This course shows the modelling process in the context of differential equations and case studies from a number of areas such as population dynamics, economics, electric circuits, mechanical systems, fluid flow, physics and astrophysics. Analytic methods from the elementary theory of differential equations and calculus will be provided to allow for the analysis of the various models being investigated. The numerical package MATLAB will be used to study model behaviour and to obtain deeper understanding of the consequences of analytical studies.

Topics to be covered include:

First order differential equations; second order linear equations; systems of first order equations; nonlinear differential equations; power series solutions; Bessel and Legendre equations; the gamma function.

Advanced Vector Calculus - Curves and surfaces in three dimensions; parametric representations; curvilinear coordinate systems; Surface and volume integrals; use of Jacobians; gradient, divergence and curl; identities involving vector differential operators; the Laplacian; Green's and Stokes' theorems.

Learning Outcomes

Upon successful completion, students will have the knowledge and skills to:

On successful completion of this course, students will be able to:

1. Explain the fundamental concepts of differential equations and vector calculus and their role in modern applied mathematics and real-world contexts.
2. Demonstrate accurate and efficient use of techniques involved in solving differential equations and applying vector differential operators.
3. Demonstrate capacity for mathematical reasoning through analyzing, proving and explaining concepts from the theory of differential equations.
4. Apply problem-solving using techniques in differential equations and vector calculus in diverse situations in physics, engineering and other mathematical contexts.

Research-Led Teaching

Techniques covered in this course will be linked to applications in the physical and biological sciences, engineering and information technologies, economics and commerce.

Examination Material or equipment

A double sided A4 summary page (handwritten) is allowed in each of the exams.

Required Resources

Students need a computer to complete online quizzes, use Matlab and to access Wattle (they can use either an ANU computer or they can use their own device). They also need to have a web camera if they need/choose to participate in online workshops.

Recommended Resources

Highly recommended textbooks:

"Essential Calculus" by James Stewart (2nd Edition). This is the same textbook used in MATH1013 and MATH1014.

"A First Course in Differential Equation with Modelling Applications" by Dennis G. Zill,.

Recommended student system requirements 

ANU courses commonly use a number of online resources and activities including:

• video material, similar to YouTube, for lectures and other instruction
• two-way video conferencing for interactive learning
• email and other messaging tools for communication
• interactive web apps for formative and collaborative activities
• print and photo/scan for handwritten work
• home-based assessment.

To fully participate in ANU learning, students need:

• A computer or laptop. Mobile devices may work well but in some situations a computer/laptop may be more appropriate.
• Webcam
• Speakers and a microphone (e.g. headset)
• Reliable, stable internet connection. Broadband recommended. If using a mobile network or wi-fi then check performance is adequate.
• Suitable location with minimal interruptions and adequate privacy for classes and assessments.
• Printing, and photo/scanning equipment

For more information please see https://www.anu.edu.au/students/systems/recommended-student-system-requirements

 

Staff Feedback

Students will be given feedback in the following forms in this course:

• written comments
• verbal comments
• feedback to whole class, groups, individuals, focus group etc

Student Feedback

ANU is committed to the demonstration of educational excellence and regularly seeks feedback from students. Students are encouraged to offer feedback directly to their Course Convener or through their College and Course representatives (if applicable). The feedback given in these surveys is anonymous and provides the Colleges, University Education Committee and Academic Board with opportunities to recognise excellent teaching, and opportunities for improvement. The Surveys and Evaluation website provides more information on student surveys at ANU and reports on the feedback provided on ANU courses.

Other Information

Further information about assessments, including due dates, are provided on the course Wattle site.

Computer Labs

Introductory Matlab sessions will be held in the second, third and sixth weeks. Students may drop in these sessions at any time they find suitable and as many times as they wish. No booking or enrollment is necessary. The purpose of these sessions is to introduce Matlab to students that haven't used it before, or are not confident in their ability to use Matlab. Demonstrators will answer your questions on Matlab. The assessments will have Matlab questions and you will need to submit Matlab code in assignments. We highly recommend to attend the introductory sessions and ask as many questions as you can. This is not a programming course and you will not be asked to do any serious Matlab programming. Rather, the idea is to use Matlab to explore the properties of different mathematical models.

Course communication

Office hours are listed on the course Wattle page. If you would like to talk to the lecturer outside of those hours send us an e-mail (contact details are also on the Wattle page).

