Course coordinator
Yao-Zhong Zhang is the lecturer for the second part (i.e. the PDEs part) of the course. Please contact Yao-Zhong Zhang for questions related to lecture material, tutorials and assignments of the second (PDEs) part of the course.
ODE's - Systems: variation of constants, fundamental matrix. Laplace transform, transform for systems, transfer function. Stability, asymptotic stability; phase-lane analysis. PDE's - Fourier series. Wave, heat, Laplace's equations. Simple maximum & uniqueness principles. Separation of variables in rectangular & polar coordinates.
This course will cover the following 4 topics.
This course will build on foundations that you have obtained in earlier courses: differential and integral calculus, linear algebra, vector analysis,ᅠ and especially differential equations.ᅠ It is your responsibility to fill in any gaps in the assumed knowledge.ᅠ You may need to undertake background reading to understand the lecture material.ᅠᅠ Chaptersᅠ1, 2, 7, 8, 9ᅠand 10 of the set textᅠ (E. Kreyszig, Advanced Engineering Mathematicsᅠ, 9th Edition) cover most of the background material.ᅠᅠ
IMPORTANT: For any administrative questions related to the course (such as switching tutorial/practical groups,ᅠtextbook requirements, etc.), please send an email to math2100@uq.edu.au (this email will be common for MATH2100, MATH2010, MATH2011 and MATH7100). The course coordinator and lecturers will be available to discuss academic questions during consultation hours.
You can't enrol in this course if you've already completed the following:
MATH2100 (co-taught), MATH2010, MATH2011
Yao-Zhong Zhang is the lecturer for the second part (i.e. the PDEs part) of the course. Please contact Yao-Zhong Zhang for questions related to lecture material, tutorials and assignments of the second (PDEs) part of the course.
Ivana Carrizo Molina is the lecturer for the first part (i.e. the ODEs part) of the course. Please contact Ivana Carrizo Molina for questions related to lecture material, tutorials and assignments of the first (ODEs) part of the course.
The timetable for this course is available on the UQ Public Timetable.
All classes will be conducted on campus – consult your personal timetable for times and locations. Students are expected to attend these sessions in person unless they have a valid reason for being unable to attend (such as illness).
The lectures are taught during weeks 1-13:ᅠThe first part of the course on ODEs is taught during weeks 1-6. The second part on PDEs is taught during weeks 7-13. Tutorials are taught in weeks 2-13.
This course is built around four mathematical concepts: Systems of ordinary differential equations (ODEs); Laplace transforms; Fourier series; and Partial Differential Equations (PDEs).
Systems of ODEs generalise the idea of an ODE, as you have seen it covered in MATH1052, for example. Now we have several unknown functions of a single independent variable, say the time t, and we have ODEs linking the unknowns together. We deal mostly with systems of two coupled first-order equations to see the sorts of things that can happen. The notion of the phase-plane is introduced, where the ODEs determine the trajectory of a representative point for the system. Basic notions of stability and instability of equilibrium (critical) points of the system are explored. Illustrative applications are described, such as predator-prey systems, an epidemic model, electrical and mechanical oscillators.
The Laplace Transform is a tool still widely used to deal with linear ODEs and PDEs, especially in engineering and biological applications. We introduce the basic concepts, including applications to simple systems of ODEs.
Fourier series were introduced as a tool for solving linear PDEs, but are important in their own right, and contain the germ of the ideas underlying the most advanced forms of linear analysis. The essence of the idea is to expand an arbitrary periodic signal in terms of harmonics. Again, we introduce the basic ideas with illustrative examples rather than detailed theory.
The final topic in the course is an introduction to PDEs. Here we deal with functions (fields) depending on several variables such as x, y, z and t. Many important applications are described by PDEs, and we look at some of these to introduce the three main types of linear PDEs in two independent variables: heat conduction and molecular diffusion, waves on a stretched string, and steady temperature distributions in 2-dimensions. In particular,
After successfully completing this course you should be able to:
LO1.
Ordinary Differential equations - use the software package Mathematica to solve systems of differential equations and plot the solutions
LO2.
Ordinary Differential equations - solve linear systems of ODEs and to be able to interpret their behaviour in the phase plane.
LO3.
