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Camie Fons
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.
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.
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.
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.
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
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.
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.
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.
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.
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 -administration/assessments-exams/examination-timetable to confirm the date, time and location exam.
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.
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.
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.
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 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.
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.
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.
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).
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