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This is a glossary of graph theory. Graph theory is the study of graphs, systems of nodes or vertices connected in pairs by lines or edges.
== Symbols ==
Square brackets [ ]
G[S] is the induced subgraph of a graph G for vertex subset S.
Prime symbol '
The prime symbol is often used to modify notation for graph inva... | Wikipedia/Infinite_graph |
In graph theory, a perfect graph is a graph in which the chromatic number equals the size of the maximum clique, both in the graph itself and in every induced subgraph. In all graphs, the chromatic number is greater than or equal to the size of the maximum clique, but they can be far apart. A graph is perfect when thes... | Wikipedia/Perfect_graph |
In graph theory, a planar graph is a graph that can be embedded in the plane, i.e., it can be drawn on the plane in such a way that its edges intersect only at their endpoints. In other words, it can be drawn in such a way that no edges cross each other. Such a drawing is called a plane graph, or a planar embedding ... | Wikipedia/Planar_graph |
In the mathematical field of graph theory, the term "null graph" may refer either to the order-zero graph, or alternatively, to any edgeless graph (the latter is sometimes called an "empty graph").
== Order-zero graph ==
The order-zero graph, K0, is the unique graph having no vertices (hence its order is zero). It ... | Wikipedia/Null_graph |
In the mathematical field of graph theory, a distance-transitive graph is a graph such that, given any two vertices v and w at any distance i, and any other two vertices x and y at the same distance, there is an automorphism of the graph that carries v to x and w to y. Distance-transitive graphs were first defined in 1... | Wikipedia/Distance-transitive_graph |
In the mathematical field of graph theory, the complement or inverse of a graph G is a graph H on the same vertices such that two distinct vertices of H are adjacent if and only if they are not adjacent in G. That is, to generate the complement of a graph, one fills in all the missing edges required to form a complete ... | Wikipedia/Complement_graph |
In graph theory, a cycle in a graph is a non-empty trail in which only the first and last vertices are equal. A directed cycle in a directed graph is a non-empty directed trail in which only the first and last vertices are equal.
A graph without cycles is called an acyclic graph. A directed graph without directed cycle... | Wikipedia/Cycle_(graph_theory) |
In mathematics, and more specifically in graph theory, a multigraph is a graph which is permitted to have multiple edges (also called parallel edges), that is, edges that have the same end nodes. Thus two vertices may be connected by more than one edge.
There are 2 distinct notions of multiple edges:
Edges without ow... | Wikipedia/Multigraph |
In graph theory, a connected graph G is said to be k-vertex-connected (or k-connected) if it has more than k vertices and remains connected whenever fewer than k vertices are removed.
The vertex-connectivity, or just connectivity, of a graph is the largest k for which the graph is k-vertex-connected.
== Definitions =... | Wikipedia/K-vertex-connected_graph |
A geometric network is an object commonly used in geographic information systems to model a series of interconnected features. A geometric network is similar to a graph in mathematics and computer science, and can be described and analyzed using theories and concepts similar to graph theory. Geometric networks are ofte... | Wikipedia/Geometric_networks |
In graph theory, the strong product is a way of combining two graphs to make a larger graph. Two vertices are adjacent in the strong product when they come from pairs of vertices in the factor graphs that are either adjacent or identical. The strong product is one of several different graph product operations that have... | Wikipedia/Strong_product_of_graphs |
In mathematics, computer science and network science, network theory is a part of graph theory. It defines networks as graphs where the vertices or edges possess attributes. Network theory analyses these networks over the symmetric relations or asymmetric relations between their (discrete) components.
Network theory ha... | Wikipedia/Network_theory |
In universal algebra and in model theory, a structure consists of a set along with a collection of finitary operations and relations that are defined on it.
Universal algebra studies structures that generalize the algebraic structures such as groups, rings, fields and vector spaces. The term universal algebra is used f... | Wikipedia/Structure_(model_theory) |
In the mathematical field of graph theory, the Petersen graph is an undirected graph with 10 vertices and 15 edges. It is a small graph that serves as a useful example and counterexample for many problems in graph theory. The Petersen graph is named after Julius Petersen, who in 1898 constructed it to be the smallest b... | Wikipedia/Petersen_graph |
In graph theory, a tree is an undirected graph in which any two vertices are connected by exactly one path, or equivalently a connected acyclic undirected graph. A forest is an undirected graph in which any two vertices are connected by at most one path, or equivalently an acyclic undirected graph, or equivalently a di... | Wikipedia/Tree_(graph_theory) |
In the mathematical field of graph theory, a complete bipartite graph or biclique is a special kind of bipartite graph where every vertex of the first set is connected to every vertex of the second set.
