Mathematics for Engineers 2 - Ordinary Differential Equations

These flashcards cover key vocabulary and concepts related to ordinary differential equations as outlined in the lecture notes for Mathematics for Engineers 2.

Ordinary Differential Equation (ODE)

An equation involving functions and their derivatives, which contains only ordinary derivatives.

First Order ODE

A differential equation where the highest order derivative present is the first derivative.

Separable ODE

A differential equation that can be expressed in a form where all instances of one variable can be separated from the instances of another, allowing for integration.

Linear ODE

An ordinary differential equation where the dependent variable and its derivatives appear to the first power and the coefficients are functions of the independent variable.

Homogeneous ODE

A linear ordinary differential equation where the non-homogeneous term is zero.

General solution

A solution of a differential equation that contains all possible solutions and typically includes arbitrary constants.

Particular solution

A solution of a differential equation that satisfies specific initial or boundary conditions.

Integrating factor

A function used to multiply a linear ODE to make it exact, thereby enabling integration.

Degree of a differential equation

The power of the highest derivative in the equation.

Independent variable

The variable with respect to which differentiation is carried out in a differential equation.

Dependent variable

The variable that is being differentiated in a differential equation.

Explicit solution

A solution that can be expressed as a function of the independent variable.

Implicit solution

A solution that represents a relationship between the dependent and independent variables without solving for the dependent variable explicitly.

Initial value problem

A differential equation along with specified values for the dependent variable at a given point.

Applications of ODEs in modeling

Differential equations are used to model real-world phenomena such as population dynamics, heat transfer, or electric circuits.

Singular solution

A solution to a differential equation that cannot be obtained from the general solution by choosing specific values for the constants.