Exact roots of polynomial ax² + bx + c = 0

Hypotenuse c of a Euclidean right-angled triangle

Rate of change for polynomial and power terms

Product integral transformation derived from product rule

Derivative of the product of two differentiable functions

Derivative of a ratio of two differentiable functions

Derivative of composite function operations

Unit circle trigonometric invariance for all angles θ

Generalized Pythagorean theorem for non-right triangles

Polynomial expansion of powers of a binomial sum

Fundamental bridge uniting e, i, π, 1, and 0

Infinite polynomial approximation of a smooth function about point a

Net applied force equals mass times linear acceleration

Final velocity under constant linear acceleration a

Displacement under uniform acceleration from initial velocity v₀

Velocity-displacement relation independent of elapsed time

Energy possessed by mass m moving at velocity v

Potential energy near planetary surface with acceleration g

Attractive force between two point masses separated by distance r

Total momentum remains constant in an isolated system

Electric potential across resistance R carrying current I

Electrostatic force between two point electric charges

Light bending angle across boundary between refractive indices n₁ and n₂

Wave phase propagation velocity from frequency f and wavelength λ

Equation of state for ideal non-interacting gas molecules

Number of chemical moles n from sample mass m and molar mass M

Concentration in moles of dissolved solute per liter of total solution

Logarithmic index of hydrogen ion molar activity in aqueous solutions

Spontaneous condition when ΔG < 0 at constant temperature and pressure

Temperature dependence of reaction rate constant from activation energy E_a

pH of conjugate acid-base buffer solutions

Reduction potential of an electrochemical half-cell at non-standard state

Light absorbance A proportional to molar absorptivity ε, path length b, and concentration c

Mass action ratio of products to reactants at equilibrium

Recurrence relation bounding asymptotic complexity of recursive algorithms

Logarithmic comparisons required to locate an element in sorted array

Standard asymptotic ranking of computational efficiency classes

Negation of conjunction is equivalent to disjunction of negations

Negation of disjunction is equivalent to conjunction of negations

Maximum capacity of nodes in a complete binary tree of height h

Ordered arrangements of r distinct elements from a set of n

Unordered selections of r distinct elements from n possibilities

Expected informational content / uncertainty in discrete random variable X

Conversion between arbitrary base logarithms

Internal force per unit cross-sectional area in axial loading

Dimensionless ratio of elongation deformation to initial original length

Stiffness modulus relating elastic normal stress to engineering strain

Central deflection under point load P for beam of length L and inertia I

Ratio of inertial forces to viscous forces predicting laminar vs turbulent flow

Conservation of mechanical energy along a streamline in inviscid fluid

Actual consumable working electrical power with power factor cos(θ)

Conservation of charge: sum of currents entering a circuit node equals zero

Conservation of energy: algebraic sum of potential drops in closed loop is zero

Rotational moment generated by force F applied at moment arm radius r

Expected allele frequencies (p+q=1) in non-evolving diploid populations

Rate of population increase with intrinsic per capita growth rate r

Density-dependent population growth constrained by carrying capacity K

Number of standard deviations an observation X lies from population mean μ

Standard deviation of sample mean estimator across sample size n

Posterior probability updated from prior belief and likelihood evidence

Measure of statistical dispersion about the arithmetic sample mean

Discrepancy test between observed counts O and theoretical expected counts E