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 the following:
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.
Note: This course is co-taught with MATH2305 but students are assessed separately.
Learning Outcomes
Upon successful completion, students will have the knowledge and skills to:
- Explain the fundamental concepts of differential equations and vector calculus and their role in modern mathematics and applied contexts.
- Develop and demonstrate accurate and efficient use of techniques involved in solving differential equations and applying vector differential operators.
- Demonstrate capacity for mathematical reasoning through analyzing, proving and explaining concepts from the theory of differential equations.
- Apply problem-solving using techniques in differential equations and vector calculus in diverse situations in physics, engineering and other mathematical contexts.
- Use deep knowledge and understanding of ODEs and vector calculus to formulate responses to complex concrete and abstract problems.
Indicative Assessment
- Exams
(50) [LO 1,2,3,4] - Workshop participation and presentations (10) [LO 1,2,3,4]
- Assignments (15) [LO 1,2,3,4,5]
- Online Homework (MATLAB Grader) (5) [LO 1,2,3,4]
- Written report (20) [LO 1,2,3,4,5]
The ANU uses 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. While the use of Turnitin is not mandatory, the ANU highly recommends Turnitin is used by both teaching staff and students. For additional information regarding Turnitin please visit the ANU Online website.
Workload
The expected workload will consist of approximately 130 hours throughout the semester including:
- Face-to face component which may include 2 hours of lectorials or 4 hours of lectures per week and up to 20 hours of workshops throughout the semester.
- Approximately 67 hours of self-directed study throughout the semester, including weekly MATLAB Grader homework and other assessment tasks
Inherent Requirements
No specific inherent requirements have been identified for this course.
Requisite and Incompatibility
You will need to contact the Mathematical Sciences Institute to request a permission code to enrol in this course.
Prescribed Texts
- Dennis G. Zill, A First Course in Differential Equation with Modelling Applications.
- James Stewart, Essential Calculus (the same textbook used in MATH1013 and MATH1014).
Assumed Knowledge
N/A
Fees
Tuition fees are for the academic year indicated at the top of the page.
Commonwealth Support (CSP) Students
If you have been offered a Commonwealth supported place, your fees are set by the Australian Government for each course. At ANU 1 EFTSL is 48 units (normally 8 x 6-unit courses). More information about your student contribution amount for each course at Fees.
- Student Contribution Band:
- 1
- Unit value:
- 6 units
If you are a domestic graduate coursework student with a Domestic Tuition Fee (DTF) place or international student you will be required to pay course tuition fees (see below). Course tuition fees are indexed annually. Further information for domestic and international students about tuition and other fees can be found at Fees.
Where there is a unit range displayed for this course, not all unit options below may be available.
| Units | EFTSL |
|---|---|
| 6.00 | 0.12500 |
Offerings, Dates and Class Summary Links
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.
Class summaries, if available, can be accessed by clicking on the View link for the relevant class number.
First Semester
| Class number | Class start date | Last day to enrol | Census date | Class end date | Mode Of Delivery | Class Summary |
|---|---|---|---|---|---|---|
| 2682 | 23 Feb 2026 | 02 Mar 2026 | 31 Mar 2026 | 29 May 2026 | In Person | N/A |