Graph theory itself is typically dated as beginning with Leonhard Euler's 1736 work on the Seven Bridges of Königsber... | Wikipedia/Complete_bipartite_graph |
In graph theory, a path in a graph is a finite or infinite sequence of edges which joins a sequence of vertices which, by most definitions, are all distinct (and since the vertices are distinct, so are the edges). A directed path (sometimes called dipath) in a directed graph is a finite or infinite sequence of edges wh... | Wikipedia/Path_(graph_theory) |
In probability theory, a probability density function (PDF), density function, or density of an absolutely continuous random variable, is a function whose value at any given sample (or point) in the sample space (the set of possible values taken by the random variable) can be interpreted as providing a relative likelih... | Wikipedia/Probability_density_function |
In mathematics, the characteristic equation (or auxiliary equation) is an algebraic equation of degree n upon which depends the solution of a given nth-order differential equation or difference equation. The characteristic equation can only be formed when the differential equation is linear and homogeneous, and has con... | Wikipedia/Characteristic_equation_(calculus) |
In quantum mechanics, the Hamiltonian of a system is an operator corresponding to the total energy of that system, including both kinetic energy and potential energy. Its spectrum, the system's energy spectrum or its set of energy eigenvalues, is the set of possible outcomes obtainable from a measurement of the system'... | Wikipedia/Hamiltonian_(quantum_mechanics) |
In mathematics, a field is a set on which addition, subtraction, multiplication, and division are defined and behave as the corresponding operations on rational and real numbers. A field is thus a fundamental algebraic structure which is widely used in algebra, number theory, and many other areas of mathematics.
The be... | Wikipedia/Field_(algebra) |
In mathematics and its applications, a Sturm–Liouville problem is a second-order linear ordinary differential equation of the form
d
d
x
... | Wikipedia/Sturm–Liouville_theory |
Solid mechanics (also known as mechanics of solids) is the branch of continuum mechanics that studies the behavior of solid materials, especially their motion and deformation under the action of forces, temperature changes, phase changes, and other external or internal agents.
Solid mechanics is fundamental for civil, ... | Wikipedia/Solid_mechanics |
In mathematics, a square-integrable function, also called a quadratically integrable function or
L
2
{\displaystyle L^{2}}
function or square-summable function, is a real- or complex-valued measurable function for which th... | Wikipedia/Square-integrable_function |
Q methodology is a research method used in psychology and in social sciences to study people's "subjectivity"—that is, their viewpoint. Q was developed by psychologist William Stephenson. It has been used both in clinical settings for assessing a patient's progress over time (intra-rater comparison), as well as in rese... | Wikipedia/Q_methodology |
In numerical analysis, one of the most important problems is designing efficient and stable algorithms for finding the eigenvalues of a matrix. These eigenvalue algorithms may also find eigenvectors.
== Eigenvalues and eigenvectors ==
Given an n × n square matrix A of real or complex numbers, an eigenvalue λ and it... | Wikipedia/Eigenvalue_algorithm |
The Schrödinger equation is a partial differential equation that governs the wave function of a non-relativistic quantum-mechanical system.: 1–2 Its discovery was a significant landmark in the development of quantum mechanics. It is named after Erwin Schrödinger, an Austrian physicist, who postulated the equation in 1... | Wikipedia/Schrödinger_equation |
Molecular physics is the study of the physical properties of molecules and molecular dynamics. The field overlaps significantly with physical chemistry, chemical physics, and quantum chemistry. It is often considered as a sub-field of atomic, molecular, and optical physics. Research groups studying molecular physics ar... | Wikipedia/Molecular_physics |
In quantum physics, a measurement is the testing or manipulation of a physical system to yield a numerical result. A fundamental feature of quantum theory is that the predictions it makes are probabilistic. The procedure for finding a probability involves combining a quantum state, which mathematically describes a quan... | Wikipedia/Measurement_in_quantum_mechanics |
In mathematics, specifically in spectral theory, an eigenvalue of a closed linear operator is called normal if the space admits a decomposition into a direct sum of a finite-dimensional generalized eigenspace and an invariant subspace where
A
−
λ
I
{\displ... | Wikipedia/Normal_eigenvalue |
The moment of inertia, otherwise known as the mass moment of inertia, angular/rotational mass, second moment of mass, or most accurately, rotational inertia, of a rigid body is defined relatively to a rotational axis. It is the ratio between the torque applied and the resulting angular acceleration about that axis.: 27... | Wikipedia/Principal_axis_(mechanics) |
In numerical analysis, a numerical method is a mathematical tool designed to solve numerical problems. The implementation of a numerical method with an appropriate convergence check in a programming language is called a numerical algorithm.