If you have a question that may be of interest to the class as a whole please use the discussion board. And if you post a question on the discussion that you would like one of the lecturers to answer, please address it to us specifically so we know that you are expecting us to answer it. We will not generally get involved in the discussion, so if you do not address it to us we will assume that you are expecting another student to reply.

Gradebook

Please check the records in the gradebook regularly and notify your demonstrator immediately if you believe there is a mistake. The grade for each workshop and assignment will be displayed in the gradebook for three weeks, after which time we will assume the grade is correct and it will be removed from display. A running total of your grades will remain. Our reason for doing this is to encourage you to notify the demonstrators promptly if there is a mistake, while the information is still fresh in everyone's minds. It is no good coming to the lecturers at the end of the semester complaining that the grade for workshop 1 is wrong, nobody is going to remember what happened ten weeks earlier.

Class Schedule

Week/Session	Summary of Activities	Assessment
1	Vector calculus
2	Vector calculus; Introductory Matlab session	Online quiz 1
3	Vector calculus; Introductory Matlab session	Workshop 1 Online quiz 2
4	Vector calculus	Workshop 2 Online quiz 3
5	Vector calculus	Workshop 3 Online quiz 4 Assignment 1
6	Ordinary Differential Equations; Introductory Matlab session	Workshop 4 Online quiz 5 Lectorial 1
7	Ordinary Differential Equations	Workshop 5 Online quiz 6 Lectorial 2
8	Ordinary Differential Equations	Workshop 6 Online quiz 7 Lectorial 3
9	Ordinary Differential Equations	Workshop 7 Online quiz 8 Lectorial 4 Assignment 2
10	Ordinary Differential Equations	Workshop 8 Online quiz 9 Lectorial 5
11	Ordinary Differential Equations	Workshop 9 Online quiz 10 Lectorial 6 Assignment 3
12	Ordinary Differential Equations	Workshop 10 Online quiz 11 Lectorial 7

Tutorial Registration

Workshops will be held during the semester and will start in Week 3. Students are required to enrol in one of the available weekly workshop groups by following a process that will be detailed on the course Wattle page (open at the end of week 1).

Assessment Summary

Assessment task	Value	Due Date	Return of assessment	Learning Outcomes
Mid-semester exam	20 %	*	*	1,2,3,4
End of semester exam	45 %	02/06/2022	30/06/2022	1,2,3,4
Workshop presentations	8 %	*	*	1,2,3,4
Assignments	15 %	*	*	1,2,3,4
Online quizzes	9 %	*	*	2,3,4
Lectorial activities	3 %	*	*	1,2,3,4

* If the Due Date and Return of Assessment date are blank, see the Assessment Tab for specific Assessment Task details

Policies

ANU has educational policies, procedures and guidelines, which are designed to ensure that staff and students are aware of the University’s academic standards, and implement them. Students are expected to have read the Academic Misconduct Rule before the commencement of their course. Other key policies and guidelines include:

• Student Assessment (Coursework) Policy and Procedure
• Special Assessment Consideration Policy and General Information 
• Student Surveys and Evaluations
• Deferred Examinations
• Student Complaint Resolution Policy and Procedure

Assessment Requirements

The ANU is using Turnitin to enhance student citation and referencing techniques, and to assess assignment submissions as a component of the University's approach to managing Academic Integrity. For additional information regarding Turnitin please visit the Academic Integrity . In rare cases where online submission using Turnitin software is not technically possible; or where not using Turnitin software has been justified by the Course Convener and approved by the Associate Dean (Education) on the basis of the teaching model being employed; students shall submit assessment online via ‘Wattle’ outside of Turnitin, or failing that in hard copy, or through a combination of submission methods as approved by the Associate Dean (Education). The submission method is detailed below.

Moderation of Assessment

Marks that are allocated during Semester are to be considered provisional until formalised by the College examiners meeting at the end of each Semester. If appropriate, some moderation of marks might be applied prior to final results being released.

Participation

In Semester 1 2022, this course is delivered on campus with adjustments for remote participants. Note that participation is required in Workshops from weeks 3--12 and Lectorials, from weeks 6--12.

Examination(s)

This course includes a mid-semester and a final examination. The details and mode of delivery for exams will be communicated through the course Wattle site and the ANU examination timetable.

