Maths AI terms: D

49 of the Maths AI glossary’s terms, each with the part of the syllabus where you first meet it.

IB Maths AI glossary: D | Augment Education

D

DampingHL only · also damped, damping term, damping force, damping coefficient: A resistance to motion, modelled by a term proportional to the velocity $\dot{x}$ in an equation of motion, that removes energy from an oscillating system so that its motion dies away.
Introduced in 5.18 Second-order differential equations
Damping factorHL only: In PageRank, the probability $d$ that at each step the random surfer follows a link from the current page; with probability $1 - d$ the surfer instead jumps to a page chosen at random from the whole network.
Introduced in 3.15 Adjacency matrices
De Moivre's theoremHL only · also De Moivre theorem, powers in polar form: The result that for any integer $n$ , $\big(r(\cos\theta + \mathrm{i}\sin\theta)\big)^n = r^n(\cos n\theta + \mathrm{i}\sin n\theta)$
Decay constantHL only · also rate constant, continuous decay rate, decay constants: The positive constant $k$ in an exponential decay model $N(t) = N_0\mathrm{e}^{-kt}$ ; it measures how fast the quantity decreases, as a proportion of its current value per unit of time.
Introduced in
Decay factoralso decay factors, decay multiplier: The number between 0 and 1 by which a quantity is multiplied in each time period when it decreases by a fixed percentage; for a decrease of $p\%$ it equals $1 - \frac{p}{100}$ .
Introduced in 1.3 Geometric sequences and series
DecelerationHL only · also decelerating, slowing down, decelerate, retardation: A decrease in speed, which happens when the velocity and the acceleration have opposite signs.
Introduced in 5.13 Kinematics
Decibelalso dB, decibels, sound intensity level: The unit of a logarithmic scale of the ratio of two powers or intensities; a sound of intensity $I$ has level $L = 10\log_{10}\left(\frac{I}{I_0}\right)$
Decimal placesalso d.p., dp, decimal place: The number of digits written after the decimal point; rounding to $n$ decimal places keeps $n$ digits after the point.
Introduced in 1.6 Approximation and error
Decision ruleHL only · also decision rules, rejection rule: A statement, fixed before the data are collected, of which observed values will lead to rejecting the null hypothesis and which will not.
Introduced in 4.18 Further hypothesis testing
Decreasing functionalso decreasing, decreasing on an interval, decreasing functions, strictly decreasing: A function is decreasing on an interval if, for any two values $x_1 < x_2$ in the interval, $f(x_1) > f(x_2)$
Definite integralalso definite integrals: The number $\int_a^b f(x)\,\mathrm{d}x$ , the limit of the sum of $f(x)$ times the strip width over the interval from $x = a$
Degree (angle)HL only · also degrees, degree measure, °: A unit of angle equal to $\frac{1}{360}$ of a full turn, written with the symbol °.
Introduced in 3.7 Radian measure
Degree of a polynomialalso degree, order of a polynomial, degrees of polynomials: The highest power of the variable that appears with a non-zero coefficient in the polynomial.
Introduced in 1.8 Equations and systems using technology
Degree of a vertexHL only · also vertex degree, order of a vertex, valency: The number of edge-ends that meet at the vertex, so each ordinary edge adds 1 and each loop adds 2; it is written $\deg(V)$ .
Introduced in 3.14 Graph theory
Degree of accuracyalso accuracy, appropriate accuracy, level of accuracy, appropriate degree of accuracy: The precision to which a value is given, stated as a number of decimal places, a number of significant figures or a unit of rounding such as the nearest 10 or the nearest cent.
Introduced in 1.6 Approximation and error
Degrees of freedomalso ν, nu, df, degree of freedom: The number of frequencies in a chi-squared calculation that can vary freely once the totals are fixed, written $\nu$ (or df).
Introduced in 4.11 Hypothesis testing
Delaunay triangulationalso Delaunay triangulations, Delaunay graph: The division of the region between a set of sites into triangles, formed by joining every two sites whose Voronoi cells share an edge.
Introduced in 3.6 Voronoi diagrams
Deleted vertex algorithmHL only · also deleted-vertex algorithm, deleted vertex method: A method for a lower bound for the travelling salesman problem that deletes one vertex and its edges, finds a minimum spanning tree of the remaining graph, and adds the weights of the two edges of least weight from the deleted vertex.
Introduced in 3.16 Tree and cycle algorithms
Dependent variablealso output variable, dependent variables, response variable: The output of a function, whose value depends on the value of the independent variable, usually plotted on the vertical axis.
Introduced in 2.2 Functions, domain and range
Depositalso down payment, initial payment, up-front payment: The part of the price of an item paid at the time of purchase from the buyer's own money, so that only the remainder is borrowed.
Introduced in 1.7 Amortisation and annuities
Depreciationalso annual depreciation, depreciate, depreciates, depreciated, reducing balance depreciation: The fall in the value of an asset over time; it is often modelled as a fixed percentage of the current value lost each year.
Introduced in 1.4 Financial applications of geometric sequences
Derivativealso gradient function, f′(x), dy/dx, first derivative, derived function, derivatives: The function $f'(x)$ , also written $\frac{\mathrm{d}y}{\mathrm{d}x}$ , that gives the gradient of the graph of
Derivative of a constantalso constant rule, derivative of a constant term, d/dx(c) = 0: The derivative of any constant $c$ is 0, because the graph of $y = c$ is a horizontal line, whose gradient is 0 everywhere.
Introduced in 5.3 Differentiating polynomials
DeterminantHL only · also det A, det, determinants, det(A): A number calculated from the elements of a square matrix $A$ , written $\det A$ or $|A|$ ; for $A = \begin{pmatrix} a & b \\ c & d \end{pmatrix}$