Ordinary Differential equations - find equilibrium solutions to nonlinear systems of ODE's and analyse their stability characteristics.
LO4.
Ordinary Differential equations - use the Laplace Transform to solve linear ODE's and systems of ODE's with continuous and discontinuous forcing.
LO5.
Ordinary Differential equations - use the methods described above to analyse systems from Biology, Chemistry, Physics and Engineering (mass spring systems, mixing problems, simple electrical circuit systems, simple chemical rate equations and simple predator prey systems).
LO6.
Partial Differential Equations - Use ideas such as linear equations, the superposition principle and separation of variables to solve a range partial differential equations.
LO7.
Partial Differential Equations - Use various notions related to Fourier analysis to find and manipulate Fourier series for a range of functions.
LO8.
Partial Differential Equations - Solve a range of boundary- and initial-value problems, among them the wave equation, the heat equation and Laplace's equation.
Category | Assessment task | Weight | Due date |
---|---|---|---|
Tutorial/ Problem Set | 4 Assignments | 40% |
Assignment 1: 16/08/2024 4:15 pm Assignment 2: 6/09/2024 4:15 pm Assignment 3: 4/10/2024 4:15 pm Assignment 4: 25/10/2024 4:15 pm |
Examination |
Final 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.
Assignment 1: 16/08/2024 4:15 pm
Assignment 2: 6/09/2024 4:15 pm
Assignment 3: 4/10/2024 4:15 pm
Assignment 4: 25/10/2024 4:15 pm
Assignments will comprise problems based on material presented in lectures and tutorials. Each assignment is equally weighted.
All assessment items should be submitted electronically through Blackboard.
You may be able to apply for an extension.
The maximum extension allowed is 7 days. Extensions are given in multiples of 24 hours.
See ADDITIONAL ASSESSMENT INFORMATION for the extension and deferred examination information relating to this assessment item.
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.
You are required to submit assessable items on time. If you fail to meet the submission deadline for any assessment item, then the listed penalty will be deducted per day for up to 7 calendar days, at which point any submission will not receive any marks unless an extension has been approved. Each 24-hour block is recorded from the time the submission is due.
End of Semester Exam Period
2/11/2024 - 16/11/2024
The final examination in this course will be held during the end-of-semester examination period. It will be an in-person exam held on campus.
Planning time | 10 minutes |
---|---|
Duration | 120 minutes |
Calculator options | No calculators permitted |
Open/closed book | Closed Book examination - no written materials permitted |
Exam platform | Paper based |
Invigilation | Invigilated in person |
You may be able to defer this exam.
See ADDITIONAL ASSESSMENT INFORMATION for the extension and deferred examination information relating to this assessment item.
Full criteria for each grade is available in the Assessment Procedure.
Grade | Description |
---|---|
1 (Low Fail) |
Absence of evidence of achievement of course learning outcomes. Course grade description: The student demonstrates very little understanding of the theory of the topics listed in the syllabus and very little ability to apply the associated techniques to solve problems. Overall score below 20%. |
2 (Fail) |
Minimal evidence of achievement of course learning outcomes. Course grade description: The student demonstrates little understanding of the theory of the topics listed in the syllabus and little ability to apply the associated techniques to solve problems. Overall score of at least 20%, which does not meet the requirements for a higher grade. |
3 (Marginal Fail) |
Demonstrated evidence of developing achievement of course learning outcomes Course grade description: The student demonstrates only limited understanding of the theory of the topics listed in the syllabus and limited ability to apply the associated techniques to solve straightforward problems. Overall score of at least 45% and at least 35% of the marks for the final exam, which does not meet the requirements for a higher grade. |
4 (Pass) |
Demonstrated evidence of functional achievement of course learning outcomes. Course grade description: The student must satisfy the basic learning requirements for the course, such as understanding of the fundamental concepts and performance of basic skills. They must demonstrate knowledge of techniques used to solve problems. Overall score of at least 50% and at least 38% of the marks for the final exam, which does not meet the requirements for a higher grade. |
5 (Credit) |
Demonstrated evidence of proficient achievement of course learning outcomes. Course grade description: The student must demonstrate a good understanding of the course material and an ability to apply techniques to successfully solve problems, using fundamental concepts and skills of the course. Overall score of at least 65%, which does not meet the requirements for a higher grade. |
6 (Distinction) |
Demonstrated evidence of advanced achievement of course learning outcomes. Course grade description: The student must demonstrate a comprehensive understanding of the course material and be proficient in applying techniques to solve problems. Overall score of at least 75%, which does not meet the requirements for a higher grade. |
7 (High Distinction) |
Demonstrated evidence of exceptional achievement of course learning outcomes. Course grade description: The student must demonstrate an excellent understanding of the course material, and be highly proficient in applying appropriate techniques to accurately solve problems. Overall score of at least 85%. |
Supplementary assessment is available for this course.
