• Offered by Department of Mathematics
• ANU College ANU Joint Colleges of Science
• Course subject Mathematics
• Areas of interest Mathematics
• Course convener
• AsPr Barry Croke
• Dr Raquel Salmeron
• Mode of delivery In Person
• Offered in First Semester 2015
Differential Equations and Applications (MATH2305)

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.

## 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 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.

## Indicative Assessment

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)

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.

48 lectures and 10 tutorials

## Requisite and Incompatibility

To enrol in this course you must have successfully completed MATH1014 or MATH1116. You are not able to enrol in this course if you have previously completed MATH2405.

## 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).

## Fees

Tuition fees are for the academic year indicated at the top of the page.

If you are a domestic graduate coursework or international student you will be required to pay tuition fees. Tuition fees are indexed annually. Further information for domestic and international students about tuition and other fees can be found at Fees.

Student Contribution Band:
2
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.

Units EFTSL
6.00 0.12500

## Course fees

Domestic fee paying students
Year Fee
2015 \$3096
International fee paying students
Year Fee
2015 \$4146
Note: Please note that fee information is for current year only.

## 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.

The list of offerings for future years is indicative only.
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
1805 16 Feb 2015 06 Mar 2015 31 Mar 2015 29 May 2015 In Person N/A