1. Handbook
  2. Subjects
  3. Differential Equations

Differential Equations (MAST20030)

Undergraduate level 2Points: 12.5On Campus (Parkville)

You’re viewing the 2024 Handbook:
Or view archived Handbooks

Overview

Availability
Semester 2
FeesLook up fees

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 understand the structure of the general solutions.  It balances basic theory with concrete applications.  Topics include:
- linear ordinary differential equations and initial-value problems, including systems of first-order linear ordinary differential equations;
- Taylor series solutions of linear ordinary differential equations;
- Laplace transform methods for solving dynamical models with discontinuous inputs;
- boundary-value problems for linear ordinary differential equations and their interpretation in terms of eigenvalues and eigenfunctions;
- Fourier series solutions of certain linear partial differential equations on spatially bounded domains using separation of variables and eigenfunction expansion;
- Fourier transform solutions of certain linear partial differential equations on unbounded spatial domains.

Intended learning outcomes

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

  • Explain how linear algebra dictates the structure of the solution space of a linear differential equation;
  • Apply series methods to construct solutions of linear differential equations and initial-/boundary-value problems;
  • Utilise transform methods to find exact solutions of certain initial-/boundary-value problems;
  • Employ eigenfunction expansions in solving linear partial differential equations that naturally arise in applications.

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.

Last updated: 3 October 2024