Should you fail a course with a grade of 3, you may be eligible for supplementary assessment. Refer to my.UQ for information on supplementary assessment and how to apply.
Supplementary assessment provides an additional opportunity to demonstrate you have achieved all the required learning outcomes for a course.
If you apply and are granted supplementary assessment, the type of supplementary assessment set will consider which learning outcome(s) have not been met.
Supplementary assessment in this course will be a 2-hour examination similar in style to the end-of-semester examination. To receive a passing grade of 3S4, you must obtain a mark of 50% or more on the supplementary assessment.
Important note
Tutors will record your assignment marks on Blackboard. It is your responsibility to check that the mark is correctly recorded. No discussion about incorrect or missing assignment marks will be entertained 21 calendar days after marks are released.
Artificial Intelligence
The assessment tasks in this course evaluate students’ abilities, skills and knowledge without the aid of Artificial Intelligence (AI). Students are advised that the use of AI technologies to develop responses is strictly prohibited and may constitute misconduct under the Student Code of Conduct.
Applications for Extensions to Assessment Due Dates
Extension requests are submitted online via my.UQ – applying for an extension. Extension requests received in any other way will not be approved. Additional details associated with extension requests, including acceptable and unacceptable reasons, may be found at my.UQ.
Please note:
Applications to defer an exam
In certain circumstances you can apply to take a deferred examination for in-semester and end-of-semester exams. You'll need to demonstrate through supporting documentation how unavoidable circumstances prevented you from sitting your exam. If you can’t, you can apply for a one-off discretionary deferred exam.
Deferred Exam requests are submitted online via mySi-net. Requests received in any other way will not be approved. Additional details associated with deferred examinations, including acceptable and unacceptable reasons may be found at my.UQ.
Please note:
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.
Find the required and recommended resources for this course on the UQ Library website.
If we've listed something under further requirement, you'll need to provide your own.
Item | Description | Further Requirement |
---|---|---|
MATH2010 Course Workbook | This is the workbook for the first (ODEs) part of the course. It is available as a PDF from the course Blackboard page and is also available as a hard copy from UQ Print. The workbook covers all the lecture material presented throughout the semester. Students should bring this document to all lectures. | own item needed |
MATH2011 Course Workbook | This is the workbook for the second (PDEs) part of the course. It is available as a PDF from the course Blackboard page and is also available as a hard copy from UQ Print. The workbook covers all the lecture material presented throughout the semester. Students should bring this document to all lectures. | own item needed |
A different workbook will be used for each part of the course. They will be both available from blackboard.
The learning activities for this course are outlined below. Learn more about the learning outcomes that apply to this course.
Filter activity type by
Learning period | Activity type | Topic |
---|---|---|
Multiple weeks From Week 1 To Week 6 |
Lecture |
ODEs and Laplace transform 3 lectures per week. Lectures will be on-campus. Learning outcomes: L01, L02, L03, L04, L05 |
Multiple weeks From Week 2 To Week 13 |
Tutorial |
Problem Solving One Tutorial per week (from Week 2), in which a tutor demonstrates solutions of selected problems and is available to answer questions about the tutorial sheets and assignment problems. Students work on solving problems and understanding course material and are able to ask questions. Learning outcomes: L01, L02, L03, L04, L05, L06, L07, L08 |
Multiple weeks From Week 7 To Week 13 |
Lecture |
Fourier Series and PDEs 3 lectures per week. Lectures will be on-campus. Learning outcomes: L06, L07, L08 |
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:
Learn more about UQ policies on my.UQ and the Policy and Procedure Library.