== Mathematical definition ==
Let
F
(
... | Wikipedia/Numerical_method |
In mathematics, an integral is the continuous analog of a sum, which is used to calculate areas, volumes, and their generalizations. Integration, the process of computing an integral, is one of the two fundamental operations of calculus, the other being differentiation. Integration was initially used to solve problems ... | Wikipedia/Integration_(calculus) |
In mathematics, power iteration (also known as the power method) is an eigenvalue algorithm: given a diagonalizable matrix
A
{\displaystyle A}
, the algorithm will produce a number
λ
{\displaystyle \lambda }
, which is the greatest (i... | Wikipedia/Power_method |
In mathematics, spectral theory is an inclusive term for theories extending the eigenvector and eigenvalue theory of a single square matrix to a much broader theory of the structure of operators in a variety of mathematical spaces. It is a result of studies of linear algebra and the solutions of systems of linear equat... | Wikipedia/Spectral_theory |
In computational mathematics, an iterative method is a mathematical procedure that uses an initial value to generate a sequence of improving approximate solutions for a class of problems, in which the i-th approximation (called an "iterate") is derived from the previous ones.
A specific implementation with termination... | Wikipedia/Iterative_method |
The moment of inertia, otherwise known as the mass moment of inertia, angular/rotational mass, second moment of mass, or most accurately, rotational inertia, of a rigid body is defined relatively to a rotational axis. It is the ratio between the torque applied and the resulting angular acceleration about that axis.: 27... | Wikipedia/Inertia_tensor |
Mechanics (from Ancient Greek μηχανική (mēkhanikḗ) 'of machines') is the area of physics concerned with the relationships between force, matter, and motion among physical objects. Forces applied to objects may result in displacements, which are changes of an object's position relative to its environment.
Theoretical e... | Wikipedia/Mechanics |
In mathematics, a stereographic projection is a perspective projection of the sphere, through a specific point on the sphere (the pole or center of projection), onto a plane (the projection plane) perpendicular to the diameter through the point. It is a smooth, bijective function from the entire sphere except the cente... | Wikipedia/Stereographic_projection |
In mathematics, a homothety (or homothecy, or homogeneous dilation) is a transformation of an affine space determined by a point S called its center and a nonzero number k called its ratio, which sends point X to a point X′ by the rule,
S
... | Wikipedia/Homothetic_transformation |
The Roothaan equations are a representation of the Hartree–Fock equation in a non orthonormal basis set which can be of Gaussian-type or Slater-type. It applies to closed-shell molecules or atoms where all molecular orbitals or atomic orbitals, respectively, are doubly occupied. This is generally called Restricted Hart... | Wikipedia/Roothaan_equations |
In physics, the number of degrees of freedom (DOF) of a mechanical system is the number of independent parameters required to completely specify its configuration or state. That number is an important property in the analysis of systems of bodies in mechanical engineering, structural engineering, aerospace engineering... | Wikipedia/Degrees_of_freedom_(mechanics) |
In linear algebra, a Householder transformation (also known as a Householder reflection or elementary reflector) is a linear transformation that describes a reflection about a plane or hyperplane containing the origin. The Householder transformation was used in a 1958 paper by Alston Scott Householder.
