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Notes
Engineering
3 min read
Composites
Composite structure & types, critical fibre length, fibre volume fraction, isostrain/isostress, metal matrix, ceramic matrix, polymer matrix
Engineering Notes
2 min read
A-Level Maths Cheat Sheet
This is absolutely not a cheat sheet... We do not endorse cheating at all! It's just a better name than "List of vital but forgettable...
Engineering
4 min read
The Second Law of Thermodynamics
Reversible & irreversible processes, heat engines, actual vs ideal efficiency, Clausius' & Kelvin-Planck statement and improving efficiency.
Engineering
4 min read
Entropy & The Second Law
The Clausius Inequality, Entropy, Temperature-Entropy T-S diagrams, enthalpy-entropy h-s diagrams, isotropic (adiabatic) efficiency.
A-Level Further Maths
3 min read
Elasticity & Collisions
Hooke's law, modulus of elasticity, elastic potential energy, elastic collisions in one and two dimensions, direct impact, oblique impact.
A-Level Further Maths
2 min read
Momentum, Impulse, Work, Energy & Power
The impulse-momentum principle, the principle of conservation of momentum, the work-energy principle, potential & kinetic energy, power.
A-Level Further Maths
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.
A-Level Further Maths
1 min read
Proof by Induction
Proof by mathematical induction with sums, proving divisibility results and proof with matrices.
A-Level Further Maths
2 min read
Series
Sums of natural numbers, squares & cubes, the method of differences, the Maclaurin series expansion and standard results.
A-Level Further Maths
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...
A-Level Further Maths
3 min read
Vectors
Vector & Cartesian equations for lines & planes, scalar product, angles between lines & planes, points of intersection and perpendiculars.
A-Level Further Maths
3 min read
Further Integration
Improper integrals, converging/diverging integrals, mean value of functions, inverse trigonometry, partial fractions & volumes of revolution
A-Level Further Maths
2 min read
Polar Coordinates
Converting between polar and Cartesian systems, sketching polar curves, finding area enclosed by polar curves and finding tangents.
A-Level Further Maths
1 min read
Hyperbolic Functions
Hyperbolic functions as exponential functions, hyperbolic graphs, inverse hyperbolic functions, integrating & differentiating hyperbolics.
A-Level Further Maths
3 min read
Matrices & Linear Transformations
Matrix addition & multiplication, determinants, inverse matrices, matrix systems & geometry, reflections, rotations, stretches & reverses.
A-Level Further Maths
4 min read
Differential Equations
Integrating factor, second-order homogeneous and non-homogeneous differential equations, simple harmonic motion and coupled simultaneous.
A-Level Maths
2 min read
Modelling in Mechanics
Modelling assumptions, scalar & vector quantities, SI base units & derived units, weight, and representing forces on free body diagrams.
A-Level Maths
3 min read
Acceleration, Projectiles & Kinematics
Velocity is the rate of change of an object's position, and therefore has direction. This makes it a vector quantity, unlike speed which...
A-Level Maths
3 min read
Forces, Friction & Motion
Newton's Laws, F=ma, forces in two dimensions, moments, equilibrium, tilting, friction, static rigid bodies, connected particles and pulleys
A-Level Maths
5 min read
Data
To start off with, there is some terminology you need to be familiar with. A population is the whole set of items that are of interest A...
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