Please note that, where a date range is used in the Assessment Summary in relation to exams, the due date and return date for mid-semester exams indicate the approximate timeframe in which the exam will be held; the due and return date for end of semester exams indicate the approximate timeframe in which the exam will be held and the date official end of Semester results are released on ISIS. Students should consult the course Wattle site and the ANU final examination timetable to confirm the date, time and mode of the exam.

Assessment Task 1

Mid-semester exam

Please check the course Wattle site and the ANU Examination Timetable to confirm the date, time and mode of the mid semester exam. The mid-semester exam will be online, using an invigilation system such as Proctorio.

Assessment Task 2

End of semester exam

The date range in the Assessment Summary indicates the start of the end of semester exam period and the date official end of semester results are released on ISIS. Please check the ANU final Examination Timetable http://www.anu.edu.au/students/program-administration/assessments-exams/examination-timetable to confirm the date, time and mode if the exam. The final exam may be online, using an invigilation system such as Proctorio.

Please note: 

• If your overall grade is a passing grade, but you get less than 45% in the final exam, you must sit further examination. If you get 45% or more in the additional exam, you will be awarded 50PS. If you get less than 45% in the additional exam, you will receive NCN.
• If your overall grade is a passing grade and you get 45% or more in your final exam, you will be awarded your overall grade.
• If your overall grade is greater than or equal to 45%, but less than 50%, you will be offered a supplementary exam. If you pass the supplementary exam you will be awarded a grade of 50PS, otherwise you will receive N.
• No further examination will be offered if your overall grade is less than 45%.

The above requirements on passing the course are contingent on a student abiding by the university examination rules. Please make sure you are familiar with the ANU Science Rules and Policies, as well as the policy for Academic Honesty and Plagiarism and the Code of practice for teaching and learning.

Assessment Task 3

Workshop presentations

During each of the workshops in weeks 3-12, you will be working in a small group (either in person or participating remotely). Each week, you will be in charge of leading your peers through at least one problem. This presentation is worth 1% each week. You are expected to prepare for this before class, but it is OK to make mistakes.

We will take your best 8 out of 10 marks for workshops, so you can miss up to two weeks without being penalised. Please do not send medical certificates if you have to miss a week.

The solutions to the worksheets will not be posted on Wattle, they are to be presented and discussed in the workshop.

Assessment Task 4

Assignments

There are 3 assignments due over the semester. One assignment will be for vector calculus part of the course and the other for the ODE part of the course.

Where possible, you are expected to check the answers to your assignment questions. For example, if you have to find the solution to a differential equation you can check if you have the right answer. This is a good habit to get into. A half mark will be taken off your grade if you do not show that you checked the answer, even if you have the right answer. If you are required to construct a differential equation to model some system, then there is no straight forward way to check your answer so you will not loose any marks if you don't. Talk to your demonstrator if you are not sure when you will be expected to check your answer. (Note that you should show some working when checking your answer, simply rewriting the original equation is not checking your answer).

When you use Matlab (or some other package) as part of the solution (including generating plots), you must submit your code with the assignment. This can either be printed and scanned with a hand written solution, or cut and pasted into a typeset solution.

It is intended that marked assignments be returned to students two weeks after the submission's deadline.

Assignment 1 available on Friday week 3. Due Tuesday (week 5)

Assignment 2 available on Friday week 7. Due Tuesday (week 9)

Assignment 3 available on Friday week 9. Due Tuesday (week 11)

Assessment Task 5

Online quizzes

There are 11 online weekly quizzes due at the start of each week from week 2 onwards. These quizzes will use Matlab grader, so you will need to register for a MathWorks account with your ANU email address. You are encouraged to work with other students on these problems, and can explain the method for doing these problems, but please do not just share answers to these problems.

From week 6--12, these quizzes will be on material in notes and videos not yet covered in class. In this part of the course, you are expected to spend at least 2 extra hours on self study learning course material from notes and videos, as there are 2 weekly hours of lectorial instead of 4 weekly hours of lectures.

Assessment Task 6

Lectorial activities

There will be 7 Lectorials on Ordinary Differential Equations, held weekly from weeks 6 through week 12 at 9--11am on Wednesdays and Thursdays. You must participate live in lectorial activities to receive marks, although an option of remote participation will be available at one of the two weekly workshop times. You are only required to participate in one lectorial per week, with the choice of Wednesday or Thursday up to you.

Academic Integrity

Academic integrity is a core part of the ANU culture as a community of scholars. At its heart, academic integrity is about behaving ethically, committing to honest and responsible scholarly practice and upholding these values with respect and fairness.

