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Finding values for variables that make an equation true
all solutions of an equation is its solution set. An equation may be solved either numerically or symbolically. Solving an equation numerically means that
Equation_solving
Differential equation containing derivatives with respect to only one variable
In mathematics, an ordinary differential equation (ODE) is a differential equation (DE) dependent on only a single independent variable. As with any other
Ordinary differential equation
Ordinary_differential_equation
Several equations of degree 1 to be solved simultaneously
\end{alignedat}}} One method for solving such a system is as follows. First, solve the top equation for x {\displaystyle x} in terms of y {\displaystyle
System_of_linear_equations
Type of functional equation (mathematics)
velocity as a function of time involves solving a differential equation and verifying its validity. Differential equations can be classified several different
Differential_equation
Mathematical formula expressing equality
consisting of two expressions related with an equals sign is an equation. Solving an equation containing variables consists of determining which values of
Equation
Methods used to find numerical solutions of ordinary differential equations
also refer to the computation of integrals. Many differential equations cannot be solved exactly. For practical purposes, however – such as in engineering –
Numerical methods for ordinary differential equations
Numerical_methods_for_ordinary_differential_equations
Polynomial equation of degree two
Solving these two linear equations provides the roots of the quadratic. For most students, factoring by inspection is the first method of solving quadratic
Quadratic_equation
Roots of multiple multivariate polynomials
methods for solving directly the equation, while software are available for automatically solving the corresponding system. When solving a system over
System of polynomial equations
System_of_polynomial_equations
Algorithms for zeros of functions
small isolating intervals for real roots or disks for complex roots. Solving an equation f(x) = g(x) is the same as finding the roots of the function h(x)
Root-finding_algorithm
Type of Diophantine equation
Pell's equation, also called the Pell–Fermat equation, is any Diophantine equation of the form x 2 − n y 2 = 1 , {\displaystyle x^{2}-ny^{2}=1,} where
Pell's_equation
faster matrix multiplication Solving systems of linear equations Biconjugate gradient method: solves systems of linear equations Conjugate gradient: an algorithm
List_of_algorithms
Polynomial equation, generally univariate
out X − α. Solving P(x) = 0 thus reduces to solving the degree n − 1 equation Q(x) = 0. See for example the case n = 3. To solve an equation of degree
Algebraic_equation
Polynomial equation whose integer solutions are sought
improvements these methods cannot solve most Diophantine equations. The difficulty of solving Diophantine equations is illustrated by Hilbert's tenth
Diophantine_equation
Polynomial equation of degree 4
Divide both sides by 2, This is a cubic equation in y. Solve for y using any method for solving such equations (e.g. conversion to a reduced cubic and
Quartic_equation
Basic concepts of algebra
enables solving a broader scope of problems. Many quantitative relationships in science and mathematics are expressed as algebraic equations. In mathematics
Elementary_algebra
Polynomial function of degree 5
Equation – more details on methods for solving Quintics. Solving Solvable Quintics Archived 2012-03-07 at the Wayback Machine – a method for solving solvable
Quintic_function
Pattern defining an infinite sequence of numbers
methods for solving differentiable equations to apply to solving difference equations, and therefore recurrence relations. Summation equations relate to
Recurrence_relation
Differential equation for the description of waves or standing wave
The wave equation is a second-order linear partial differential equation for the description of waves or standing wave fields such as mechanical waves
Wave_equation
Partial differential equation describing the evolution of temperature in a region
specifically thermodynamics), the heat equation is a parabolic partial differential equation. The theory of the heat equation was first developed by Joseph Fourier
Heat_equation
equations in quantum mechanics List of equations in nuclear and particle physics Variables commonly used in physics Equation solving Theory of equations
List_of_equations
Engineering Equation Solver (EES) is a commercial software package used for solution of systems of simultaneous non-linear equations. It provides many
Engineering_Equation_Solver
Equation whose side(s) describe a transcendental function
