Linearization, the Glossary

Table of Contents

1. 42 relations: Autonomous system (mathematics), Computational mechanics, Decision rule, Derivative, Differentiable function, Dotdash Meredith, Dynamical system, Ecology, Economics, Eigenvalues and eigenvectors, Engineering, Equilibrium point (mathematics), Function (mathematics), Functional equation (L-function), Gradient, Hartman–Grobman theorem, Hyperbolic equilibrium point, International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, Jacobian matrix and determinant, Linear approximation, Linear function, Linear stability, Linear system, Mathematical optimization, Mathematics, Maximum and minimum, Microeconomics, Multiphysics simulation, Newton's method, Nonlinear system, Physics, Physics of magnetic resonance imaging, Quasilinearization, Simplex algorithm, Slope, Stability derivatives, Stability theory, System, Tangent, Taylor series, Taylor's theorem, Utility maximization problem.

2. Approximations

Autonomous system (mathematics)

In mathematics, an autonomous system or autonomous differential equation is a system of ordinary differential equations which does not explicitly depend on the independent variable. Linearization and autonomous system (mathematics) are dynamical systems.

See Linearization and Autonomous system (mathematics)

Computational mechanics

Computational mechanics is the discipline concerned with the use of computational methods to study phenomena governed by the principles of mechanics.

See Linearization and Computational mechanics

Decision rule

In decision theory, a decision rule is a function which maps an observation to an appropriate action.

See Linearization and Decision rule

Derivative

The derivative is a fundamental tool of calculus that quantifies the sensitivity of change of a function's output with respect to its input. Linearization and derivative are differential calculus.

See Linearization and Derivative

Differentiable function

In mathematics, a differentiable function of one real variable is a function whose derivative exists at each point in its domain. Linearization and differentiable function are differential calculus.

See Linearization and Differentiable function

Dotdash Meredith

Dotdash Meredith (formerly The Mining Company, About.com and Dotdash) is an American digital media company based in New York City.

See Linearization and Dotdash Meredith

Dynamical system

In mathematics, a dynamical system is a system in which a function describes the time dependence of a point in an ambient space, such as in a parametric curve. Linearization and dynamical system are dynamical systems.

See Linearization and Dynamical system

Ecology

Ecology is the natural science of the relationships among living organisms, including humans, and their physical environment.

See Linearization and Ecology

Economics

Economics is a social science that studies the production, distribution, and consumption of goods and services.

See Linearization and Economics

Eigenvalues and eigenvectors

In linear algebra, an eigenvector or characteristic vector is a vector that has its direction unchanged by a given linear transformation.

See Linearization and Eigenvalues and eigenvectors

Engineering

Engineering is the practice of using natural science, mathematics, and the engineering design process to solve technical problems, increase efficiency and productivity, and improve systems.

See Linearization and Engineering

Equilibrium point (mathematics)

In mathematics, specifically in differential equations, an equilibrium point is a constant solution to a differential equation. Linearization and equilibrium point (mathematics) are dynamical systems.

See Linearization and Equilibrium point (mathematics)

Function (mathematics)

In mathematics, a function from a set to a set assigns to each element of exactly one element of.

See Linearization and Function (mathematics)

Functional equation (L-function)

In mathematics, the L-functions of number theory are expected to have several characteristic properties, one of which is that they satisfy certain functional equations.

See Linearization and Functional equation (L-function)

Gradient

In vector calculus, the gradient of a scalar-valued differentiable function f of several variables is the vector field (or vector-valued function) \nabla f whose value at a point p gives the direction and the rate of fastest increase. Linearization and gradient are differential calculus.

See Linearization and Gradient

Hartman–Grobman theorem

In mathematics, in the study of dynamical systems, the Hartman–Grobman theorem or linearisation theorem is a theorem about the local behaviour of dynamical systems in the neighbourhood of a hyperbolic equilibrium point. Linearization and Hartman–Grobman theorem are approximations.

See Linearization and Hartman–Grobman theorem

Hyperbolic equilibrium point

In the study of dynamical systems, a hyperbolic equilibrium point or hyperbolic fixed point is a fixed point that does not have any center manifolds.

See Linearization and Hyperbolic equilibrium point

International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

International Journal of Bifurcation and Chaos in Applied Sciences and Engineering (often abbreviated as IJBC) is a peer-reviewed scientific journal published by World Scientific.

See Linearization and International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

Jacobian matrix and determinant

In vector calculus, the Jacobian matrix of a vector-valued function of several variables is the matrix of all its first-order partial derivatives. Linearization and Jacobian matrix and determinant are differential calculus.

See Linearization and Jacobian matrix and determinant

Linear approximation

In mathematics, a linear approximation is an approximation of a general function using a linear function (more precisely, an affine function). Linearization and linear approximation are differential calculus.

See Linearization and Linear approximation

Linear function

In mathematics, the term linear function refers to two distinct but related notions.

See Linearization and Linear function

Linear stability

In mathematics, in the theory of differential equations and dynamical systems, a particular stationary or quasistationary solution to a nonlinear system is called linearly unstable if the linearization of the equation at this solution has the form dr/dt.