== Definition ... | Wikipedia/Householder_transformation |
In physics, scattering is a wide range of physical processes where moving particles or radiation of some form, such as light or sound, are forced to deviate from a straight trajectory by localized non-uniformities (including particles and radiation) in the medium through which they pass. In conventional use, this also ... | Wikipedia/Scattering_theory |
In mathematics, a recurrence relation is an equation according to which the
n
{\displaystyle n}
th term of a sequence of numbers is equal to some combination of the previous terms. Often, only
k
{\displaystyle k}
previous terms of th... | Wikipedia/Difference_equation |
In applied mathematics, antieigenvalue theory was developed by Karl Gustafson from 1966 to 1968. The theory is applicable to numerical analysis, wavelets, statistics, quantum mechanics, finance and optimization.
The antieigenvectors
x
{\displaystyle x}
are the vectors most tu... | Wikipedia/Antieigenvalue_theory |
Structural equation modeling (SEM) is a diverse set of methods used by scientists for both observational and experimental research. SEM is used mostly in the social and behavioral science fields, but it is also used in epidemiology, business, and other fields. A common definition of SEM is, "...a class of methodologies... | Wikipedia/Structural_equation_model |
In mathematics, particularly in functional analysis, the spectrum of a bounded linear operator (or, more generally, an unbounded linear operator) is a generalisation of the set of eigenvalues of a matrix. Specifically, a complex number
λ
{\displaystyle \lambda }
is said to b... | Wikipedia/Spectrum_(functional_analysis) |
In continuum mechanics, stress is a physical quantity that describes forces present during deformation. For example, an object being pulled apart, such as a stretched elastic band, is subject to tensile stress and may undergo elongation. An object being pushed together, such as a crumpled sponge, is subject to compress... | Wikipedia/Stress_(mechanics) |
The Lanczos algorithm is an iterative method devised by Cornelius Lanczos that is an adaptation of power methods to find the
m
{\displaystyle m}
"most useful" (tending towards extreme highest/lowest) eigenvalues and eigenvectors of an
n
×
... | Wikipedia/Lanczos_algorithm |
In mathematics, stability theory addresses the stability of solutions of differential equations and of trajectories of dynamical systems under small perturbations of initial conditions. The heat equation, for example, is a stable partial differential equation because small perturbations of initial data lead to small v... | Wikipedia/Stability_theory |
In mathematics, an eigenfunction of a linear operator D defined on some function space is any non-zero function
f
{\displaystyle f}
in that space that, when acted upon by D, is only multiplied by some scaling factor called an eigenvalue. As an equation, this condition can be ... | Wikipedia/Eigenfunction |
In mathematics, the quadratic eigenvalue problem (QEP), is to find scalar eigenvalues
λ
{\displaystyle \lambda }
, left eigenvectors
y
{\displaystyle y}
and right eigenvectors
x
{\displaystyle ... | Wikipedia/Quadratic_eigenvalue_problem |
In quantum physics, a wave function (or wavefunction) is a mathematical description of the quantum state of an isolated quantum system. The most common symbols for a wave function are the Greek letters ψ and Ψ (lower-case and capital psi, respectively). Wave functions are complex-valued. For example, a wave function mi... | Wikipedia/Wavefunction |
Poisson's equation is an elliptic partial differential equation of broad utility in theoretical physics. For example, the solution to Poisson's equation is the potential field caused by a given electric charge or mass density distribution; with the potential field known, one can then calculate the corresponding electro... | Wikipedia/Poisson's_equation |
In mathematics and physics (more specifically thermodynamics), the heat equation is a parabolic partial differential equation. The theory of the heat equation was first developed by Joseph Fourier in 1822 for the purpose of modeling how a quantity such as heat diffuses through a given region. Since then, the heat equat... | Wikipedia/Heat_equation |
Energy (from Ancient Greek ἐνέργεια (enérgeia) 'activity') is the quantitative property that is transferred to a body or to a physical system, recognizable in the performance of work and in the form of heat and light. Energy is a conserved quantity—the law of conservation of energy states that energy can be converted ... | Wikipedia/Energy |
In mathematics, spectral graph theory is the study of the properties of a graph in relationship to the characteristic polynomial, eigenvalues, and eigenvectors of matrices associated with the graph, such as its adjacency matrix or Laplacian matrix.