high-order equations can be solved by “separation” of the unknowns, reducing them to algebraic equations. The following can also be used when solving transcendental
Transcendental_equation
Procedure in mathematics
Solving the geodesic equations is a procedure used in mathematics, particularly Riemannian geometry, and in physics, particularly in general relativity
Solving the geodesic equations
Solving_the_geodesic_equations
Polynomial equation of degree 3
could not solve this with a compass and straightedge construction, a task which is now known to be impossible. Methods for solving cubic equations appear
Cubic_equation
Type of mathematical expression
polynomial equation for which one is interested only in the solutions which are integers is called a Diophantine equation. Solving Diophantine equations is generally
Polynomial
Orbital mechanics term
equivalent to solving for the true anomaly, or the difference between the true anomaly and the mean anomaly, which is called the "Equation of the center"
Kepler's_equation
Equation to derive time of sunset and sunrise
coordinate system to the horizontal coordinate system, and then solving the equation for an altitude of zero. We then obtain cos H 0 = − tan ϕ tan
Sunrise_equation
Differential equation exhibiting high rate of dissipation
stalls. By contrast, implicit methods for stiff equations require costly "algebraic" equation solving on each step. The extra work per step is offset
Stiff_equation
Mathematical model of waves on a shallow water surface
Miura developed the classical inverse scattering method to solve the KdV equation. The KdV equation was first introduced by Joseph Valentin Boussinesq (1877
Korteweg–De_Vries_equation
Formula that provides the solutions to a quadratic equation
quadratic equation. Other ways of solving quadratic equations, such as completing the square, yield the same solutions. Given a general quadratic equation of
Quadratic_formula
Scientific calculator by Hewlett-Packard
equation solver and library of built-in equations. This feature allows a multi-variable equation to be entered by the user, and the equation solved for
HP-22S
Topics referred to by the same term
organization Solve (advertising agency) "Solve" (song), by Japanese pop band Dream HSwMS Sölve Equation solving Problem solving Solution (disambiguation) This disambiguation
Solve
Type of differential equation
"unknown" that solves the equation. However, it is often impossible to write down explicit formulas for solutions of partial differential equations. Hence there
Partial_differential_equation
Mathematical software
computational chemistry and packages for physical computation solvers for differential equations pretty-printing output to conform to standard mathematical
Computer_algebra_system
Aspect of general relativity
field equations are metrics of spacetimes that result from solving the Einstein field equations (EFE) of general relativity. Solving the field equations gives
Solutions of the Einstein field equations
Solutions_of_the_Einstein_field_equations
Branch of numerical analysis
The method of lines (MOL, NMOL, NUMOL) is a technique for solving partial differential equations (PDEs) in which all dimensions except one are discretized
Numerical methods for partial differential equations
Numerical_methods_for_partial_differential_equations
Optimality condition in optimal control theory
Bellman equation. While classical variational problems, such as the brachistochrone problem, can be solved using the Hamilton–Jacobi–Bellman equation, the
Hamilton–Jacobi–Bellman equation
Hamilton–Jacobi–Bellman_equation
Object of a mathematical operation, quantity on which an operation is performed
on. Unknown operands in equalities of expressions can be found by equation solving. The following arithmetic expression shows an example of operators
Operand
Any type of calculation
that is well-defined. Common examples of computation are mathematical equation solving and the execution of computer algorithms. Mechanical or electronic
Computation
Necessary condition for optimality associated with dynamic programming
(x)}\{F(x,a)+\beta V(T(x,a))\}.} The Bellman equation is classified as a functional equation, because solving it means finding the unknown function V {\displaystyle
Bellman_equation
Differential equation that is linear with respect to the unknown function
algebraic case, the theory allows deciding which equations may be solved by quadrature, and if possible solving them. However, for both theories, the necessary
Linear_differential_equation
Equation whose unknown is a function
and integral equations are functional equations. However, a more restricted meaning is often used, where a functional equation is an equation that relates
Functional_equation
