regardless of your final mark. Students who achieve a total mark of 50 or greater but do not pass the IVA hurdle will receive a grade of 3.Exam details
| Planning time | 10 minutes |
|---|---|
| Duration | 120 minutes |
| Calculator options | (In person) Casio FX82 series or UQ approved , labelled calculator only |
| Open/closed book | Closed Book examination - no written materials permitted |
| Exam platform | Paper based |
| Invigilation | Invigilated in person |
Submission guidelines
Deferral or extension
You may be able to defer this exam.
Course grading
Full criteria for each grade is available in the Assessment Procedure.
| Grade | Cut off Percent | Description |
|---|---|---|
| 1 (Low Fail) | 0.00 - 29.99 |
Absence of evidence of achievement of course learning outcomes. Course grade description: Fail: Overall grade. |
| 2 (Fail) | 30.00 - 44.99 |
Minimal evidence of achievement of course learning outcomes. Course grade description: Fail: Overall grade 30.0 to 44.99%. |
| 3 (Marginal Fail) | 45.00 - 45.99 |
Demonstrated evidence of developing achievement of course learning outcomes Course grade description: Fail: Falls short of satisfying basic requirements for a Pass. Overall grade: 45-49.99% or less that 40% in the IVA requirement explained below. |
| 4 (Pass) | 50.00 - 64.99 |
Demonstrated evidence of functional achievement of course learning outcomes. Course grade description: Pass: Satisfies all of the basic learning requirements for the course, such as knowledge of fundamental concepts and performance of basic skills; demonstrates sufficient quality of performance to be considered satisfactory or adequate or competent or capable in the course. Overall grade 50-64.99% and a minimum score of 40% in the IVA requirement explained below. |
| 5 (Credit) | 65.00 - 74.99 |
Demonstrated evidence of proficient achievement of course learning outcomes. Course grade description: Credit: Demonstrates ability to use and apply fundamental concepts and skills of the course, going beyond mere replication of content knowledge or skill to show understanding of key ideas, awareness of their relevance, some use of analytical skills, and some originality or insight. Overall grade 65-74.99% and a minimum score of 40% in the IVA requirement explained below. |
| 6 (Distinction) | 75.00 - 84.99 |
Demonstrated evidence of advanced achievement of course learning outcomes. Course grade description: Distinction: Demonstrates awareness and understanding of deeper and subtler aspects of the course, such as ability to identify and debate critical issues or problems, ability to solve non-routine problems, ability to adapt and apply ideas to new situations, and ability to invent and evaluate new ideas. Overall grade 75- 84.99% and a minimum score of 40% in the IVA requirement explained below. |
| 7 (High Distinction) | 85.00 - 100.00 |
Demonstrated evidence of exceptional achievement of course learning outcomes. Course grade description: High Distinction: Demonstrates imagination, originality or flair, based on proficiency in all the learning objectives for the course; work is interesting or surprising or exciting or challenging or erudite. Overall grade 85 - 100% and a minimum score of 40% in the IVA requirement explained below. |
Additional course grading information
Grading Criteria
Specific grading criteria will be provided for each assessment item. These are available on Blackboard in the assessment folder.
Identity verified assessment.
Identity verified assessment (IVA)ﾠwill be through obtainingﾠat least 40% of the available marksﾠin the final exam.
You need to pass the IVA hurdle to pass the course regardless of your final mark. Students who achieve a total mark of 50 or greater but do not pass the IVA hurdle will receive a grade of 3.
Supplementary assessment
Supplementary assessment is available for this course.
Additional assessment information
Students will not be given exemptions, or partial credit from any previous attempt of this course, for any piece of assessment. You must complete all of the learning activities and assessment items each time you take a course.
A failure to reference AI use may constitute student misconduct under the Student Code of Conduct.
Learning resources
You'll need the following resources to successfully complete the course. We've indicated below if you need a personal copy of the reading materials or your own item.
Library resources
Find the required and recommended resources for this course on the UQ Library website.
