AP ECET key terms

A single number computed from the entries of a square matrix that indicates whether the matrix is invertible; it is zero exactly when the rows or columns are linearly dependent.

The number of linearly independent rows or columns in a matrix, equal to the order of the largest non-zero minor; it measures how many independent equations or directions the matrix represents.

A scalar for which a square matrix multiplied by a non-zero vector equals that scalar times the vector; it identifies a direction the matrix stretches or shrinks without rotating.

The value that a function or sequence approaches as its input approaches a specified point; the limit can exist even when the function itself is undefined at that point.

A property of a function at a point where the function's value equals the limit of the function there; informally, the graph has no break, jump, or hole at that point.

The instantaneous rate at which a function changes with respect to its variable, defined as the limit of a difference quotient; geometrically it gives the slope of the tangent line.

The derivative of a function of several variables taken with respect to one variable while the others are held constant; it measures how sensitive the function is to that single input.

The largest and smallest values a function takes, either locally within a neighbourhood or globally over a domain; candidates occur where the derivative is zero, undefined, or at endpoints.

The signed area between a function's graph and the horizontal axis over a stated interval, computed as the limit of a sum of thin rectangles; it also represents total accumulation.

An equation containing an unknown function and one or more of its derivatives; solving it means finding a function that satisfies the equation, often together with initial or boundary conditions.

The net force acting on a body equals the rate of change of its momentum; for constant mass this becomes force equals mass times acceleration, linking force, mass, and motion.

The net work done on a body by all forces equals the change in its kinetic energy; it allows problems to be solved by tracking energy rather than forces and time.

A body's resistance to angular acceleration about a chosen axis, equal to the sum of each mass element multiplied by the square of its distance from that axis.

Oscillation in which the restoring force is proportional to displacement and directed toward equilibrium, producing sinusoidal motion whose period is independent of amplitude.

For a metallic conductor at constant temperature, the current through it is directly proportional to the potential difference across it; the constant of proportionality is the resistance.

Two circuit rules: the junction rule states that charge entering a node equals charge leaving; the loop rule states that potential changes around any closed loop sum to zero.

The emission of electrons from a metal surface when light of sufficiently high frequency strikes it; the maximum electron energy depends on frequency, not intensity, supporting the photon model.

The boundary formed when p-type and n-type semiconductors are joined; diffusion creates a depletion region with a built-in potential that allows current mainly in one direction.

The amount of substance containing Avogadro's number of elementary entities, approximately 6.022 × 10^23; it connects a sample's mass to the number of particles it contains.

The concentration of a solution expressed as moles of solute per litre of solution; it changes slightly with temperature because the solution's volume expands or contracts.

A logarithmic scale of hydrogen-ion activity in a solution, defined as the negative base-ten logarithm of the hydrogen-ion concentration; values below seven are acidic at room temperature.

When a system at equilibrium is disturbed by a change in concentration, pressure, or temperature, it shifts in the direction that partially counteracts the disturbance and restores equilibrium.

A bookkeeping charge assigned to an atom in a compound by assuming bonding electrons belong to the more electronegative atom; changes in it identify oxidation and reduction.

The mixing of atomic orbitals of similar energy to form new equivalent orbitals with shapes suited to bonding; it explains geometries such as tetrahedral sp3 and planar sp2 carbon.

A device that converts chemical energy into electrical energy, or the reverse, through oxidation at the anode and reduction at the cathode; its potential depends on the electrode reactions and concentrations.

The sum of the powers to which reactant concentrations are raised in an experimentally determined rate law; it is not necessarily related to the stoichiometric coefficients of the overall equation.

Internal force per unit area within a material that resists deformation; normal stress acts perpendicular to a surface, while shear stress acts parallel to it, and both are measured in pascals.

The fractional deformation of a material, such as change in length divided by original length for tensile strain; it is dimensionless and relates to stress through the material's elastic modulus.

A linear electrical network can be replaced, as seen from two terminals, by a single voltage source in series with a single resistance; this simplifies calculations of load current and voltage.

A sequence of processes that returns a working fluid to its initial state, allowing net work output or input; examples include the Rankine cycle for steam power plants and the Otto cycle for petrol engines.

A way of organizing and storing data so that operations such as insertion, deletion, search, and traversal can be performed efficiently; examples include arrays, linked lists, stacks, queues, trees, and graphs.

A heat treatment that heats a metal and then cools it slowly to soften it, relieve internal stresses, and refine its microstructure; it often follows cold working or welding.

The controlled supply of fresh air and removal of dust, heat, and harmful gases from underground workings; it relies on fans, shafts, and airways to keep oxygen levels safe.

A vessel in which living cells or enzymes carry out biochemical reactions under controlled conditions of temperature, pH, aeration, and nutrient supply to produce a desired product.