A-level Mathematics/OCR/FP3

This is the Further Pure Mathematics 3 module of the A-level Mathematics book. This module assumes that you are familiar with the ../C1/, ../C2/, ../C3/, ../C4/ and ../FP1/ modules. Please post all questions to A-level Mathematics/Discussion.

Contents

 * 1) /More About Differential Equations/
 * 2) /More About Vectors/
 * 3) /Hyperbolic Functions/
 * 4) /Complex Numbers/
 * 5) /Groups/

Formulae
By the end of this module you will be expected to have learnt the following formulae:

Differential Equations

 * An integrating factor of $$\frac{dy}{dx} + P(x)y = Q(x) $$ is $$ e^{\int P(x)\, dx}$$

Vectors

 * The vector equation of a plane through point $$\mathbf{a}$$ with normal vector $$\mathbf{n}$$ is $$(\mathbf{r}-\mathbf{a})\cdot\mathbf{n} = 0 $$

Complex Numbers
If $$ z = e^{i\theta}$$ then:
 * $$ \cos \theta = \frac{1}{2}\left(z+\frac{1}{z}\right) $$
 * $$ \sin \theta = \frac{1}{2i}\left(z-\frac{1}{z}\right) $$