The adjacency matrix of a simple undirected graph is a real symmetric m... | Wikipedia/Spectral_graph_theory |
In numerical linear algebra, the QR algorithm or QR iteration is an eigenvalue algorithm: that is, a procedure to calculate the eigenvalues and eigenvectors of a matrix. The QR algorithm was developed in the late 1950s by John G. F. Francis and by Vera N. Kublanovskaya, working independently. The basic idea is to perf... | Wikipedia/QR_algorithm |
In algebra, the terms left and right denote the order of a binary operation (usually, but not always, called "multiplication") in non-commutative algebraic structures.
A binary operation ∗ is usually written in the infix form:
s ∗ t
The argument s is placed on the left side, and the argument t is on the right side. Ev... | Wikipedia/Left_and_right_(algebra) |
In mathematics and physics, Laplace's equation is a second-order partial differential equation named after Pierre-Simon Laplace, who first studied its properties in 1786. This is often written as
∇
2
f
=
0
... | Wikipedia/Laplace's_equation |
In linear algebra, eigendecomposition is the factorization of a matrix into a canonical form, whereby the matrix is represented in terms of its eigenvalues and eigenvectors. Only diagonalizable matrices can be factorized in this way. When the matrix being factorized is a normal or real symmetric matrix, the decompositi... | Wikipedia/Generalized_eigenvalue_problem |
Atomic physics is the field of physics that studies atoms as an isolated system of electrons and an atomic nucleus. Atomic physics typically refers to the study of atomic structure and the interaction between atoms. It is primarily concerned with the way in which electrons are arranged around the nucleus and
the proces... | Wikipedia/Atomic_physics |
A multiplication algorithm is an algorithm (or method) to multiply two numbers. Depending on the size of the numbers, different algorithms are more efficient than others. Numerous algorithms are known and there has been much research into the topic.
The oldest and simplest method, known since antiquity as long multipli... | Wikipedia/Multiplication_algorithm |
In the mathematical subfield of numerical analysis, de Boor's algorithm is a polynomial-time and numerically stable algorithm for evaluating spline curves in B-spline form. It is a generalization of de Casteljau's algorithm for Bézier curves. The algorithm was devised by German-American mathematician Carl R. de Boor. ... | Wikipedia/De_Boor's_algorithm |
In the mathematical field of numerical analysis, De Casteljau's algorithm is a recursive method to evaluate polynomials in Bernstein form or Bézier curves, named after its inventor Paul de Casteljau. De Casteljau's algorithm can also be used to split a single Bézier curve into two Bézier curves at an arbitrary paramete... | Wikipedia/De_Casteljau's_algorithm |
In numerical analysis, the Clenshaw algorithm, also called Clenshaw summation, is a recursive method to evaluate a linear combination of Chebyshev polynomials. The method was published by Charles William Clenshaw in 1955. It is a generalization of Horner's method for evaluating a linear combination of monomials.
It ge... | Wikipedia/Clenshaw_algorithm |
In mathematics, Lill's method is a visual method of finding the real roots of a univariate polynomial of any degree. It was developed by Austrian engineer Eduard Lill in 1867. A later paper by Lill dealt with the problem of complex roots.
Lill's method involves drawing a path of straight line segments making right angl... | Wikipedia/Lill's_method |
A microcontroller (MC, uC, or μC) or microcontroller unit (MCU) is a small computer on a single integrated circuit. A microcontroller contains one or more CPUs (processor cores) along with memory and programmable input/output peripherals. Program memory in the form of NOR flash, OTP ROM, or ferroelectric RAM is also of... | Wikipedia/Microcontroller |
The felicific calculus is an algorithm formulated by utilitarian philosopher Jeremy Bentham (1748–1832) for calculating the degree or amount of pleasure that a specific action is likely to induce. Bentham, an ethical hedonist, believed the moral rightness or wrongness of an action to be a function of the amount of plea... | Wikipedia/Felicific_calculus |
A finite difference is a mathematical expression of the form f(x + b) − f(x + a). Finite differences (or the associated difference quotients) are often used as approximations of derivatives, such as in numerical differentiation.
