607 templates · page 3 of 7
LaTeX (KaTeX) templates
Mathematical typesetting: equations, derivations, matrices, commutative diagrams. Renders LaTeX math in the browser.
Physics — Cosmological Parameters
Density parameter, critical density and the flatness condition.
Chemistry & PhysicsPhysics — Kepler's Laws
The three laws of planetary motion.
Chemistry & PhysicsPhysics — Relativistic Dynamics
Total energy, kinetic energy and relativistic momentum.
Chemistry & PhysicsPhysics — Viscous Flow
Reynolds number, Stokes' drag and Poiseuille flow.
Chemistry & PhysicsChemistry — Organic Mechanism Types
The major classes of organic reaction mechanism.
Chemistry & PhysicsChemistry — Addition to Alkenes
Markovnikov's rule and electrophilic addition.
Chemistry & PhysicsChemistry — Common Ion Effect
Solubility product and the common-ion suppression of solubility.
Chemistry & PhysicsChemistry — Redox Half-Equations
Writing and combining oxidation/reduction half-equations.
Chemistry & PhysicsMath — Propositional Logic
De Morgan, implication and distributive laws of logic.
MathematicsMath — Graph Theory
Handshaking lemma, trees and Euler's formula.
MathematicsMath — Recurrence Relations
Arithmetic, geometric and linear recurrences.
MathematicsMath — Correlation & Covariance
Covariance, the Pearson and Spearman coefficients.
MathematicsMath — Confidence Intervals
Confidence intervals for a mean and a proportion.
MathematicsBiology — The Genetic Code
Codons, start/stop signals and degeneracy.
Life SciencesBiology — Fick's Law of Diffusion
Surface area, concentration gradient and exchange-surface design.
Life SciencesBiology — Gel Electrophoresis
How DNA fragments separate by size.
Life SciencesPhysics — Torque & Equilibrium
Conditions for static equilibrium and the principle of moments.
Chemistry & PhysicsPhysics — Kinetic Theory of Gas Pressure
Pressure from molecular motion and the link to temperature.
Chemistry & PhysicsPhysics — Damped & Forced Oscillations
The damped-oscillator equation, its solution and Q-factor.
Chemistry & PhysicsPhysics — Heat Engines & Refrigerators
Engine efficiency, the Carnot limit and the coefficient of performance.
Chemistry & PhysicsPhysics — Electric Potential Energy
Potential energy of charges, work and capacitor energy.
Chemistry & PhysicsPhysics — Independence of Motion
Horizontal and vertical components of projectile motion.
Chemistry & PhysicsChemistry — Combustion Analysis
Finding empirical formula from combustion products.
Chemistry & PhysicsChemistry — Rate from Concentration–Time
Defining and measuring reaction rate from a graph.
Chemistry & PhysicsChemistry — VSEPR Geometry
Electron-pair count and the resulting molecular shape.
Chemistry & PhysicsChemistry — Kc from Equilibrium Amounts
Computing the equilibrium constant from concentrations.
Chemistry & PhysicsMath — Related Rates
Chain rule in time for related quantities.
MathematicsMath — Expectation & Variance
Mean and variance of a discrete random variable.
MathematicsMath — Systems of Linear Equations
Matrix form, inverse solution and the determinant test.
MathematicsMath — Solving Trigonometric Equations
General solutions of basic trig equations.
MathematicsMath — Surds & Indices
The laws of indices and surd manipulation.
MathematicsBiology — Gas Transport in Blood
Oxygen binding, the Bohr shift and CO2 carriage.
Life SciencesBiology — Renal Clearance & GFR
Clearance, glomerular filtration rate and the nephron balance.
Life SciencesBiology — Nerve Conduction
What sets conduction speed along an axon.
Life SciencesBiology — Genetic Linkage & Mapping
Recombination frequency and genetic map distance.
Life SciencesBiology — Photosynthesis & Respiration
The complementary overall equations and energy yield.
Life SciencesPhysics — Particle Physics
The fundamental particles and hadron composition.
Chemistry & PhysicsPhysics — Wave Optics
Thin-film interference, Malus's law and Brewster's angle.
Chemistry & PhysicsPhysics — Simple Machines
Mechanical advantage, velocity ratio and efficiency.
Chemistry & PhysicsPhysics — Electromagnetic Waves
Speed of light, the field ratio and the Poynting vector.
Chemistry & PhysicsPhysics — Dimensional Analysis
Dimensions of common quantities and homogeneity checks.
Chemistry & PhysicsPhysics — Semiconductors
Doping, band gap and the diode equation.
Chemistry & PhysicsChemistry — Spectroscopy Basics
NMR chemical shift, IR, mass spectrometry and the n+1 rule.
Chemistry & PhysicsChemistry — Enthalpy of Phase Change
Latent-heat enthalpies and their additivity.
Chemistry & PhysicsChemistry — Haber Process Equilibrium
The ammonia equilibrium and the industrial compromise.
Chemistry & PhysicsChemistry — Water Hardness
Causes of hard water and how it is softened.
Chemistry & PhysicsMath — Vector Geometry
Magnitude, dot product, unit vectors and parallelism.
MathematicsMath — Loci on the Argand Diagram
Common complex-number loci.
MathematicsMath — Proof by Induction
The structure of an inductive proof.