See Linearization and Linear stability

Linear system

In systems theory, a linear system is a mathematical model of a system based on the use of a linear operator. Linearization and linear system are dynamical systems.

See Linearization and Linear system

Mathematical optimization

Mathematical optimization (alternatively spelled optimisation) or mathematical programming is the selection of a best element, with regard to some criteria, from some set of available alternatives.

See Linearization and Mathematical optimization

Mathematics

Mathematics is a field of study that discovers and organizes abstract objects, methods, theories and theorems that are developed and proved for the needs of empirical sciences and mathematics itself.

See Linearization and Mathematics

Maximum and minimum

In mathematical analysis, the maximum and minimum of a function are, respectively, the largest and smallest value taken by the function.

See Linearization and Maximum and minimum

Microeconomics

Microeconomics is a branch of economics that studies the behavior of individuals and firms in making decisions regarding the allocation of scarce resources and the interactions among these individuals and firms.

See Linearization and Microeconomics

Multiphysics simulation

In computational modelling, multiphysics simulation (often shortened to simply "multiphysics") is defined as the simultaneous simulation of different aspects of a physical system or systems and the interactions among them.

See Linearization and Multiphysics simulation

Newton's method

In numerical analysis, Newton's method, also known as the Newton–Raphson method, named after Isaac Newton and Joseph Raphson, is a root-finding algorithm which produces successively better approximations to the roots (or zeroes) of a real-valued function.

See Linearization and Newton's method

Nonlinear system

In mathematics and science, a nonlinear system (or a non-linear system) is a system in which the change of the output is not proportional to the change of the input. Linearization and nonlinear system are dynamical systems.

See Linearization and Nonlinear system

Physics

Physics is the natural science of matter, involving the study of matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force.

See Linearization and Physics

Physics of magnetic resonance imaging

Magnetic resonance imaging (MRI) is a medical imaging technique mostly used in radiology and nuclear medicine in order to investigate the anatomy and physiology of the body, and to detect pathologies including tumors, inflammation, neurological conditions such as stroke, disorders of muscles and joints, and abnormalities in the heart and blood vessels among others.

See Linearization and Physics of magnetic resonance imaging

Quasilinearization

In mathematics, quasilinearization is a technique which replaces a nonlinear differential equation or operator equation (or system of such equations) with a sequence of linear problems, which are presumed to be easier, and whose solutions approximate the solution of the original nonlinear problem with increasing accuracy.

See Linearization and Quasilinearization

Simplex algorithm

In mathematical optimization, Dantzig's simplex algorithm (or simplex method) is a popular algorithm for linear programming.

See Linearization and Simplex algorithm

Slope

In mathematics, the slope or gradient of a line is a number that describes the direction and steepness of the line.

See Linearization and Slope

Stability derivatives

Stability derivatives, and also control derivatives, are measures of how particular forces and moments on an aircraft change as other parameters related to stability change (parameters such as airspeed, altitude, angle of attack, etc.). For a defined "trim" flight condition, changes and oscillations occur in these parameters.

See Linearization and Stability derivatives

Stability theory

In mathematics, stability theory addresses the stability of solutions of differential equations and of trajectories of dynamical systems under small perturbations of initial conditions. Linearization and stability theory are dynamical systems.

See Linearization and Stability theory

System

A system is a group of interacting or interrelated elements that act according to a set of rules to form a unified whole.

See Linearization and System

Tangent

In geometry, the tangent line (or simply tangent) to a plane curve at a given point is, intuitively, the straight line that "just touches" the curve at that point.

See Linearization and Tangent

Taylor series

In mathematics, the Taylor series or Taylor expansion of a function is an infinite sum of terms that are expressed in terms of the function's derivatives at a single point.

See Linearization and Taylor series

Taylor's theorem

In calculus, Taylor's theorem gives an approximation of a k-times differentiable function around a given point by a polynomial of degree k, called the k-th-order Taylor polynomial. Linearization and Taylor's theorem are approximations.

See Linearization and Taylor's theorem

Utility maximization problem

Utility maximization was first developed by utilitarian philosophers Jeremy Bentham and John Stuart Mill.

See Linearization and Utility maximization problem

See also

Approximations

• Approximate computing
• Approximation
• Approximation algorithms
• Approximation theory
• Approximations of π
• Back-of-the-envelope calculation
• Binomial approximation
• Born–Huang approximation
• Born–Oppenheimer approximation
• Clearance (civil engineering)
• Diophantine approximation
• Engineering tolerance
• Hartman–Grobman theorem
• Linearization
• Milü
• Numerical analysis
• Precision (computer science)
• Relaxation (approximation)
• Rough set
• Series expansions
• Stirling's approximation
• Successive-approximation ADC
• Supersymmetric WKB approximation
• Taylor's theorem
• Tolerance interval
• Tolerance relation
• Ultrarelativistic limit
• Variational method (quantum mechanics)
• WKB approximation

References

[1] https://en.wikipedia.org/wiki/Linearization

Also known as Linear regime, Linearisation, Linearized, Linerization, Local linearization, State-Space Approach, Statespace approach to linearization.