Notes

5 min read

Complex Numbers, Argand Diagrams & Loci

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

1 min read

Proof by Induction

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

2 min read

Series

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

2 min read

Roots of Polynomials

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...

3 min read

Vectors

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

3 min read

Further Integration

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

2 min read

Polar Coordinates

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

1 min read

Hyperbolic Functions

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

3 min read

Matrices & Linear Transformations

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

4 min read

Differential Equations

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