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LaTeX (KaTeX) templates
Mathematical typesetting: equations, derivations, matrices, commutative diagrams. Renders LaTeX math in the browser.
Equation Set
A block of display-mode equations (Bayes, Schrödinger, regression).
MathematicsMatrix & Linear Algebra
Matrices, eigen-decomposition, SVD.
MathematicsStatistics Formulae
Common estimators and test statistics.
MathematicsThermo / Stat Mech
Partition function, free energy, Boltzmann distribution.
MathematicsPhysics Formulae
Quantum mechanics, relativity, electromagnetism.
MathematicsSet Theory & Logic
Sets, quantifiers, common logical and topological statements.
MathematicsCalculus (Derivatives, Integrals, Limits)
Fundamental theorem, chain rule, integration by parts, common limits.
MathematicsLinear Algebra (full)
Matrix operations, eigen-decomposition, SVD, projections.
MathematicsProbability Distributions
PDF / PMF of common distributions side-by-side.
MathematicsML Loss Functions
MSE, cross-entropy, hinge, KL divergence, contrastive — formatted for slides.
MathematicsPhysics — Kinematics (SUVAT)
The four constant-acceleration equations of motion.
Chemistry & PhysicsPhysics — Newton's Laws & Dynamics
Second law, third law, linear momentum and friction.
Chemistry & PhysicsPhysics — Work, Energy & Power
Work–energy theorem, kinetic and potential energy, power.
Chemistry & PhysicsPhysics — Momentum & Impulse
Momentum, impulse and conservation in collisions.
Chemistry & PhysicsPhysics — Circular & Rotational Motion
Centripetal acceleration, torque, angular momentum.
Chemistry & PhysicsPhysics — Newtonian Gravitation
Universal gravitation, field strength, gravitational potential energy and Kepler's third law.
Chemistry & PhysicsPhysics — Simple Harmonic Motion
Defining equation, displacement, mass–spring and pendulum periods.
Chemistry & PhysicsPhysics — Waves & Sound
Wave equation, travelling wave, wavenumber and Doppler shift.
Chemistry & PhysicsPhysics — Laws of Thermodynamics
First and second laws, expansion work and Carnot efficiency.
Chemistry & PhysicsPhysics — Ideal Gas & Kinetic Theory
Ideal gas law, mean kinetic energy and rms speed.
Chemistry & PhysicsPhysics — Electrostatics
Coulomb's law, field, potential and Gauss's law.
Chemistry & PhysicsPhysics — DC Circuits
Ohm's law, power dissipation, series and parallel resistance.
Chemistry & PhysicsPhysics — Magnetism & Induction
Lorentz force, force on a current, Faraday's and Ampère's laws.
Chemistry & PhysicsPhysics — Maxwell's Equations
The four Maxwell equations in differential form.
Chemistry & PhysicsPhysics — Geometric Optics
Thin-lens equation, magnification, Snell's law and critical angle.
Chemistry & PhysicsPhysics — Special Relativity
Lorentz factor, time dilation, length contraction, mass–energy.
Chemistry & PhysicsPhysics — Quantum Foundations
Planck relation, de Broglie wavelength, photoelectric effect, uncertainty.
Chemistry & PhysicsPhysics — The Schrödinger Equation
Time-dependent and time-independent forms; particle in a box.
Chemistry & PhysicsPhysics — Nuclear & Radioactivity
Exponential decay, half-life, mass–energy and activity.
Chemistry & PhysicsPhysics — Fluid Mechanics
Hydrostatic pressure, continuity, Bernoulli and buoyancy.
Chemistry & PhysicsChemistry — Chemical Equilibrium
Equilibrium constants, reaction quotient and the van 't Hoff link.
Chemistry & PhysicsChemistry — Reaction Kinetics
Rate law, Arrhenius equation, first-order integrated rate and half-life.
