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 the online quizzes via the WebAssign platform, and to access Wattle (they can use either an ANU computer or they can use their own device).

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,.

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

Please note, that where there are multiple assessment tasks of the same type, e.g weekly quizzes, a date range is used in the Assessment Summary. The first date is the approximate due date of the first task, the return date is the approximate return date for the final task. Further information is provided in the assessment section of the class summary, and details are provided on the course wattle site

Class Schedule

Week/Session	Summary of Activities	Assessment
1	Vector fields, Line integrals, the fundamental theorem of line integrals.	Assignment 1 Online WebAssign quiz 1
2	Green's Theorem, curl and divergence, Parametric surfaces and their areas.	Assignment 1 Online WebAssign quiz 2
3	Surface integrals, Stokes' Theorem.	Assignment 2 Online WebAssign quiz 3
4	The Divergence Theorem, basics of ODES, separable equations	Assignment 2, Assignment 3 Online WebAssign quiz 4
5	First order linear ODEs, exact equations, introduction to higher order equations	Assignment 4 Online WebAssign quiz 5
6	Second order ODEs, method of reduction of order, second order ODEs with constant coefficients	Assignment 4 Online WebAssign quiz 6
7	Nonhomogeneous equations and their solutions	Assignment 5 Online WebAssign quiz 7
8	Higher order linear differential equations	Assignment 5 Online WebAssign quiz 8
9	Linear system of differential equations	Assignment 6 Online WebAssign quiz 9
10	Phase plane for linear system, nonlinear system of differential equations	Assignment 7 Online WebAssign quiz 10
11	Power series solutions	Assignment 8 Online WebAssign quiz 11
12	Special functions and numerical solutions of ODEs	Review Exercises

Tutorial Registration

Workshops start in Week 3. If students do not attend a workshop or attend a workshop but do not participate in the class activities, they get no marks for that workshop.

Introductory MATLAB computer labs will be held in week 2. It is not compulsory to attend these labs, but it is highly recommended if you have not used MATLAB before. Demonstrators will be available to answer any questions you have.

Assessment Summary

Assessment task	Value	Due Date	Return of assessment	Learning Outcomes
Mid-semester exam	20 %	30/03/2020	24/04/2020	1,2,3,4,5
End of semester exam	43 %	04/06/2020	02/07/2020	1,2,3,4,5
Workshop participation	10 %	10/03/2020	29/05/2020	1,2,3,4,5
Assignments	16 %	10/03/2020	29/05/2020	1,2,3,4,5
Quizzes	11 %	02/03/2020	25/05/2020	1,2,3,4,5

* 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 ANU Online 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

Workshop participation: At the start of each workshop, the class will divide into small groups so that each person presenting a solution can check their answer with their peers and demonstrator. The person presenting the solution should feel free to ask for as much help as they want. All students should participate and ask questions. The remaining time will be left free for students to ask questions or get some feedback about the assignments etc. If students do not attend the correct workshop group they will not receive a participation grade. However, If students are unable to attend a workshop due to unforeseen circumstances (e.g. illness) they must contact the lecturer to arrange to attend another workshop. Demonstrators will keep track of students' participation. This means that students are encouraged to ask questions and contribute to the running of the workshops. It is not enough for students to turn up. They need to actively participate and work together.

Examination(s)

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 venue 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 location of the mid semester exam.

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 location exam.

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%.

Assessment Task 3

Workshop participation

Students are expected to contribute on an on-going basis throughout the semester. The date range for this task comprises the start of the semester and the last day of the teaching period. We will count the best 8 out of 10 scores, so if students miss up to two workshops due, for example, to illness students will not need to give the lecturer medical certificates.

Assessment Task 4

Assignments

There are 8 assignments due over the semester. Assignments will become available one week prior to the submission date.

It is intended that marked assignments be returned to students two weeks after the submission's deadline. Further details can be found on the Course Wattle site.

Assignment 1 available on Friday week 2. Due Friday March the 20th (week 4)

Assignment 2 available on Friday week 4. Due Friday March the 27th (week 5)

Assignment 3 available on Friday week 5. Due Friday April the 24th (week 7)

Assignment 4 available on Friday week 7. Due Friday May the 1st (week 8)

Assignment 5 available on Friday week 8. Due Friday May the 8th (week 9)

Assignment 6 available on Friday week 9. Due Friday May the 15th (week 10)

Assignment 7 available on Friday week 10. Due Friday May the 22nd (week 11)

Assignment 8 available on Friday week 11. Due Friday May the 29th (week 12)

Assessment Task 5

Quizzes

There are 11 online WebAssign weekly quizzes due over the semester. We will count the best 9 out of 11 scores.

1. Online WebAssign quiz 1 due on Monday the 2nd of March (week 2) by 11.59pm.
2. Online WebAssign quiz 2 due on Tuesday the 10th of March (week 3) by 11.59pm
3. Online WebAssign quiz 3 due on March the 16th (week 4) by 11.59pm.
4. Online WebAssign quiz 4 due on Monday the 23rd of March (week 5) by 11.59pm.
5. Online WebAssign quiz 5 due on Monday the 30th of March (week 6) by 11.59pm.
6. Online WebAssign quiz 6 due on Monday the 20th April (week 7) by 11.59pm.
7. Online WebAssign quiz 7 due on Monday the 27th of April (week 8) by 11.59pm.
8. Online WebAssign quiz 8 due on Monday the 4th of May (week 9) by 11.59pm.
9. Online WebAssign quiz 9 due on Monday the 11th of May (week 10) by 11.59pm.
10. Online WebAssign quiz 10 due on Monday the 18th of May (week 11) by 11.59pm.
11. Online WebAssign quiz 11 due on Monday the 25th of May (week 12) by 11.59pm.

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 electronically sign a declaration as part of the submission of your assignment. Please keep a copy of the assignment for your records. Unless an exemption has been approved by the Associate Dean (Education) submission must be through Turnitin.

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