System where changes of output are not proportional to changes of input
all roots or the real roots; see real-root isolation. Solving systems of polynomial equations, that is finding the common zeros of a set of several polynomials
Nonlinear_system
Book by George Boole
mathematical foundations involving equations; Extending the class of problems it could treat from assessing validity to solving equations, and; Expanding the range
The_Laws_of_Thought
Polynomial function of degree 4
the solution of a general quartic equation to be calculated. A quartic equation arises also in the process of solving the crossed ladders problem, in which
Quartic_function
Branch of mathematics
polynomial equations in several variables, the subject of algebraic geometry begins with finding specific solutions via equation solving, and then proceeds
Algebraic_geometry
Software for a class of mathematical problems
of mathematical software. Problem solving environment: a specialized software combining automated problem-solving methods with human-oriented tools for
Solver
Description of a quantum-mechanical system
The Schrödinger equation is a partial differential equation that governs the wave function of a non-relativistic quantum-mechanical system. Its discovery
Schrödinger_equation
Equations describing classical electromagnetism
electric and magnetic scalar potentials are preferred for explicitly solving the equations as a boundary value problem, analytical mechanics, or for use in
Maxwell's_equations
decisively move to the static equation-solving stage until Al-Khwarizmi introduced generalized algorithmic processes for solving algebraic problems. Dynamic
History_of_algebra
Fredholm operators. The integral equation was studied by Ivar Fredholm. A useful method to solve such type of equations, the Adomian decomposition method
Fredholm_integral_equation
Non-linear second order differential equation and its attractor
The Duffing equation (or Duffing oscillator), named after Georg Duffing (1861–1944), is a non-linear second-order differential equation used to model
Duffing_equation
Equations for calculations of the Darcy friction factor
formulae are equations that allow the calculation of the Darcy friction factor, a dimensionless quantity used in the Darcy–Weisbach equation, for the description
Darcy friction factor formulae
Darcy_friction_factor_formulae
Method for solving certain nonlinear partial differential equations
simplifies solving a nonlinear partial differential equation to solving 2 linear ordinary differential equations and an ordinary integral equation, a method
Inverse_scattering_transform
Scientific calculator by Hewlett-Packard
built-in functions, such as a matrix editor, complex number support, an equation solver, user-defined menus, and basic graphing capabilities (the 42S can draw
HP-42S
Process of achieving a goal by overcoming obstacles
former is an example of simple problem solving (SPS) addressing one issue, whereas the latter is complex problem solving (CPS) with multiple interrelated obstacles
Problem_solving
Second-order partial differential equation describing motion of mechanical system
functional is stationary at its local extrema, the Euler–Lagrange equation is useful for solving optimization problems in which, given some functional, one seeks
Euler–Lagrange_equation
Branch of pure mathematics
also provides formulas that are used to solve congruences with unknowns in a similar vein to equation solving in algebra, such as the Chinese remainder
Number_theory
Technique for solving differential equations
of several methods for solving ordinary and partial differential equations, in which algebra allows one to rewrite an equation so that each of two variables
Separation_of_variables
Software framework
written in C++ and uses several Fortran numerical libraries for linear equation solving. The license permits the use, reproduction, modification, and distribution
OpenSees
Transformation of a polynomial induced by a transformation of its roots
transformations are often used to simplify the solution of algebraic equations. Let P ( x ) = a 0 x n + a 1 x n − 1 + ⋯ + a n {\displaystyle
Polynomial_transformation
Type of differential equation
In mathematics, a Riccati equation in the narrowest sense is any first-order ordinary differential equation that is quadratic in the unknown function
Riccati_equation
Equation used for physiological interfaces, polymer science, and semiconductors
mesoscopic system. This is done by solving the Poisson–Boltzmann equation analytically in the three-dimensional case. Solving this results in expressions of
Poisson–Boltzmann_equation
Branch of physics
("cells"), and solve Maxwell's equations simultaneously across all cells. Discretization consumes computer memory, and solving the relevant equations takes significant
