First Order Differential Equations of Mathematics

1
OUTLINE
• Objective
• First Order Differential Equations
• Basic Concepts and Ideas
• Differentiation Standard Forms
• Summary

OBJECTIVE
• To study the ordinary differential equations and their orders
• To understand the basic concepts and ideas
• To study the differentiation standard forms
(Such as : Product rule, Quotient rule, Chain rule)
2

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First Order Differential Equations
 We begin our program of studying ordinary differential equations and their
applications.
 This includes the derivation of differential equations.
 We start with the simplest equations.
 These are called differential equations of the first order because they
involve only the first derivation of the unknown function.

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Basic Concepts and Ideas
• An ordinary differential equation is an equation that contains one or several
derivatives of an unknown functions.
• The word “ordinary” distinguishes them from partial differential equations.
• They involve an unknown function of two or more variables and to partial
derivatives.

5
Differentiation Standard Forms

 =
 (u ± v) =

6
 =
 = . . (Product rule)
 () = (Quotient rule)

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 (Chain rule)
 =
 =
 =

8
 =
 = .
 = .
 =

9
 =
 =
 =
 =

10
 =
 =
 =
 =

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 =
 =
 = .
 = .

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Summary
• Ensure that they have already known the first order differential
equations.
• They must have knowledge of basic concepts and ideas.
• Make sure that they understand the differentiation standard forms
(such as: Product rule, Quotient rule and Chain rule)

First Order Differential Equations of Mathematics

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First Order Differential Equations of Mathematics