Notes 

Adding, subtracting & multiplying complex numbers, complex equations, locust of points, modulus-argument & exponential form and de Moivre's.

Proof by mathematical induction with sums, proving divisibility results and proof with matrices.

Sums of natural numbers, squares & cubes, the method of differences, the Maclaurin series expansion and standard results.

Won't lie, this topic isn't particularly fun. It's just a whole lot of algebra and equations that you need to know and get right. At...

Vector & Cartesian equations for lines & planes, scalar product, angles between lines & planes, points of intersection and perpendiculars.

Improper integrals, converging/diverging integrals, mean value of functions, inverse trigonometry, partial fractions & volumes of revolution

Converting between polar and Cartesian systems, sketching polar curves, finding area enclosed by polar curves and finding tangents.

Hyperbolic functions as exponential functions, hyperbolic graphs, inverse hyperbolic functions, integrating & differentiating hyperbolics.

Matrix addition & multiplication, determinants, inverse matrices, matrix systems & geometry, reflections, rotations, stretches & reverses.

Integrating factor, second-order homogeneous and non-homogeneous differential equations, simple harmonic motion and coupled simultaneous.