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MATH2860U:
Chapter 1
1
INTRODUCTION TO DIFFERENTIAL
EQUATIONS
Definitions and Terminology (Section 1.1, pg. 2)
Recall:
Back in Calculus II, we introduced the concept of a differential equation.
Definition:
A
differential equation
is an equation which contains the derivatives of an
unknown function (dependent variable) with respect to one or more independent
variables.
Notation:
In order for us to talk about differential equations and figure out how to solve them, it
helps to classify them according to a few criteria:
type, order, and linearity.
Ordinary Differential Equation vs Partial Differential Equation
Definition:
An
ordinary differential equation
(
ODE
) is one in which the unknown
function depends on a single
independent variable.
A
partial differential equation
(
PDE
) is one in which the unknown function depends on more than one independent
variables.
Order of a Differential Equation
Definition:
The
order
of a differential equation (either ODE or PDE) is the order of the
highest derivative in the equation.
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View Full DocumentMATH2860U:
Chapter 1
2
Note:
If we write a differential equation in the form
)
,
,
,
,
,
(
)
1
(
n
n
n
y
y
y
y
x
f
dx
y
d
where
f
is a realvalued continuous function, then the differential equation is said to be in
normal form
.
Linear vs Nonlinear Differential Equations
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 Spring '10
 Kidnan

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