A-level Mathematics/OCR/FP3

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This is the Futher 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

[edit] Contents

  1. More About Differential Equations Development stage: 00% (as of {{{2}}})
  2. More About Vectors Development stage: 00% (as of {{{2}}})
  3. Hyperbolic Functions Development stage: 00% (as of {{{2}}})
  4. Complex Numbers Development stage: 00% (as of {{{2}}})
  5. Groups Development stage: 00% (as of {{{2}}})

[edit] Formulae

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

[edit] Differential Equations

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

[edit] 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

[edit] Complex Numbers

If z = eiθ then:

  • \cos \theta = \frac{1}{2}\left(z+\frac{1}{z}\right)
  • \sin \theta = \frac{1}{2i}\left(z-\frac{1}{z}\right)
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