A-level Mathematics/AQA/MFP3

Series and limitsEdit

Two important limits:

  for any real number k

  for all k > 0

The basic series expansionsEdit








Improper intergralsEdit

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 coordinatesEdit

A diagram illustrating the relationship between polar and Cartesian coordinates.





The area bounded by a polar curveEdit

For the curve    


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

Numerical methods for the solution of first order differential equationsEdit

Euler's formulaEdit


The mid-point formulaEdit


The improved Euler formulaEdit






Second order differential equationsEdit

Further readingEdit

The AQA's free textbook [1]