Additional learning resources information
Everything that you need to set up a good Python environment for engineering computation is freely available on the Internet.ﾠIf you are running a Windows system, a good system to install is the Anaconda distribution from Continuum.ﾠ If you run another system, install Python, numpy, matplotlib, Scipy, to get about the same environment. ﾠNote that you must install binary packages that are compatible with the particular version of Python that you choose.
Learning activities
The learning activities for this course are outlined below. Learn more about the learning outcomes that apply to this course.
Filter activity type by
Please select
| Learning period | Activity type | Topic |
|---|---|---|
Multiple weeks From Week 1 To Week 13 |
Lecture |
Lectures - Modelling and Numerical Methods This Learning Activity will cover the following topics: Week 1 - Course introduction. Problem solving; A numerical approach. Floating-point numbers and error. Week 2 - Interpolation (High-order polynomials, Lagrange basis functions, Chebyshev points). Good programming practices. Week 3 - Numerical differentiation (Finite difference formulas and associated errors). Week 4 - Numerical integration (Newton-Cotes formulas-Trapezoidal rule, Simpson's 1/3 rule, etc., Composite quadrature). Week 5 - Direct solutions to linear systems (Gauss-Jordan elimination, LU decomposition). Week 6 - Iterative solutions to linear systems (Jacobi, Gauss-Seidel, Relaxation methods, Least-Squares approach for over-constrained systems). Week 7 - Numerical solutions to ODEs (Euler's, Modified Euler's, Runge-Kutta, Runge-Kutta-Fehlberg, Systems of Equations). Week 8 - Solving non-linear equations (Bisection, Fixed-Point Iteration, Gradient-based methods). Week 9 - Data fitting and optimisation (Least-squares, Chebyshev polynomials, Golden search, Bracketing). Week 10 - Intro to numerical solutions of PDEs and Parabolic PDEs (Classifications, finite difference schemes, diffusion problems). Week 11 - Parabolic PDEs conti. and Hyperbolic PDEs (Boundary conditions, stability of parabolic PDE solutions, Wave equation). Week 12 - Nonlinear Hyperbolic PDEs and Elliptic PDEs (Euler equations, inviscid Burgers equation, shocks, boundary value problems, solution approaches). Week 13 - Semester review and feedback. |
Multiple weeks From Week 1 To Week 12 |
General contact hours |
Contact - Weekly interactive problem-solving Weekly workshops that begin with a physical engineering problem and work through the entire problem-solving process from defining the problem, to coding up the solution and interpreting the results, getting input from the class at every stage. |
Multiple weeks From Week 2 To Week 13 |
Practical |
Computer Lab Sessions To achieve the learning objectives of the course, you will need to work through weekly problem sets on solving engineering problems using numerical methods. This involves writing and executing code and interpreting the results. In order to do this at a time when tutorial assistance is available, you will need to attend one of the lab sessions that will be held each week. These are labelled I01 through I06. |
Multiple weeks From Week 4 To Week 13 |
Not Timetabled |
Assignment You will need to complete assignments based on the analysis of mechanical engineering problems and the interpretation of numerical results relevant to those problems. |
Additional learning activity information
1. Lectures: During lectures, key concepts will be presented together with simple examples of application. Lecture content can be used as a guide to further independent reading and study.
2. Contacts: These workshops begin with a physical engineering problem and work through the entire problem-solving process from defining the problem to coding up the solution and interpreting the results, getting input from the class at every stage.
3. Tutorial exercises and assignments: Application of the principles discussed in lectures to a collection of small and large exercises. The smaller exercises are an opportunity for independent study while the assignments will be an opportunity for small-group work.
4. Computer Laboratory Classes: These sessions give the student the opportunity to implement their numerical models as part of the assigned exercises. The computers in the laboratory are equipped with the required software. For these sessions, tutors will be present, however, please take the opportunity to try the exercises yourself before asking for help.
Policies and procedures
University policies and procedures apply to all aspects of student life. As a UQ student, you must comply with University-wide and program-specific requirements, including the:
- Student Code of Conduct Policy
- Student Integrity and Misconduct Policy and Procedure
- Assessment Procedure
- Examinations Procedure
- Reasonable Adjustments - Students Policy and Procedure
Learn more about UQ policies on my.UQ and the Policy and Procedure Library.