MathematicsMath — Differentiation from First Principles
The limit definition of the derivative.
MathematicsBiology — Chargaff's Rules & DNA
Base-pairing ratios and helix dimensions.
Life SciencesBiology — Body Mass Index
BMI and its standard categories.
Life SciencesBiology — Osmolarity & Water Balance
Osmolarity, osmotic pressure and body fluids.
Life SciencesBiology — Genetic Probability
Combining probabilities in genetics problems.
Life SciencesBiology — Population Change
Demographic change and age-structure shapes.
Life SciencesPhysics — Medical Ultrasound
Acoustic impedance, reflection and depth from echo timing.
Chemistry & PhysicsPhysics — X-ray Attenuation
Beer–Lambert attenuation and the half-value layer.
Chemistry & PhysicsPhysics — Radiation Dose
Absorbed dose, equivalent dose and effective dose.
Chemistry & PhysicsPhysics — The Eye & Lens Power
Lens power in dioptres and correction of vision defects.
Chemistry & PhysicsPhysics — Hydrostatics
Pressure with depth, force, upthrust and connected fluids.
Chemistry & PhysicsPhysics — Rotational Power
Torque, rotational work, energy and angular momentum.
Chemistry & PhysicsChemistry — Amino Acids & Isoelectric Point
Zwitterions and the isoelectric point of an amino acid.
Chemistry & PhysicsChemistry — Coupled Reactions
Driving endergonic reactions with ATP hydrolysis.
Chemistry & PhysicsChemistry — Partition & Distribution
The distribution coefficient and solvent extraction.
Chemistry & PhysicsChemistry — Colorimetry
Beer–Lambert calibration to find concentration.
Chemistry & PhysicsChemistry — Radiochemical Dating
Radioactive decay used for dating and tracers.
Chemistry & PhysicsMath — Maclaurin Series
Standard Maclaurin expansions.
MathematicsMath — Iterative Methods
Fixed-point iteration and Newton–Raphson.
MathematicsMath — Normal Approximation
Approximating the binomial by a normal distribution.
MathematicsMath — Forces as Vectors
Resolving and combining forces in mechanics.
MathematicsMath — Conditional Probability
Multiplication, total probability and Bayes.
MathematicsBiology — ATP Yield of Respiration
ATP accounting across the stages of respiration.
Life SciencesBiology — Microbial Growth
Binary fission, generation time and exponential growth.
Life SciencesBiology — Resting Membrane Potential
Ion pumping and the resting potential of a neuron.
Life SciencesBiology — Epidemiology (R0)
Basic reproduction number and herd immunity.
Life SciencesPhysics — Lagrangian & Hamiltonian Mechanics
The Euler–Lagrange equation and Hamilton's equations.
Chemistry & PhysicsPhysics — Statistical Mechanics
Partition function, ensemble averages and entropy.
Chemistry & PhysicsPhysics — Quantum Operators
Momentum operator, commutator and expectation values.
Chemistry & PhysicsPhysics — Quantum Harmonic Oscillator
Energy levels, Hamiltonian and ladder operators.
Chemistry & PhysicsPhysics — Thermodynamic Potentials
Differentials of U, H, G and a Maxwell relation.
Chemistry & PhysicsPhysics — The Wave Equation
The 1-D wave equation, d'Alembert solution and 3-D form.
Chemistry & PhysicsChemistry — Chemical Potential
Chemical potential, activity and the equilibrium condition.
Chemistry & PhysicsChemistry — Hydrogenic Orbitals
Separable wavefunction, energy and normalisation.
Chemistry & PhysicsChemistry — Steady-State Kinetics
Steady-state and pre-equilibrium approximations.
Chemistry & PhysicsChemistry — Nernst Equation & Activity
Cell potential with activities and the K–E link.
Chemistry & PhysicsMath — Eigendecomposition
Diagonalisation, matrix powers and the spectral theorem.
MathematicsMath — Fourier Series & Transform
Fourier coefficients and the Fourier transform.
MathematicsMath — Laplace Transforms
Definition and standard Laplace transforms.
MathematicsMath — Group Theory
Group axioms and Lagrange's theorem.
MathematicsMath — Limits (Epsilon–Delta)
The formal definition of a limit.
MathematicsBiology — Genetic Drift
Drift variance, inbreeding and effective population size.
Life SciencesBiology — Allometric Scaling
Power-law scaling of traits with body mass.
Life SciencesBiology — Cooperative Binding (Hill)
The Hill equation for cooperative ligand binding.
Life SciencesBiology — Pharmacokinetics
First-order drug elimination and clearance.
Life SciencesBiology — Neuronal Cable Theory
Length/time constants and the Hodgkin–Huxley current.
Life SciencesPhysics — Nuclear Reactions
Alpha and beta decay with conservation laws.
Chemistry & PhysicsPhysics — Charged Particle in a Field
Circular motion of a charge in a magnetic field.
Chemistry & PhysicsPhysics — Sensors & Potential Dividers
Potential divider output and common sensing components.
Chemistry & PhysicsPhysics — Power Transmission
Why electricity is transmitted at high voltage.
Chemistry & PhysicsPhysics — Compton Scattering
Photon momentum and the Compton wavelength shift.
Chemistry & Physics