Complex Numbers, Argand Diagrams & Loci
Adding, subtracting & multiplying complex numbers, complex equations, locust of points, modulus-argument & exponential form and de Moivre's.
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Notes
Proof by Induction
Proof by mathematical induction with sums, proving divisibility results and proof with matrices.
Series
Sums of natural numbers, squares & cubes, the method of differences, the Maclaurin series expansion and standard results.
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...
Vectors
Vector & Cartesian equations for lines & planes, scalar product, angles between lines & planes, points of intersection and perpendiculars.
Further Integration
Improper integrals, converging/diverging integrals, mean value of functions, inverse trigonometry, partial fractions & volumes of revolution
Polar Coordinates
Converting between polar and Cartesian systems, sketching polar curves, finding area enclosed by polar curves and finding tangents.
Hyperbolic Functions
Hyperbolic functions as exponential functions, hyperbolic graphs, inverse hyperbolic functions, integrating & differentiating hyperbolics.
Matrices & Linear Transformations
Matrix addition & multiplication, determinants, inverse matrices, matrix systems & geometry, reflections, rotations, stretches & reverses.
Differential Equations
Integrating factor, second-order homogeneous and non-homogeneous differential equations, simple harmonic motion and coupled simultaneous.
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