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.

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

 

Learning Outcomes

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

1. Explain the fundamental concepts of differential equations and vector calculus and their role in modern applied mathematics and real-world contexts.
   
2. Develop and 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

Refer to announcements / information on Wattle.

Required Resources

Students need a computer to complete online quizzes, use Matlab, access Wattle, and upload assignments to Gradescope.

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.

There are a variety of online platforms you will use to participate in your study program at ANU, across all of your courses. These could include videos 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/or photo/scan for handwritten work and drawings, and home-based assessment.

ANU outlines recommended student system requirements to ensure you are able to participate fully in your learning. Other information is also available about the various Learning Platforms you may use.

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). Feedback can also be provided to Course Conveners and teachers via the Student Experience of Learning & Teaching (SELT) feedback program. SELT surveys are confidential and also provide the Colleges and ANU Executive with opportunities to recognise excellent teaching, and opportunities for improvement.

Other Information

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

Course communication: if you have a question that may be of interest to the class as a whole please use the discussion board on Wattle. If you have a question about administrative or non-technical matters, please email both lecturers together.

Use of Artificial Intelligence (AI): unless explicitly allowed in the assessment instructions, assessment tasks for this course should be completed without the assistance of generative AI (for example, without using ChatGPT).

Class Schedule

Week/Session	Summary of Activities	Assessment
1	Vector calculus content will be delivered throughout Weeks 1 to 12 (one lecture per week in most weeks).
2	Ordinary Differential Equations (ODEs) content will be delivered throughout Weeks 1 to 12 (three lectures per week in most weeks).

Tutorial Registration

Workshops will be held during the semester and will start in Week 2. Students must use mytimetable to enrol in one of the available weekly workshop groups. Workshops will be 90 minutes in length. ANU utilises MyTimetable to enable students to view the timetable for their enrolled courses, browse, then self-allocate to small teaching activities / tutorials so they can better plan their time. Find out more on the Timetable webpage.

Assessment Summary

Assessment task	Value	Learning Outcomes
Assignments	21 %	1,2,3,4
Weekly quizzes	12 %	1,2,3,4
Workshop problems	7 %	1,2,3,4
Mid-semester exam	15 %	1,2,3,4
Final Exam	45 %	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 Integrity Rule before the commencement of their course. Other key policies and guidelines include:

• Academic Integrity Policy and Procedure
• Student Assessment (Coursework) Policy and Procedure
• Extenuating Circumstances Application
• Student Surveys and Evaluations
• Deferred Examinations
• Student Complaint Resolution Policy and Procedure
• Code of practice for teaching and learning

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 Skills website. 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

This course is delivered on campus. Note that participation is required in workshops from weeks 2 - 12. Students are also strongly advised to attend lectures, but Echo recordings will be available to accommodate clashes.

Examination(s)

This course includes a mid-semester exam and a final examination. Details will be posted on Wattle.

Assessment Task 1

Assignments

Students will complete 3 written assignments, due 11 March, 14 April, and 12 May.

Assessment Task 2

Weekly quizzes

Students will complete 11 weekly quizzes via Matlab Grader. Grader accounts will be made available to students during Week 1.

You are encouraged to work with other students on these problems and may explain the method for doing these problems, but each student must prepare their own solutions for submission.

Assessment Task 3

Workshop problems

Students must attend at least 7 workshops during the semester. Students will be assessed based on collaborative participation and problems completed at the workshop.

Assessment Task 4

Mid-semester exam

There will be an in-class mid-semester exam on 26 March.

Assessment Task 5

Final Exam

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 of the exam. There is a hurdle requirement that to pass the course you must achieve a mark of at least 35% on the final exam.

Please note: 

• If your final exam mark is less than 35% and your overall course grade is greater than or equal to 45, then you will be offered a supplementary exam. If you then pass the supplementary exam you will be awarded a grade of 50PS, otherwise you will receive a failing NCN grade.
• If you meet the hurdle requirement with an overall grade is greater than or equal to 45 and less than 50, then you will also be offered a supplementary exam. If you pass the supplementary exam you will be awarded a grade of 50PS, otherwise you will receive a failing N grade.
• 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 ANU Rules and Policies, as well as the policy for Academic Honesty and Plagiarism and the Code of practice for teaching and learning.

Academic Integrity

Academic integrity is a core part of the ANU culture as a community of scholars. The University’s students are an integral part of that community. The academic integrity principle commits all students to engage in academic work in ways that are consistent with, and actively support, academic integrity, and to uphold this commitment by behaving honestly, responsibly and ethically, and with respect and fairness, in scholarly practice.

The University expects all staff and students to be familiar with the academic integrity principle, the Academic Integrity Rule 2021, the Policy: Student Academic Integrity and Procedure: Student Academic Integrity, and to uphold high standards of academic integrity to ensure the quality and value of our qualifications.

The Academic Integrity Rule 2021 is a legal document that the University uses to promote academic integrity, and manage breaches of the academic integrity principle. The Policy and Procedure support the Rule by outlining overarching principles, responsibilities and processes. The Academic Integrity Rule 2021 commences on 1 December 2021 and applies to courses commencing on or after that date, as well as to research conduct occurring on or after that date. Prior to this, the Academic Misconduct Rule 2015 applies.

 

The University commits to assisting all students to understand how to engage in academic work in ways that are consistent with, and actively support academic integrity. All coursework students must complete the online Academic Integrity Module (Epigeum), and Higher Degree Research (HDR) students are required to complete research integrity training. The Academic Integrity website provides information about services available to assist students with their assignments, examinations and other learning activities, as well as understanding and upholding academic integrity.

Online Submission

As part of the submission of your assignments, you will be required to agree to a declaration that you understand and have abided by 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 hardcopy 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 and the submitted work must be legible. 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 solutions are posted.

Referencing Requirements

The Academic Skills website has information to assist you with your writing and assessments. The website includes information about Academic Integrity including referencing requirements for different disciplines. There is also information on Plagiarism and different ways to use source material. Any use of artificial intelligence must be properly referenced. Failure to properly cite use of Generative AI will be considered a breach of academic integrity.

Returning Assignments

Assignments will be submitted and returned via Gradescope.

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 Accessibility 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 supports you make your own decisions about how you learn and manage your workload.
• ANU Counselling promotes, supports and enhances mental health and wellbeing within the University student community.
• ANUSA supports and represents all ANU students