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# MTH220 Ordinary Differential Equations (8)

### Abstract

 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).

### + Subject Availability Modes and Location

Session 1
DistanceBathurst 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

One sessionHD/FLSchool of Computing and Mathematics

Prerequisite(s)
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

 The 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.

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The information contained in the 2016 CSU Handbook was accurate at the date of publication: 06 September 2016. The University reserves the right to vary the information at any time without notice.