The ANU commits to assisting all members of our community to understand how to engage in academic work in ways that are consistent with, and actively support academic integrity. The ANU expects staff and students to be familiar with the academic integrity principle and Academic Misconduct Rule, uphold high standards of academic integrity and act ethically and honestly, to ensure the quality and value of the qualification that you will graduate with.

The Academic Misconduct Rule is in place to promote academic integrity and manage academic misconduct. Very minor breaches of the academic integrity principle may result in a reduction of marks of up to 10% of the total marks available for the assessment. The ANU offers a number of online and in person services to assist students with their assignments, examinations, and other learning activities. Visit the Academic Skills website for more information about academic integrity, your responsibilities and for assistance with your assignments, writing skills and study.

Online Submission

You will be required to agree to a declaration as part of the submission of your assignments, that will record your understanding of ANU academic integrity principles. Please keep a copy of the assignment for your records. MATH2305 does not use Turnitin, having been granted an exemption.

Hardcopy Submission

No hard copy submissions will be accepted unless approved by the lecturer. Students should either type their assignments or scan/take a photograph of their hand-written assignments and submit them for marking via Wattle. They also must utilise the Assignment Cover Sheet. The quality of scans/photographs must be good. If the demonstrator cannot read parts of an assignment they will give zero marks to that part. Please keep a copy of tasks completed for your own records.

Late Submission

Late submissions of assignments without an extension that is approved by the lecturer are penalised at the rate of 5% of the possible marks available per working day or part thereof. Late submission of assignments will not be accepted after a date to be specified when the assignment is set.

Referencing Requirements

Accepted academic practice for referencing sources that you use in presentations can be found via the links on the Wattle site, under the file named “ANU and College Policies, Program Information, Student Support Services and Assessment”. Alternatively, you can seek help through the Students Learning Development website.

Returning Assignments

Assignments will be submitted and returned via Wattle.

Extensions and Penalties

Extensions and late submission of assessment pieces are covered by the Student Assessment (Coursework) Policy and Procedure. Extensions may be granted for assessment pieces that are not examinations or take-home examinations. If you need an extension, you must request an extension in writing on or before the due date. If you have documented and appropriate medical evidence that demonstrates you were not able to request an extension on or before the due date, you may be able to request it after the due date.

Resubmission of Assignments

No resubmission is permitted.

Privacy Notice

The ANU has made a number of third party, online, databases available for students to use. Use of each online database is conditional on student end users first agreeing to the database licensor’s terms of service and/or privacy policy. Students should read these carefully. In some cases student end users will be required to register an account with the database licensor and submit personal information, including their: first name; last name; ANU email address; and other information.
In cases where student end users are asked to submit ‘content’ to a database, such as an assignment or short answers, the database licensor may only use the student’s ‘content’ in accordance with the terms of service – including any (copyright) licence the student grants to the database licensor. Any personal information or content a student submits may be stored by the licensor, potentially offshore, and will be used to process the database service in accordance with the licensors terms of service and/or privacy policy.
If any student chooses not to agree to the database licensor’s terms of service or privacy policy, the student will not be able to access and use the database. In these circumstances students should contact their lecturer to enquire about alternative arrangements that are available.

Distribution of grades policy

Academic Quality Assurance Committee monitors the performance of students, including attrition, further study and employment rates and grade distribution, and College reports on quality assurance processes for assessment activities, including alignment with national and international disciplinary and interdisciplinary standards, as well as qualification type learning outcomes.

Since first semester 1994, ANU uses a grading scale for all courses. This grading scale is used by all academic areas of the University.

Support for students

The University offers students support through several different services. You may contact the services listed below directly or seek advice from your Course Convener, Student Administrators, or your College and Course representatives (if applicable).

• ANU Health, safety & wellbeing for medical services, counselling, mental health and spiritual support
• ANU Diversity and inclusion for students with a disability or ongoing or chronic illness
• ANU Dean of Students for confidential, impartial advice and help to resolve problems between students and the academic or administrative areas of the University
• ANU Academic Skills and Learning Centre supports you make your own decisions about how you learn and manage your workload.
• ANU Counselling Centre promotes, supports and enhances mental health and wellbeing within the University student community.
• ANUSA supports and represents undergraduate and ANU College students
• PARSA supports and represents postgraduate and research students