Ordinary Differential Equations

You are viewing an older version of this academic item. To access a different version, adjust the year in the field above. For handbooks published prior to 2023, click the "Previous Handbooks" button at the bottom of the page.

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. … For more content click the Read More button below.

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).

Syllabus

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 … For more content click the Read More button below.

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.

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, and Bernoulli 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.

Enrolment restrictions

Available to undergraduate students only. Not available to students who have completed MTH404.

Pre-requisite

Incompatible