Composites
Composite structure & types, critical fibre length, fibre volume fraction, isostrain/isostress, metal matrix, ceramic matrix, polymer matrix
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Notes
Engineering Notes
- 2 min
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
The Second Law of Thermodynamics
Reversible & irreversible processes, heat engines, actual vs ideal efficiency, Clausius' & Kelvin-Planck statement and improving efficiency.
Engineering
- 4 min
Entropy & The Second Law
The Clausius Inequality, Entropy, Temperature-Entropy T-S diagrams, enthalpy-entropy h-s diagrams, isotropic (adiabatic) efficiency.
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.
A-Level Maths
- 2 min
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
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
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
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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