Advanced Multivariate Calculus & Ordinary Differential Equations (MATH1072)

Course overview

Vector calculus, arc-length, line integrals, applications. Calculus of 2 and; 3 variables: partial derivatives, conservative fields, maxima ; minima. 1st order ; linear 2nd order differential equations (constant coefficients). Applications (dynamical systems etc), numerical methods for non-linear equations and differential equations. Introduction to mathematical modelling and programming.

(MATH1072 can be studied concurrently with MATH1051)

MATH1072 covers similar content to MATH1052, but is delivered at an advanced level. Students enrolled in MATH1072 will be expected to undertake more independent learning activities compared to students enrolled in MATH1052.

The first part of MATH1072 extends knowledge of single-variable calculus to functions of more than one variable. This enables differentiation of multivariate functions to locate maxima and minima. This formulation is essential in solving many optimisation problems in science and engineering, and is also applicable to several other areas such as artificial intelligence and economics.

The second part of MATH1072 introduces ordinary differential equations (ODEs), one of the basic tools in mathematical modelling. In science and engineering ODEs can be used to describe, for instance, the motion of particles and satellites, the rate of chemical reactions, the behaviour of electrical circuits, and population dynamics in biological systems (e.g. the spread of epidemics).

The web page for MATH1072 is on Blackboard. Current course information will be available at this site, including problem sheets, assignment sheets, and solutions. Ed will also be used, as a discussion board.

Course requirements

Assumed background

Prerequisites are MATH1051 or MATH1071, or you may take MATH1051 in the same semester.

Algebra: Finding roots and factoring polynomials. Expansion and simplification of algebraic expressions. Trigonometric functions and identities. Logarithmic and the exponential function. Solving systems of linear equations. Complex numbers.

Calculus of one variable: Limits, continuity, and derivatives. Finding maxima and minima. The indefinite integral, the definite integral and area.

Advanced Calculus: Techniques of integration (substitution, parts, partial fractions), the Taylorﾠseries. ﾠ

Vectors: Vectors in 2D and 3D space. Addition of vectors. Angles between vectors; 2 X 2 matrices and inverses.

MATLAB: Students should have an understanding or be in the process of developing an understanding of the basics in MATLAB: command line calculations, writing small programs and functions (M-files), loops, vectors and matrices and plotting. All of these have been covered in MATH1051 or MATH1071.

Students who have trouble because of gaps in their background should work through problem sheets and discuss their difficulties with the lecturers. Individual help is available at the First Year Learning Centre. From week 2, students can obtain help at the First-Year Learning Centre (time and place to be advised).

Prerequisites

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

A grade of 6 or above in MATH1050; or a grade of B or higher in Queensland Year 12 Specialist Mathematics (Units 3 & 4) (or equivalent).

Companion or co-requisite courses

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

MATH1051 or MATH1071

Incompatible

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

MATH1052, MATH7052, MATH7502

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.ﾠConsult your personal timetable for times and/or locations. Students are expected to attend these sessions in person unless they have a valid reason for being unable to attend (such as illness). Alternative arrangements will be advised on Blackboard should the campus be closed for any reason. Important: if you are ill, then do not attend any classes in person. Alternative arrangements can be organised – consult Blackboard for details.

MATH1072 has a variety of classes: lectures, tutorials and computer practical classes.

There are three lectures per week. Lectures will be recorded. The content of these will follow the MATH1072 workbook or reading notes or will draw on external content as required.

There is one tutorial per week, running from Week 2. The tutorial classes will be held on campus. This gives students an opportunity to ask for help on the content covered in lectures. It is strongly recommended that you attempt problem sheets or assignment questions before the tutorial, so that you can seek help if necessary, or take part in discussions.

There are public holidays on August 14ﾠ and October 7. There will be no lecture on Wednesday, August 14. There will be no tutorial on Wednesday, August 14. If you are allocated to a tutorial on this day, please see blackboard for information on the ﾠmakeup tutorial.

There will be computer classes running from Week 2. These will only run on certain weeks. See timetable for details. Students will have the opportunity to write and test code associated with assessment items. These skills will be needed to complete some assignment tasks related to the lecture content. The computer classes will be held on campus.

Aims and outcomes

This course aims to provide students with fundamental knowledge of ordinary differential equations, multivariate calculus, and vector calculus. Students will learn analytical and numerical skills useful in developing and studying mathematical models of real-world phenomena, and will cultivate programming skills.

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

Assignment Series

Mode

Written

Category

Tutorial/ Problem Set

Weight

40% Four assignments, each 10%.

Due date

A1: 12/08/2024 1:00 pm

A2: 2/09/2024 1:00 pm

A3: 30/09/2024 1:00 pm

A4: 21/10/2024 1:00 pm

Task description

Submission guidelines

Submit via Blackboard as a single PDF.

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.

See ADDITIONAL ASSESSMENT INFORMATION for 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.

All marks for the assignments must be finalised by Friday, 1/11/2024. Discussions about missing/incorrect marks will not take place after that date.ﾠ 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.

Examination

• Hurdle
• Identity Verified
• In-person

Mode

Written

Category

Examination

Weight

60%

Due date

End of Semester Exam Period

2/11/2024 - 16/11/2024

Other conditions

Student specific, Time limited.

See the conditions definitions

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.

Additional course grading information

Note from the above criteria:

Students will need a mark of at least 40% on the final exam to achieve a passing grade in this course, regardless of their other marks; andﾠa mark of at least 35% on the final exam to achieve aﾠgrade of 3 in this course, regardless of their other marks.

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

Students should check that assignment marks are correctly entered in Grade Centre on Blackboard.ﾠAny questions or concernsﾠabout incorrect/missing marks shouldﾠbe raised with the course coordinator as soon as possible, and must be withinﾠthree weeks ofﾠthe due date of the assessment piece. It is your responsibility to check that the marks entered on the Blackboard Grade Centre have been correctly entered. If you feel an error has been made in assessing your work, then in the firstﾠinstance, you should speak with the person who marked your work (usually your tutor). If you cannot resolve this issue, then speak with the course coordinator.

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.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

Reference texts:ﾠ In addition to those already listed, there are many other texts in the UQ Library. Visit the UQ library homepage and search online.

MATLAB: MATLAB is available in the labs (you will need your username and password to log on). You may also install and use MATLAB on your own device free of charge. See http://its.uq.edu.au/StudentMatlab for details.

Blackboard: You will have access to the MATH1072 course blackboard pages. Electronic copies of learning materials and assessment items will be available. Please check Blackboard regularly for updates.

First-Year Learning Centre: From week 2, students can receiveﾠhelp at the First-Year Learning Centre (times and location to be advised).

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.