# A-level Mathematics/AQA/MFP3

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< A-level Mathematics | AQA

## Contents

## 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 Eular formula[edit]

where

and

## Second order differential equations[edit]

### Euler's identity[edit]

When substituting into the identity gives

## Further reading[edit]

The AQA's free textbook [1]