Chemistry & PhysicsChemistry — Thermochemistry
Enthalpy of reaction, Gibbs free energy, calorimetry and equilibrium.
Chemistry & PhysicsChemistry — Acids, Bases & pH
pH, water ionic product, conjugate relation and Henderson–Hasselbalch.
Chemistry & PhysicsChemistry — Electrochemistry
Cell potential, Nernst equation, free energy and Faraday's law.
Chemistry & PhysicsChemistry — Gas Laws
Ideal gas law, combined law, van der Waals and Dalton's law.
Chemistry & PhysicsChemistry — Solutions & Concentration
Molarity, dilution and colligative properties.
Chemistry & PhysicsChemistry — Spectroscopy (Beer–Lambert)
Absorbance, transmittance and photon energy.
Chemistry & PhysicsChemistry — Atomic Structure (Bohr / Rydberg)
Hydrogen energy levels, Rydberg formula and Bohr radius.
Chemistry & PhysicsMath — Quadratics & Polynomials
Quadratic formula, discriminant, Vieta's formulas and difference of squares.
MathematicsMath — Binomial Theorem & Sequences
Binomial expansion, combinations, arithmetic and geometric series.
MathematicsMath — Trigonometric Identities
Pythagorean identity, angle-sum and double-angle formulas.
MathematicsMath — Differentiation Rules
Power, product, quotient and chain rules.
MathematicsMath — Common Integrals
Standard antiderivatives every calculus course relies on.
MathematicsMath — Fundamental Theorem & Techniques
FTC, integration by parts and by substitution.
MathematicsMath — Limits & L'Hôpital
Standard limits, the definition of e and L'Hôpital's rule.
MathematicsMath — Taylor & Maclaurin Series
General Taylor series plus exponential, sine and geometric series.
MathematicsMath — Complex Numbers
Imaginary unit, Euler's formula and polar form.
MathematicsMath — Vectors
Dot product, cross product, magnitude and unit vector.
MathematicsMath — Matrices & Determinants
2×2 determinant, transpose of a product, inverse and identity.
MathematicsMath — Eigenvalues & Diagonalization
Eigen-equation, characteristic polynomial, diagonalization and trace.
MathematicsMath — Probability
Addition rule, conditional probability, Bayes' theorem and expectation.
MathematicsMath — Probability Distributions
Binomial, Poisson and normal distributions plus variance identity.
MathematicsMath — Logarithms & Exponentials
Product rule, change of base, inverse identity and exponential form.
MathematicsMath — Geometry & Mensuration
Circle, sphere, cone and the Pythagorean theorem.
MathematicsBiology — Hardy–Weinberg Equilibrium
Allele and genotype frequency relations for a non-evolving population.
Life SciencesBiology — Population Growth Models
Exponential and logistic growth with the carrying-capacity solution.
Life SciencesBiology — Enzyme Kinetics (Michaelis–Menten)
Rate equation, Lineweaver–Burk form and catalytic efficiency.
Life SciencesBiology — Membrane & Nernst Potential
Equilibrium potential and the Goldman–Hodgkin–Katz equation.
Life SciencesPhysics — Projectile Motion
Range, height and trajectory for projectile launched at an angle.
Chemistry & PhysicsPhysics — Rotational Kinematics
Angular analogues of the SUVAT equations.
Chemistry & PhysicsPhysics — Elasticity & Hooke's Law
Spring force, stress, strain, Young's modulus and elastic energy.
Chemistry & PhysicsPhysics — Capacitance
Capacitance, parallel-plate formula, stored energy, combinations.
Chemistry & PhysicsPhysics — AC Circuits & Resonance
Reactance, impedance and the resonant frequency of an LC circuit.
Chemistry & PhysicsPhysics — Thermal Radiation
Wien's law, Stefan–Boltzmann and the Planck radiation law.
Chemistry & PhysicsPhysics — Heat & Calorimetry
Specific & latent heat, conduction and thermal expansion.
