Elasticity & Collisions

Hooke's law, modulus of elasticity, elastic potential energy, elastic collisions in one and two dimensions, direct impact, oblique impact.

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Elasticity & Collisions

Hooke's law, modulus of elasticity, elastic potential energy, elastic collisions in one and two dimensions, direct impact, oblique impact.

Momentum, Impulse, Work, Energy & Power

The impulse-momentum principle, the principle of conservation of momentum, the work-energy principle, potential & kinetic energy, power.

Complex Numbers, Argand Diagrams & Loci

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

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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