PURE MATHEMATICS - Differential Calculus

 

Differential Equations

 

 

Definition

example#1

example#2

Points of Infexion

 

 

 

Definition

 

An equation containing any differential coefficients (shown below) is called a differential equation.

 

 

The solution of a differential equation is an equation relating x and y and containing no differential coefficients.

 

 

General & Particular Solution

 

The General Solution includes some unknown constant in the solution of a differential equation.

 

When some data is given, say the coordinates of a point, then a Particular Solution can be formed.

 

In this example the difference between the two solutions is self evident.

 

 

 

Example #1    

 

 

 

back to top

 

 

Example #2      

 

 

 

back to top

 

 

Points of Inflection(Inflexion)

 

The value of the second derivative can give an indication whether at a point a function has a maximum, minimum or an inflection.

 

These are all called stationary points.

 

 

 

 

A point of inflection has a zero gradient, where the point is not a maximum or a minimum value.

 

 

inflection maximum minimum

 

 

The point is where the gradient of a curve decreases(or increases) to zero before increasing(or decreasing) again.

 

 

Example

 

Find the stationary points of the function:

 

 

 

 

 

back to top

 

 

 

this week's promoted video

 

 from Physics Trek

 

 

creative commons license

All downloads are covered by a Creative Commons License.
These are free to download and to share with others provided credit is shown.
Files cannot be altered in any way.
Under no circumstances is content to be used for commercial gain.

 

 

 

 

©copyright a-levelmathstutor.com 2020 - All Rights Reserved