Computational electromagnetics
Computational_electromagnetics
Non-linear partial differential equation encountered in problems of wave propagation
An eikonal equation (from Greek εἰκών, image) is a non-linear first-order partial differential equation that is encountered in problems of wave propagation
Eikonal_equation
Polynomial equation of degree 7
In algebra, a septic equation is an equation of the form a x 7 + b x 6 + c x 5 + d x 4 + e x 3 + f x 2 + g x + h = 0 , {\displaystyle
Septic_equation
Matrices satisfying a differential equation
continuous media. The inverse scattering transform makes use of the Lax equations to solve such systems. A Lax pair is a pair of matrices or operators L ( t
Lax_pair
Polynomial equation of degree 6
solving the cubic equation involves transforming variables to obtain a sextic equation having terms only of degrees 6, 3, and 0, which can be solved as
Sextic_equation
Elliptic partial differential equation
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
Poisson's_equation
Branch of mathematics
a process known as solving the equation for that variable. For example, the equation x − 7 = 4 {\displaystyle x-7=4} can be solved for x {\displaystyle
Algebra
Motion of launched objects due to gravity
α) are known, the initial velocity can be found solving for v0 in the afore-mentioned parabolic equation: v 0 = x 2 g x sin 2 θ − 2 y cos 2 θ {\displaystyle
Projectile_motion
differential equations, statistics and graphics. MLAB is intended for numerical computing, with special facilities for ordinary differential equation-solving (ODE-solving)
MLAB
Topics referred to by the same term
Solvable extension, a field extension whose Galois group is a solvable group Solvable equation, a polynomial equation whose Galois group is solvable,
Solvable
Mathematical modeling software
be used for input and output. TK Solver has three ways of solving systems of equations. The "direct solver" solves a system algebraically by the principle
TK_Solver
Eigenvalue problem for the Laplace operator
the technique of solving linear partial differential equations by separation of variables. From this observation, we obtain two equations, one for A(r),
Helmholtz_equation
equation with boundary conditions based upon surface conditions. Kernel functions can be useful in approximating and solving this integral equation.
Kernel function for solving integral equation of surface radiation exchanges
Kernel_function_for_solving_integral_equation_of_surface_radiation_exchanges
Series of graphing calculators
86603. Solving equations for a certain variable. The CAS can solve for one variable in terms of others; it can also solve systems of equations. For equations
TI-89_series
Technique to solve partial differential equations
governing equations must be solved while accounting for prior assumptions, linearization, and adequate time and space discretization. Recently, solving the
Physics-informed neural networks
Physics-informed_neural_networks
Estimation procedure for correlated data
}}V_{i}^{-1}\{Y_{i}-\mu _{i}(\beta )\}\,\!=0} Software for solving generalized estimating equations is available in MATLAB, SAS (proc genmod), SPSS (the gee
Generalized estimating equation
Generalized_estimating_equation
Mathematical statement that two values are not equal
a {\displaystyle a} and c {\displaystyle c} . Similar to equation solving, inequation solving means finding what values (numbers, functions, sets, etc
Inequation
Equation describing the transport of some quantity
A continuity equation or transport equation is an equation that describes the transport of some quantity. It is particularly simple and powerful when
Continuity_equation
Estimate of extraterrestrial civilizations
magnitude (see § Criticism). Therefore, the usefulness of the Drake equation is not in the solving, but rather in the contemplation of all the various concepts
Drake_equation
Mathematical connection between field theory and group theory
polynomial equations that are solvable by radicals in terms of properties of the permutation group of their roots—an equation is by definition solvable by radicals
Galois_theory
Class of numerical techniques
finite-difference methods (FDM) are a class of numerical techniques for solving differential equations by approximating derivatives with finite differences. Both the
Finite_difference_method
Programmable scientific calculator produced by Hewlett-Packard
the equations list, to allow solving all variables in a system of linear equations. Systems of two equations with two variables, and three equations with
HP_35s
Equations of degree 5 or higher cannot be solved by radicals
is the simplest equation that cannot be solved in radicals, and that almost all polynomials of degree five or higher cannot be solved in radicals. The