Chemistry & PhysicsPhysics — Orbital Mechanics
Circular orbital speed, escape velocity, period and total energy.
Chemistry & PhysicsPhysics — Measurement & Uncertainty
Mean, error propagation and the standard error of the mean.
Chemistry & PhysicsPhysics — Centre of Mass & Collisions
Centre of mass, momentum conservation and coefficient of restitution.
Chemistry & PhysicsPhysics — Matter Waves & Bohr Quantisation
de Broglie wavelength and quantised angular momentum.
Chemistry & PhysicsChemistry — Mole Calculations
The four routes to amount of substance.
Chemistry & PhysicsChemistry — Solubility Product
Ksp expression, solubility relations and the precipitation test.
Chemistry & PhysicsChemistry — Integrated Rate Laws
Zero-, first- and second-order integrated rate equations.
Chemistry & PhysicsChemistry — Effusion (Graham's Law)
Rate of effusion, mean kinetic energy and rms molecular speed.
Chemistry & PhysicsChemistry — Quantum Numbers
The four quantum numbers and their allowed values.
Chemistry & PhysicsChemistry — Bond Enthalpy & Hess
Reaction enthalpy from bond energies, formation enthalpies and Hess's law.
Chemistry & PhysicsChemistry — pOH & Ionic Equilibria
pOH, the pH/pOH relation and the acid dissociation constant.
Chemistry & PhysicsChemistry — Electrolysis (Faraday)
Charge, moles of electrons and mass deposited at an electrode.
Chemistry & PhysicsMath — Conic Sections
Standard equations of circle, ellipse, parabola and hyperbola.
MathematicsMath — Hyperbolic Functions
Definitions, the fundamental identity and a derivative.
MathematicsMath — De Moivre & Roots of Unity
De Moivre's theorem and the n-th roots of a complex number.
MathematicsMath — Least-Squares Regression
Slope, correlation coefficient and the coefficient of determination.
MathematicsMath — Numerical Methods
Trapezoidal & Simpson integration, Newton–Raphson, central difference.
MathematicsMath — Set Algebra & De Morgan
De Morgan's laws, distributivity and inclusion–exclusion.
MathematicsMath — Partial Fractions
Decomposition templates for integration.
MathematicsMath — Lines & Planes (3D)
Vector line, plane equation, point–plane distance and angle.
MathematicsMath — Means & Inequalities
AM–GM, triangle and Cauchy–Schwarz inequalities.
MathematicsMath — Number Theory
Congruence, gcd–lcm, Fermat's little theorem and Euler's totient.
MathematicsBiology — Water Potential
Water potential, solute potential and the direction of osmosis.
Life SciencesBiology — Microscopy Magnification
Magnification relations and the scale-bar calculation.
Life SciencesBiology — Surface Area : Volume
SA:V ratios for a cube and sphere and why size limits exchange.
Life SciencesBiology — Mark–Recapture (Lincoln Index)
Estimating population size from a capture–recapture sample.
Life SciencesBiology — Biodiversity Indices
Simpson's and Shannon diversity indices.
Life SciencesPhysics — Interference & Double Slit
Path difference, two-slit maxima and fringe spacing.
Chemistry & PhysicsPhysics — Standing Waves & Harmonics
Harmonic frequencies on strings and in open/closed pipes.
Chemistry & PhysicsPhysics — Resistivity & Conduction
Resistivity, its temperature dependence and current density.
Chemistry & PhysicsPhysics — EMF & Internal Resistance
EMF, terminal voltage and power delivery.
Chemistry & PhysicsPhysics — Transformers
Turns ratio, current relation and ideal-transformer power.
Chemistry & PhysicsPhysics — Nuclear Binding Energy
Mass defect, binding energy and reaction Q-value.
Chemistry & PhysicsPhysics — Lens Power & Lensmaker
Lens power, combinations and the lensmaker's equation.
Chemistry & Physics