Applied Mathematical Analysis (MATH2100)

Course overview

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.

• Topic 1. Systems of Ordinary Differential Equations (Kreyszig Chapter 4). Solutions to Homogeneous Linear Systems of ODE's with constant coefficients using matrices. The Phase Plane for 2-Dimensional linear and some nonlinear systems. Critical Points, linearization and the stability properties of critical points. Nonhomogeneous Linear Systems.
• Topic 2. Laplace Transforms (Kreyszig Chapter 6).The Laplace Transform and its Inverse Transform. Linearity, Shifting, Convolution and the use of Partial Fractions. Transforms of Derivatives and Integrals. Use of Laplace Transforms to solve Linear Differential Equations including those involving discontinuous functions such as the Step Function and the Dirac Delta function.
• Topic 3. Fourier Series (Brown and Churchill Chapters 1 and 2, Kreyszig Chapter 11). The idea of Fourier analysis, and of orthogonal periodic functions. Formulas for Fourier coefficients. When a Fourier expansion works. Even and odd functions and their expansions. Half-range sine and cosine series. Differentiation of Fourier series. Application of Fourier series to a forced oscillator.
• Topic 4. Partial Differential Equations (Brown and Churchill Chapters 3 to 6, Kreyszig Chapter 12). Concepts of scalar and vector fields. The operator del; grad, div and curl. Flux of a vector field. Idea of a flux integral. Gauss' divergence theorem. Conservation laws. The Laplacian operator. The heat, wave and Laplace's equation in 1, 2, and 3 dimensions. Nature of solutions of PDEs. The superposition principle and method of separation of variables. General solution of wave equation and d'Alembert's solution of the IVP. Examples. Fourier's method for wave equation. Green's function for the 1-d heat equation. Solution of IVP on whole line. Example. The error function and other examples. Heat conduction and diffusion. Temperature waves in the Earth. Kelvin's estimation of the Earth's age. Fourier's method for 1-d heat equation with source term. Short-cut when source is time independent. Revisit 1-d wave equation with forcing. Fourier's method and Laplace's equation in a 2-dimensional rectangular region. Continuation: other BCs. Idea of conjugate harmonic functions. Heat stream function. Point source for Laplace's equation in 2-d. Images for point sources/sinks. Other applications of Laplace's equation: Fluid flow, electrostatics. Potentials and stream functions.

In the School of Mathematics and Physics we are committed to creating an inclusive and empowering learning environment for all students. We value and respect the diverse range of experiences our students bring to their education, and we believe that this diversity is crucial for fostering a rich culture of knowledge sharing and meaningful exploration. We hold both students and staff accountable for actively contributing to the establishment of a respectful and supportive learning environment.

Bullying, harassment, and discrimination in any form are strictly against our principles and against UQ Policy, and will not be tolerated. We have developed a suite of resources to assist you in recognising, reporting, and addressing such behaviour. If you have any concerns about your experience in this course, we encourage you to tell a member of the course teaching team, or alternatively contact an SMP Classroom Inclusivity Champion (see Blackboard for contact details). Our Inclusivity Champions are here to listen, to understand your concerns, and to explore potential actions that can be taken to resolve them. Your well-being and a positive learning atmosphere are of utmost importance to us.

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, 7, 8, 9ﾠand 10 of the set textﾠ (E. Kreyszig, Advanced Engineering Mathematicsﾠ, 9th Edition) cover most of the background material.ﾠ ﾠ

Prerequisites

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

MATH1052 or MATH1072

Recommended companion or co-requisite courses

We recommend completing the following courses at the same time:

MATH2001 or MATH2901

Incompatible

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

MATH2010 + MATH2011

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).

Important: if you are ill, then do not attend any classes in person. Alternative arrangements can be organised – consult Blackboard for details.

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. Applied Classes are taught in weeks 2-13.

There are no Applied Classes in week 1.ﾠNote:ﾠWednesday 13ﾠAugust and Monday 6ﾠOctober are public holidays. There will be no classes on these days. If you have an applied class on one of these days, you may attend any of the other applied class groups for that week only.

Aims and outcomes

This course is built around the four mathematical notions: Systems of ordinary differential equations (ODEs); Laplace transforms; 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 and examples. 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

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

4 Assignments

Mode

Written

Category

Tutorial/ Problem Set

Weight

40%

Due date

Assignment 1: 18/08/2025 1:00 pm

Assignment 2: 8/09/2025 1:00 pm

Assignment 3: 7/10/2025 1:00 pm

Assignment 4: 27/10/2025 1:00 pm

Learning outcomes

L01, L02, L03, L04, L05, L06, L07, L08

Task description

Submission guidelines

All assessment items should be submitted electronically through Blackboard.

Deferral or extension

You may be able to apply for an extension.

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

8/11/2025 - 22/11/2025

Learning outcomes

L01, L02, L03, L04, L05, L06, L07, L08

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 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. 

Additional assessment information

Important note

Casual academics 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

To pass this course, students will be required to demonstrate a detailed understanding of course material together with a range of associated skills independent of Artificial Intelligence (AI) and Machine Translation (MT) tools.

For assessment tasks that are completed in-person (including examinations) termed “secure assessment”, the use of generative Artificial Intelligence (AI) or Machine Translation (MT) tools will not be permitted unless otherwise advised. Any attempted use of AI or MT may constitute student misconduct under the Student Code of Conduct.

Other non-secure assessment tasks (such as assignments) are designed to help you develop your understanding and skills, and to prepare you for secure assessment. You are thus generally encouraged to complete such assessment without the use of AI/MT, unless explicitly advised to the contrary in the assessment item. In any event, if you choose to use such tools, then you must clearly reference any such use within your submitted work. A failure to reference AI or MT use may constitute student 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.ﾠ

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

A different workbook will be used for each part of the course. They will be both available from blackboard.

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 for Students Policy and Procedure

Learn more about UQ policies on my.UQ and the Policy and Procedure Library.