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Differential Equations (MAST20030)

Undergraduate level 2Points: 12.5On Campus (Parkville)

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Overview

Year of offer2019
Subject levelUndergraduate Level 2
Subject codeMAST20030
Campus
Parkville
Availability
Semester 2
FeesSubject EFTSL, Level, Discipline & Census Date

Differential equations arise as common models in the physical, mathematical, biological and engineering sciences. This subject covers linear differential equations, both ordinary and partial, using concepts from linear algebra to provide the general structure of solutions for ordinary differential equations and linear systems. The differences between initial value problems and boundary value problems are discussed and eigenvalue problems arising from common classes of partial differential equations are introduced. Laplace transform methods are used to solve dynamical models with discontinuous inputs and the separation of variables method is applied to simple second order partial differential equations. Fourier series are derived and used to represent the solutions of the heat and wave equation and Fourier transforms are introduced. The subject balances basic theory with concrete applications.

Intended learning outcomes

At the completion of this subject, students should be able to

  • understand the solution structure of linear ordinary differential equations;
  • appreciate how partial differential equations arise in physical applications;
  • be able to find exact solutions of simple first and second-order partial differential equations in two variables;
  • know how eigenfunction and transform methods arise naturally and can be applied in differential equation problems.

Generic skills

In addition to learning specific skills that will assist students in their future careers in science, engineering, commerce, education or elsewhere, they will have the opportunity to develop generic skills that will assist them in any future career path. These include

  • problem-solving skills: the ability to engage with unfamiliar problems and identify relevant strategies;
  • analytical skills: the ability to construct and express logical arguments and to work in abstract or general terms to increase the clarity and efficiency of analysis.

Eligibility and requirements

Prerequisites

Code Name Teaching period Credit Points
MAST20009 Vector Calculus
Semester 1
Semester 2
12.5

plus one of

Code Name Teaching period Credit Points
MAST10007 Linear Algebra
Summer Term
Semester 1
Semester 2
12.5
MAST10008 Accelerated Mathematics 1
Semester 1
12.5
MAST10018
MAST10013

plus one of

Code Name Teaching period Credit Points
MAST10006 Calculus 2
Semester 1
Semester 2
12.5
MAST10009 Accelerated Mathematics 2
Semester 2
12.5
MAST10019

Corequisites

None

Non-allowed subjects

Students may only gain credit for one of MAST20030 Differential Equations, MAST30029 Partial Differential Equations (prior to 2014) and MAST30023 Differential Equations for Engineers (prior to 2012).

Students may only gain credit for one of MAST20030 Differential Equations and MAST20029 Engineering Mathematics.

Students may not enrol in MAST20009 Vector Calculus and MAST20030 Differential Equations concurrently.

Core participation requirements

The University of Melbourne is committed to providing students with reasonable adjustments to assessment and participation under the Disability Standards for Education (2005), and the Assessment and Results Policy (MPF1326). Students are expected to meet the core participation requirements for their course. These can be viewed under Entry and Participation Requirements for the course outlines in the Handbook.

Further details on how to seek academic adjustments can be found on the Student Equity and Disability Support website: http://services.unimelb.edu.au/student-equity/home

Assessment

Description

Three written assignments due at regular intervals during semester amounting to a total of up to 50 pages (30%), and a 3-hour written examination in the examination period (70%).

Dates & times

  • Semester 2
    Principal coordinatorDavid Ridout
    Mode of deliveryOn Campus — Parkville
    Contact hours36 one-hour lectures (three per week), 12 one-hour practice classes (one per week)
    Total time commitment170 hours
    Teaching period29 July 2019 to 27 October 2019
    Last self-enrol date 9 August 2019
    Census date31 August 2019
    Last date to withdraw without fail27 September 2019
    Assessment period ends22 November 2019

    Semester 2 contact information

Time commitment details

Estimated total time commitment of 170 hours

Further information

  • Texts

    Prescribed texts

    Recommended texts and other resources

    Boyce and DiPrima, Elementary Differential Equations and Boundary Value Problems, any edition, Wiley

  • Breadth options
  • Available through the Community Access Program

    About the Community Access Program (CAP)

    This subject is available through the Community Access Program (also called Single Subject Studies) which allows you to enrol in single subjects offered by the University of Melbourne, without the commitment required to complete a whole degree.

    Entry requirements including prerequisites may apply. Please refer to the CAP applications page for further information.

  • Available to Study Abroad and/or Study Exchange Students

    This subject is available to students studying at the University from eligible overseas institutions on exchange and study abroad. Students are required to satisfy any listed requirements, such as pre- and co-requisites, for enrolment in the subject.

Last updated: 12 June 2019