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
- the interval of integration is infinite, or;
- f(x) is not defined at one or both of the end points x=a and x=b, or;
- f(x) is not defined at one or more interior points of the interval .
Polar coordinates
edit
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]