Abel–Ruffini_theorem
Root-finding algorithm
which forms a fixed-point iteration, constructing the solution to the equation. Solving an ODE in this way is called Picard iteration, Picard's method, or
Fixed-point_iteration
Software used in mathematical applications
systems that use symbolic mathematics. They are designed to solve classical algebra equations and problems in human readable notation. Axiom Cadabra FriCAS
Mathematical_software
purpose electromagnetic solver for various applications. The name is an acronym for Higher Order Basis Based Integral Equation Solver. The software is based
HOBBIES (electromagnetic solver)
HOBBIES_(electromagnetic_solver)
Technique for solving hyperbolic partial differential equations
characteristics is a technique for solving particular partial differential equations. Typically, it applies to first-order equations, though in general characteristic
Method_of_characteristics
Partial differential equation with nonlinear terms
lot of work still remains on solving certain systems numerically, especially for the Navier–Stokes and other equations related to weather prediction
Nonlinear partial differential equation
Nonlinear_partial_differential_equation
Indian mathematician and astronomer (1114–1185)
and indeterminate equations including (the now called) Pell's equation, solving it using a kuṭṭaka method. In particular, he also solved the 61 x 2 + 1 =
Bhāskara_II
Approach to logic
in the form of equations –itself a revolutionary idea. Second, in the realm of logic's problems, Boole's addition of equation solving to logic—another
Term_logic
Relation in theoretical computer science
to whether solving word equations is NP-complete—remains open. (NP-hardness follows immediately from the fact that solving word equations generalises
Word_equation
Partial differential equation in mathematical finance
mathematical finance, the Black–Scholes equation, also called the Black–Scholes–Merton equation, is a partial differential equation (PDE) governing the price evolution
Black–Scholes_equation
Type of ordinary differential equation
{\displaystyle n=1} , it is separable. In these cases, standard techniques for solving equations of those forms can be applied. For n ≠ 0 {\displaystyle n\neq 0} and
Bernoulli differential equation
Bernoulli_differential_equation
System of complete and orthogonal polynomials
boundary condition of each problem. They also appear when solving the Schrödinger equation in three dimensions for a central force. Legendre polynomials
Legendre_polynomials
Nonlinear equation which arises on linear optimal control problems
Schur method for solving algebraic Riccati equations", Laboratory for Information and Decision Systems, MIT (Report LIDS-R-859). CARE solver help of MATLAB
Algebraic_Riccati_equation
Equations of motion for viscous fluids
Navier–Stokes equations (/nævˈjeɪ ˈstoʊks/ nav-YAY STOHKS) describe the motion of viscous fluids. This system of partial differential equations was named
Navier–Stokes_equations
Computer algebra system
programming solving equations, including those with complex roots (Figure 2) solving trigonometric equations solving differential equations (Figure 3)
Xcas
EQUATION SOLVING
EQUATION SOLVING
Girl/Female
Indian
Education
Girl/Female
Hindu, Indian, Tamil
Education
Girl/Female
Hindu
Education
Boy/Male
Indian
Education
Girl/Female
Arabic
Culture; Education
Boy/Male
Arabic, Muslim
Education
Girl/Female
Hindu
Modesty, Education
Boy/Male
Muslim
Sky, Education, Instruction
Boy/Male
Tamil
Education
Boy/Male
Hindu
Vidya--education esh-ishwar--god --god of education
Girl/Female
Tamil
Education
Girl/Female
Indian, Marathi
Education
Boy/Male
Arabic, Muslim
Education; Instruction
Girl/Female
Arabic
Culture; Education
Girl/Female
Tamil
Sarsvati | ஸரஸà¯à®µà®¤à¯€
Goddess of education
Sarsvati | ஸரஸà¯à®µà®¤à¯€
Girl/Female
Indian, Telugu
Good Education
Boy/Male
Tamil
Vidyesh | விதà¯à®¯à¯‡à®·Â
Vidya--education esh-ishwar--god --god of education
Vidyesh | விதà¯à®¯à¯‡à®·Â
Girl/Female
Indian, Punjabi, Sikh
Natural; Education
Girl/Female
Tamil
Modesty, Education
Girl/Female
Tamil
Education
EQUATION SOLVING
EQUATION SOLVING
Surname or Lastname
Jewish (American)
Jewish (American) : Americanized form of Blumfeld, an ornamental compound of Yiddish blum ‘flower’ + feld ‘field’.English : variant of the Norman habitational name Blundeville, from Blonville-sur-Mer in Calvados, France. The first element is probably an Old Norse personal name; the second is Old French ville ‘settlement’. In the 16th and 17th centuries in England, the endings -field and -ville were often used interchangeably; one branch of the Blundeville family continued using the -ville spelling while another chose Blom(e)field or Bloomfield.
