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; Laplace transforms.
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.
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 ordinary differential equations and their role in modern mathematics.
2. Use ordinary differential equations to model simple electric circuits, population growth and mass-spring systems, as well as other applications.
3. Understand the basic notion of ordinary differential equations and the underlying principals of modelling physical processes.
4. Demonstrate accurate and efficient use of the Laplace transforms and their applications in the solution of ordinary differential equations.
5. Apply problem-solving using concepts and techniques from ordinary differential equations and Laplace transforms relevant to diverse situations in physics, engineering, financial mathematics and in other mathematical contexts.
Assessment will be based on:
- One mid-semester exam (25%; LO 1-5)
- Tutorial presentation (5%; LO 1-5)
- 10 Assignments (20%; LO 1-5)
- Final exam (50%; LO 1-5)
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48 lectures and 10 tutorials
Requisite and Incompatibility
Tuition fees are for the academic year indicated at the top of the page.
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- Student Contribution Band:
- Unit value:
- 6 units
If you are an undergraduate student and 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). You can find your student contribution amount for each course at Fees. Where there is a unit range displayed for this course, not all unit options below may be available.
- Domestic fee paying students
- International fee paying students
Offerings, Dates and Class Summary Links
Class summaries, if available, can be accessed by clicking on the View link for the relevant class number.
|Class number||Class start date||Last day to enrol||Census date||Class end date||Mode Of Delivery||Class Summary|
|3324||17 Feb 2014||07 Mar 2014||31 Mar 2014||30 May 2014||In Person||N/A|