The difference operator, commonly denoted
Δ
{\displ... | Wikipedia/Calculus_of_finite_differences |
In mathematics, Laplace's method, named after Pierre-Simon Laplace, is a technique used to approximate integrals of the form
∫
a
b
e
M
f
(
... | Wikipedia/Laplace's_method |
A mathematical model is an abstract description of a concrete system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modeling. Mathematical models are used in applied mathematics and in the natural sciences (such as physics, biology, earth science, chemis... | Wikipedia/Mathematical_model |
In classical mechanics, the Newton–Euler equations describe the combined translational and rotational dynamics of a rigid body.
Traditionally the Newton–Euler equations is the grouping together of Euler's two laws of motion for a rigid body into a single equation with 6 components, using column vectors and matrices. T... | Wikipedia/Newton–Euler_equations |
In physics, motion is when an object changes its position with respect to a reference point in a given time. Motion is mathematically described in terms of displacement, distance, velocity, acceleration, speed, and frame of reference to an observer, measuring the change in position of the body relative to that frame wi... | Wikipedia/Motion_(physics) |
Calculus Made Easy is a book on infinitesimal calculus originally published in 1910 by Silvanus P. Thompson. The original text continues to be available as of 2008 from Macmillan and Co., but a 1998 update by Martin Gardner is available from St. Martin's Press which provides an introduction; three preliminary chapters ... | Wikipedia/Calculus_Made_Easy |
In calculus, the differential represents the principal part of the change in a function
y
=
f
(
x
)
{\displaystyle y=f(x)}
with respect to changes in the independent variable. The differential
d
y
... | Wikipedia/Differential_of_a_function |
The parallelogram of forces is a method for solving (or visualizing) the results of applying two forces to an object.
When more than two forces are involved, the geometry is no longer a parallelogram, but the same principles apply to a polygon of forces.
The resultant force due to the application of a number of force... | Wikipedia/Parallelogram_of_force |
The Gauss–Newton algorithm is used to solve non-linear least squares problems, which is equivalent to minimizing a sum of squared function values. It is an extension of Newton's method for finding a minimum of a non-linear function. Since a sum of squares must be nonnegative, the algorithm can be viewed as using Newton... | Wikipedia/Gauss–Newton_algorithm |
In mathematics and computational science, the Euler method (also called the forward Euler method) is a first-order numerical procedure for solving ordinary differential equations (ODEs) with a given initial value. It is the most basic explicit method for numerical integration of ordinary differential equations and is t... | Wikipedia/Euler_method |
The Heaviside cover-up method, named after Oliver Heaviside, is a technique for quickly determining the coefficients when performing the partial-fraction expansion of a rational function in the case of linear factors.
== Method ==
Separation of a fractional algebraic expression into partial fractions is the reverse o... | Wikipedia/Heaviside_cover-up_method |
"Nova Methodus pro Maximis et Minimis" is the first published work on the subject of calculus. It was published by Gottfried Leibniz in the Acta Eruditorum in October 1684. It is considered to be the birth of infinitesimal calculus.
== Full title ==
The full title of the published work is "Nova methodus pro maximis e... | Wikipedia/Nova_Methodus_pro_Maximis_et_Minimis |
In calculus, the inverse function rule is a formula that expresses the derivative of the inverse of a bijective and differentiable function f in terms of the derivative of f. More precisely, if the inverse of
f
{\displaystyle f}
is denoted as
... | Wikipedia/Inverse_function_rule |
In mathematics, the concept of a measure is a generalization and formalization of geometrical measures (length, area, volume) and other common notions, such as magnitude, mass, and probability of events. These seemingly distinct concepts have many similarities and can often be treated together in a single mathematical ... | Wikipedia/Measure_theory |
In the history of calculus, the calculus controversy (German: Prioritätsstreit, lit. 'priority dispute') was an argument between mathematicians Isaac Newton and Gottfried Wilhelm Leibniz over who had first discovered calculus. The question was a major intellectual controversy, beginning in 1699 and reaching its peak in... | Wikipedia/Newton_v._Leibniz_calculus_controversy |
In calculus, interchange of the order of integration is a methodology that transforms iterated integrals (or multiple integrals through the use of Fubini's theorem) of functions into other, hopefully simpler, integrals by changing the order in which the integrations are performed. In some cases, the order of integrati... | Wikipedia/Order_of_integration_(calculus) |
In calculus, Newton's method (also called Newton–Raphson) is an iterative method for finding the roots of a differentiable function
f
{\displaystyle f}
, which are solutions to the equation
f
(
x
)
=
0
... | Wikipedia/Newton's_method_in_optimization |
In mathematics, a linear approximation is an approximation of a general function using a linear function (more precisely, an affine function). They are widely used in the method of finite differences to produce first order methods for solving or approximating solutions to equations.