Boy/Male
Hindu, Indian, Marathi
Brave Man on the Earth
Girl/Female
Tamil
Lotus
Boy/Male
Muslim
Eloquent
Girl/Female
Assamese, Bengali, Celebrity, Gujarati, Hindu, Indian, Jain, Kannada, Malayalam, Marathi, Oriya, Sindhi, Tamil, Telugu, Traditional
Thread of Brother-sister Bonding
Boy/Male
Hindu, Indian, Tamil, Traditional
God Murugan; King of the World
Boy/Male
German
Steward; Shepherd
Boy/Male
Indian
Full of qualities, Expansionist, Vast, Spacious, Man of qualities
Girl/Female
Hindu, Indian
One who is Always Ready for New Settlement
Girl/Female
Arabic, Australian
Melody; Song
EQUATION SOLVING
EQUATION SOLVING
EQUATION SOLVING
EQUATION SOLVING
EQUATION SOLVING
n.
The process of separating a fusible substance from one less fusible, by means of a degree of heat sufficient to melt the one and not the other, as an alloy of copper and lead; liquation.
n.
Emulation; rivalry; competition.
n.
A making equal; equal division; equality; equilibrium.
n.
The process of finding the roots of an equation.
n.
A biquadratic equation.
n.
The act or process of educating; the result of educating, as determined by the knowledge skill, or discipline of character, acquired; also, the act or process of training by a prescribed or customary course of study or discipline; as, an education for the bar or the pulpit; he has finished his education.
n.
Emulation; rivalry.
n.
Act of causing a quantity to disappear from an equation; especially, in the operation of deducing from several equations containing several unknown quantities a less number of equations containing a less number of unknown quantities.
n.
Literary education.
n.
A quantity to be applied in computing the mean place or other element of a celestial body; that is, any one of the several quantities to be added to, or taken from, its position as calculated on the hypothesis of a mean uniform motion, in order to find its true position as resulting from its actual and unequal motion.
n.
The great circle of the celestial sphere, coincident with the plane of the earth's equator; -- so called because when the sun is in it, the days and nights are of equal length; hence called also the equinoctial, and on maps, globes, etc., the equinoctial line.
n.
Any itching eruption.
n.
Exudation.
n.
An expression of the condition of equality between two algebraic quantities or sets of quantities, the sign = being placed between them; as, a binomial equation; a quadratic equation; an algebraic equation; a transcendental equation; an exponential equation; a logarithmic equation; a differential equation, etc.
n.
Instruction; education.
n.
The bringing of any term of an equation from one side over to the other without destroying the equation.
adv.
With elation.
v. t.
To reduce (an equation) in a lower degree.
n.
The process of separating, by heat, an easily fusible metal from one less fusible; eliquation.
n.
An identical equation.