Ordinary Differential Equations

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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 solving ordinary differential equations (ODEs) in applications is illustrated by examples of electric circuits and phenomena that involve various types of growth (eg exponential, logistic).

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

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

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 apply Laplace transforms and power series to solve linear ODEs;

be able to investigate the convergence of a solution given by a power series.; and

be able to interpret mathematical models and communicate their output to non-mathematical audiences

Enrolment restrictions

Available to postgraduate students only.

Pre-requisite

Incompatible