Deviationalso deviations, deviation from the mean, deviations from the mean: The difference between a data value and the mean of the data, $x - \bar{x}$ ; it is positive for values greater than the mean and negative for values less than it.
Introduced in 4.3 Measures of central tendency and dispersion
Diagonal matrixHL only · also diagonal matrices: A square matrix in which every entry off the leading diagonal is zero.
Introduced in 1.15 Eigenvalues and eigenvectors
DiagonalisationHL only · also diagonalization, diagonalise, diagonalize, PDP⁻¹, diagonalising: Writing a square matrix $M$ as $M = PDP^{-1}$ , where $D$ is a diagonal matrix whose leading-diagonal entries are the eigenvalues of $M$
Difference of functionsalso (f − g)(x), (f - g)(x), difference of two functions, subtracting functions: The function $f - g$ whose output at each input is the output of $f$ minus the output of $g$ , so $(f - g)(x) = f(x) - g(x)$
Difference quotientalso gradient of a chord, symmetric difference, forward difference, backward difference, difference quotients: The gradient of a secant written as $\frac{f(a + h) - f(a)}{h}$ , the change in a function divided by the change in its input over an interval of width $h$ ; it gives an average rate of change and, for small $h$
Differential equationHL only · also DE, ODE, differential equations, ordinary differential equation: An equation that contains one or more derivatives of an unknown function; a solution is a function that makes the equation true for every value of the variable in its domain.
Introduced in 5.14 Setting up differential equations
Differentiationalso differentiate, differentiating, differentiated: The process of finding the derivative of a function.
Introduced in 5.1 Limits and the derivative
Direct variationalso direct proportion, directly proportional, varies directly: A relationship $y = ax^n$ with $n$ a positive integer, in which $y$ is proportional to the $n$ th power of $x$
Directed graphHL only · also digraph, directed edge, arc of a digraph: A graph in which every edge has a direction, from one vertex to another, shown by an arrow on the edge; it is also called a digraph.
Introduced in 3.14 Graph theory
Directed line segmentHL only · also arrow representation, directed line segments: A line segment with a direction from its starting point to its end point, drawn as an arrow, used to represent a vector; the segment from $A$ to $B$ is written $\overrightarrow{AB}$ .
Introduced in 3.10 Vectors
Direction vectorHL only · also direction vectors: A non-zero vector parallel to a line, which gives the line's direction; any non-zero scalar multiple of it is also a direction vector of the same line.
Introduced in 3.11 Vector equations of lines
Disc methodHL only · also disc, disk method, discs, method of discs: A way of finding a volume of revolution by treating the solid as a stack of thin circular discs perpendicular to the axis of rotation, each of volume $\pi r^2$ times its thickness, and integrating.
Introduced in 5.12 Areas and volumes
Discrete dataalso discrete, discrete variable: Quantitative data that can take only particular separate values, usually whole numbers obtained by counting.
Introduced in 4.1 Collecting data and sampling
Discrete random variablealso discrete random variables: A random variable that can take only separate, countable values, such as whole numbers, with gaps between them.
Introduced in 4.7 Discrete random variables
Discrete uniform distributionalso uniform distribution, discrete uniform: A probability distribution in which a random variable takes each of a finite number of values with the same probability; with $n$ values, each has probability $\frac{1}{n}$ .
Introduced in 4.7 Discrete random variables
DiscriminantHL only · also Δ, b² − 4ac, delta: For the quadratic $ax^2 + bx + c$ with $a \ne 0$ , the number $\Delta = b^2 - 4ac$
DisplacementHL only · also displacement s, position relative to the origin, displacements: The position of an object relative to a fixed origin on a line, given as a signed number whose sign shows which side of the origin the object is on; it is usually written $s$ or $x$ .
Introduced in 5.13 Kinematics
Displacement vectorHL only · also vector between two points, displacement vectors, vector AB: The vector $\overrightarrow{AB}$ from a point $A$ to a point $B$ , which describes the change in position from $A$
DistributivityHL only · also distributive, distributive law, A(B + C) = AB + AC: The property that $A(B + C) = AB + AC$ and $(A + B)C = AC + BC$
Divergent seriesHL only · also diverge, diverges, divergence, divergent: An infinite series whose partial sums do not approach a finite limit, either because they grow without bound or because they never settle on one value.
Introduced in 1.11 Infinite geometric series
Domainalso domain of a function, input set, domains: The set of all input values for which a function is defined.
Introduced in 2.2 Functions, domain and range
Domain restrictionHL only · also restricted domain, restricting the domain, restrict the domain: The replacement of a function's domain by a smaller set of inputs, usually chosen so that the function becomes one-to-one and has an inverse.
Introduced in 2.7 Composite and inverse functions
Dot notationHL only · also Newton's notation, ẋ, ẍ, x dot, dot notation for derivatives: A way of writing derivatives with respect to time in which a dot over a variable denotes its first derivative and two dots denote its second derivative, so $\dot{x} = \frac{\mathrm{d}x}{\mathrm{d}t}$ and $\ddot{x} = \frac{\mathrm{d}^2x}{\mathrm{d}t^2}$
Doubling timealso doubling period: The time taken for a quantity that increases by a constant factor to double in size.
Introduced in 1.3 Geometric sequences and series
Drawalso draw a graph, drawing a graph, drawing, accurate graph: To represent a function by an accurate, labelled graph made in pencil, on axes with a stated scale, with points correctly plotted and joined by a ruled straight line or a smooth curve.
Introduced in 2.3 Graphing functions with technology