A-level Mathematics/AQA/MFP3

Series and limits edit

Two important limits:

  for any real number k

  for all k > 0

The basic series expansions edit

 

 

 

 

 

 

 

Improper intergrals edit

The integral :  is said to be improper if

  1. the interval of integration is infinite, or;
  2. f(x) is not defined at one or both of the end points x=a and x=b, or;
  3. f(x) is not defined at one or more interior points of the interval  .

Polar coordinates edit

 
A diagram illustrating the relationship between polar and Cartesian coordinates.

 

 

 

 

The area bounded by a polar curve edit

For the curve    

 

r must be defined and be non-negative throughout the interval  

Numerical methods for the solution of first order differential equations edit

Euler's formula edit

 

The mid-point formula edit

 

The improved Euler formula edit

 

where

 

and

 

Second order differential equations edit

Further reading edit

The AQA's free textbook [1]