Analysis of Partial Differential Equations (MATH2011)

Course overview

PDE's - Fourier series. Wave, heat, Laplace's equations. Simple maximum and uniqueness principles. Separation of variables in rectangular and polar coordinates.

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. We introduce the basic ideas with illustrative examples rather than detailed theory.

The second 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, we will introduce Fourier's method of separation of variables and superposition as a key solution method in each case.

An understanding of these concepts is important for anyone who wants to apply mathematics to the real world. DEs are still the most widely used tools in mathematical modelling. They are used extensively in theoretical physics, mathematical biology and ecology, human movement studies, and all branches of engineering. In particular, they inevitably arise when we try to model anything that moves continuously in time or varies continuously in space. In this course, we lay the groundwork for more advanced modelling courses (MATH3101, 3102, 3104).

Because of their fundamental importance, the theory of differential equations is still one of the most active areas of pure mathematics research. After completing this course, you will be well-placed to go on if you wish to more advanced courses in the theory of differential equations (MATH3403, 4407).

Students with interests in the applications of mathematics to the real world, or with the development of the tools needed for such applications, will need a good understanding of the basic ideas introduced here. This includes those interested in research careers in theoretical physics, engineering, applied mathematics, pure mathematics (analysis), and numerical analysis.

The development of fast and reliable methods of solving differential equations approximately on the computer has also become one of the most active and important areas of scientific computation, and if you do MATH2100, you will be able to go on in this direction too if you wish, through MATH3201.

Note: This course is 1-unit (half of standard size of UQ course), running in the second half of semester.

Course requirements

Assumed background

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, ﾠ9ﾠand 10 of the set textﾠ (E. Kreyszig, Advanced Engineering Mathematicsﾠ, 9th Edition) cover most of the background material.ﾠ ﾠ

ﾠ

Prerequisites

You'll need to complete the following courses before enrolling in this one:

MATH1052 or MATH1072

Companion or co-requisite courses

You'll need to complete the following courses at the same time:

MATH2001or MATH2901

Incompatible

You can't enrol in this course if you've already completed the following:

MATH2100

Course contact

Course staff

Timetable

The timetable for this course is available on the UQ Public Timetable.

Additional timetable information

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).

Lectures are taught in weeks 7-13 and Tutorials are conducted in weeks 8-13 (i.e. there are no tutorials in week 7).

Aims and outcomes

The course aims to cover the following two topics: Fourier series; and Partial Differential Equations (PDEs). Students will be introduced to a number of new concepts and methods, and will be presented with theory, examples and applications in various pure and applied contexts.

Learning outcomes

After successfully completing this course you should be able to:

Assessment

Assessment summary

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

2 Assignments

Mode

Written

Category

Tutorial/ Problem Set

Weight

40%

Due date

Assignment 1: 4/10/2024 4:15 pm

Assignment 2: 25/10/2024 4:15 pm

Learning outcomes

L01, L02, L03

Task description

Submission guidelines

Assignments must be downloaded from the Blackboard website and must be submitted ONLINE through Blackboard. Assignments need to be prepared as a single pdf file, either by typing it or by scanning your handwritten work.

Deferral or extension

You may be able to apply for an extension.

The maximum extension allowed is 7 days. Extensions are given in multiples of 24 hours.

Solutions for assessment item/s will be released 7 days after the assessment is due and as such, an extension after 7 days will not be possible.

See ADDITIONAL ASSESSMENT INFORMATION for the extension and deferred examination information relating to this assessment item.

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.

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.

Final Examination

• Hurdle

Mode

Written

Category

Examination

Weight

60%

Due date

End of Semester Exam Period

2/11/2024 - 16/11/2024

Learning outcomes

L01, L02, L03

Task description

Hurdle requirements

Exam details

Submission guidelines

Deferral or extension

You may be able to defer this exam.

See ADDITIONAL ASSESSMENT INFORMATION for the extension and deferred examination information relating to this assessment item.

Course grading

Full criteria for each grade is available in the Assessment Procedure.

Supplementary assessment

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 1-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. 

Additional assessment information

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:

• Requests for an extension to an assessment due date must be submitted through your my.UQ portal and you must provide documentation of your circumstances, as soon as it becomes evident that an extension is needed. Your application must be submitted on or before the assessment item's due date and time.
• Applications for extension can take time to be processed so you should continue to work on your assessment item while awaiting a decision. We recommend that you submit any completed work by the due date, and this will be marked if your application is not approved. Should your application be approved, then you will be able to resubmit by the agreed revised due date.
• If an extension is approved, you will be notified via your my.UQ portal and the new date and time for submission provided. It is important that you check the revised date as it may differ from the date that you requested.
• If the basis of the application is a medical condition, applications should be accompanied by a medical certificate dated prior to the assignment due date. If you are unable to provide documentation to support your application by the due date and time you must still submit your application on time and attach a written statement (Word document) outlining why you cannot provide the documentation. You must then upload the documentation to the portal within 24 hours.
• If an extension is being sought on the basis of exceptional circumstances, it must be accompanied by supporting documentation (eg. Statutory declaration).
• For extensions based on a SAP you may be granted a maximum of 7 days (if no earlier maximum date applies). See the Extension or Deferral availability section of each assessment for details. Your SAP is all that is required as documentation to support your application. However, additional extension requests for the assessment item will require the submission of additional supporting documentation e.g., a medical certificate. All extension requests must be received by the assessment due date and time.
• Students may be asked to submit evidence of work completed to date. Lack of adequate progress on your assessment item may result in an extension being denied.
• If you have been ill or unable to attend class for more than 14 days, you are advised to carefully consider whether you are capable of successfully completing your courses this semester. You might be eligible to withdraw without academic penalty - seek advice from the Faculty that administers your program.
• There are no provisions for exemption from an assessment item within UQ rules. If you are unable to submit an assessment piece then, under special circumstances, you may be granted an exemption, but may be required to submit alternative assessment to ensure all learning outcomes are met.

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:

• Applications can be submitted no later than 5 calendar days after the date of the original exam.
• There are no provisions to defer a deferred exam. You need to be available to sit your deferred examination.
• Your deferred examination request(s) must have a status of "submitted" in mySI-net to be assessed.
• All applications for deferred in-semester examinations are assessed by the relevant school. Applications for deferred end-of-semester examinations are assessed by the Academic Services Division.
• You’ll receive an email to your student email account when the status of your application is updated.
• If you have a medical condition, mental health condition or disability and require alternative arrangements for your deferred exam you’ll need to complete the online alternative exam arrangements through my.UQ. This is in addition to your deferred examinations request. You need to submit this request on the same day as your request for a deferred exam or supplementary assessment. Contact Student Services if you need assistance completing your alternative exam arrangements request.

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.

Other course materials

Additional learning resources information

Any more recent editions of the listed texts are OK to use. Please make use of the "index" at the back of the book to search for relevant topics.

Learning activities

The learning activities for this course are outlined below. Learn more about the learning outcomes that apply to this course.

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.