== Definition ==
Given a twice con... | Wikipedia/Linear_approximation |
In mathematics, integrals of inverse functions can be computed by means of a formula that expresses the antiderivatives of the inverse
f
−
1
{\displaystyle f^{-1}}
of a continuous and invertible function
... | Wikipedia/Integral_of_inverse_functions |
An ethical calculus is the application of mathematics to calculate issues in ethics.
== Scope ==
Generally, ethical calculus refers to any method of determining a course of action in a circumstance that is not explicitly evaluated in one's ethical code.
A formal philosophy of ethical calculus is a development in the... | Wikipedia/Ethical_calculus |
In physics, potential energy is the energy of an object or system due to the body's position relative to other objects, or the configuration of its particles. The energy is equal to the work done against any restoring forces, such as gravity or those in a spring.
The term potential energy was introduced by the 19th-cen... | Wikipedia/Potential_energy |
A calculus (pl.: calculi), often called a stone, is a concretion of material, usually mineral salts, that forms in an organ or duct of the body. Formation of calculi is known as lithiasis (). Stones can cause a number of medical conditions.
Some common principles (below) apply to stones at any location, but for specifi... | Wikipedia/Calculus_(medicine) |
The following are important identities involving derivatives and integrals in vector calculus.
== Operator notation ==
=== Gradient ===
For a function
f
(
x
,
y
,
z
)
{\displaystyle f(x,y,z)}
in three-dimensional Ca... | Wikipedia/Vector_calculus_identities |
Itô calculus, named after Kiyosi Itô, extends the methods of calculus to stochastic processes such as Brownian motion (see Wiener process). It has important applications in mathematical finance and stochastic differential equations.
The central concept is the Itô stochastic integral, a stochastic generalization of the ... | Wikipedia/Itô_calculus |
Internal set theory (IST) is a mathematical theory of sets developed by Edward Nelson that provides an axiomatic basis for a portion of the nonstandard analysis introduced by Abraham Robinson. Instead of adding new elements to the real numbers, Nelson's approach modifies the axiomatic foundations through syntactic enri... | Wikipedia/Internal_set_theory |
Demography (from Ancient Greek δῆμος (dêmos) 'people, society' and -γραφία (-graphía) 'writing, drawing, description') is the statistical study of human populations: their size, composition (e.g., ethnic group, age), and how they change through the interplay of fertility (births), mortality (deaths), and migration.
D... | Wikipedia/Demography |
Elementary Calculus: An Infinitesimal approach is a textbook by H. Jerome Keisler. The subtitle alludes to the infinitesimal numbers of the hyperreal number system of Abraham Robinson and is sometimes given as An approach using infinitesimals. The book is available freely online and is currently published by Dover.
=... | Wikipedia/Elementary_Calculus:_An_Infinitesimal_Approach |
In mathematics, synthetic differential geometry is a formalization of the theory of differential geometry in the language of topos theory. There are several insights that allow for such a reformulation. The first is that most of the analytic data for describing the class of smooth manifolds can be encoded into certai... | Wikipedia/Synthetic_differential_geometry |
Method of Fluxions (Latin: De Methodis Serierum et Fluxionum) is a mathematical treatise by Sir Isaac Newton which served as the earliest written formulation of modern calculus. The book was completed in 1671 and posthumously published in 1736.
== Background ==
Fluxion is Newton's term for a derivative. He originally... | Wikipedia/Method_of_fluxions |
In mathematics, the inverse function theorem is a theorem that asserts that, if a real function f has a continuous derivative near a point where its derivative is nonzero, then, near this point, f has an inverse function. The inverse function is also differentiable, and the inverse function rule expresses its derivati... | Wikipedia/Inverse_function_theorem |
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