# MTH220 Ordinary Differential Equations (8)

This subject is designed to get students acquainted with the basic methods of solving ordinary differential equations. The methods considered include exact integration, Laplace transforms and power series. The following types of equations are considered in detail: separable, Bernoulli, homogeneous, first order linear and higher order linear with constant coefficients. An important role of ordinary differential equations in applications is illustrated by examples of electric circuits and phenomena that involve various types of growth (eg exponential, logistic).

## Availability

Session 1 (30)
Online
Wagga Wagga Campus

Continuing students should consult the SAL for current offering details: MTH220. Where differences exist between the Handbook and the SAL, the SAL should be taken as containing the correct subject offering details.

## Subject Information

HD/FL

One session

##### School

School of Computing and Mathematics

MTH102

## Learning Outcomes

##### Upon successful completion of this subject, students should:
• Be able to select and apply appropriate techniques to solve these important classes of differential equations: separable, homogeneous, first order linear, higher order linear with constant coefficients, Bernoulli, Bessel's and Legendre's equations;
• Be able to investigate various phenomena by using relevant ODEs;
• Be able to use Laplace transforms and power series to solve linear ODEs;
• Be able to investigate the convergence of a solution given by a power series.

## Syllabus

##### This subject will cover the following topics:
• Partial derivatives: differentials, total derivative, test for exactness of first order ODEs.
• First order ODEs: exact, separable, integrating factors, first order linear, Bernoulli, homogeneous, applications.
• Second order linear: homogeneous and equations with the right hand side, use of undetermined coefficients, differential operators, variation of parameters, Laplace transforms.
• Convergence of infinite series, power series solutions of differential equations, special functions.