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Longer titles found: Fundamental matrix (linear differential equation) (view)

searching for Linear differential equation 63 found (151 total)

alternate case: linear differential equation

Regular singular point (1,674 words) [view diff] exact match in snippet view article find links to article

substantially different. More precisely, consider an ordinary linear differential equation of n-th order f ( n ) ( z ) + ∑ i = 0 n − 1 p i ( z ) f ( i )

Riemann's differential equation (1,174 words) [view diff] exact match in snippet view article find links to article

The hypergeometric differential equation is a second-order linear differential equation which has three regular singular points, 0, 1 and ∞ {\displaystyle

Von Bertalanffy function (620 words) [view diff] exact match in snippet view article find links to article

L_{\infty }} is asymptotic size. It is the solution of the following linear differential equation: d L d a = k ( L ∞ − L ) {\displaystyle {\frac {dL}{da}}=k(L_{\infty

List of things named after Gottfried Leibniz (425 words) [view diff] exact match in snippet view article find links to article

theorem, a generalization of the Leibniz integral rule Leibniz's linear differential equation, a first-order, linear, inhomogeneous differential equation Leibniz's

Chebyshev equation (444 words) [view diff] exact match in snippet view article find links to article

Chebyshev's equation is the second order linear differential equation ( 1 − x 2 ) d 2 y d x 2 − x d y d x + p 2 y = 0 {\displaystyle (1-x^{2}){d^{2}y \over

Groundwater discharge (404 words) [view diff] exact match in snippet view article find links to article

}{\partial y^{2}}}=0} which solution is a linear differential equation. Because the solution is a linear differential equation for which superposition principle

Surrogate data testing (1,452 words) [view diff] exact match in snippet view article find links to article

mappings), linearity of system means that it can be expressed by a linear differential equation. In this hypothesis, the static measurement function is one which

HHL algorithm (4,990 words) [view diff] no match in snippet view article find links to article

The Harrow–Hassidim–Lloyd (HHL) algorithm is a quantum algorithm for numerically solving a system of linear equations, designed by Aram Harrow, Avinatan

Guess value (317 words) [view diff] exact match in snippet view article find links to article

problem as a time series, converting the problem to a (hopefully) linear differential equation, and using mean values. Further methods for determining starting

Ansatz (645 words) [view diff] exact match in snippet view article find links to article

example of an ansatz is to suppose the solution of a homogeneous linear differential equation to take an exponential form, or a power form in the case of a

Differential analyser (2,772 words) [view diff] case mismatch in snippet view article find links to article

Thomson, William (1876). "Mechanical Integration of the general Linear Differential Equation of any Order with Variable Coefficients". Proceedings of the

Richard Liboff (532 words) [view diff] exact match in snippet view article find links to article

student (G. K. Schenter) he analytically solved a second order non-linear differential equation. One of the three solutions they gave had physical relevance

Ponytail (1,855 words) [view diff] exact match in snippet view article find links to article

individual hairs. The equation itself is a fourth order non linear differential equation. The Rapunzel number is a ratio used in this equation to calculate

Synchronization of chaos (1,546 words) [view diff] exact match in snippet view article find links to article

small we can expand the vector field in series and obtain a linear differential equation - by neglecting the Taylor remainder - governing the behavior

Exponential sum (1,212 words) [view diff] exact match in snippet view article find links to article

( 0 ) {\displaystyle G(0)} , where 'G' can be defined via a linear differential equation similar to Dyson equation obtained via summation by parts. If

Biot number (1,285 words) [view diff] exact match in snippet view article find links to article

the First law of thermodynamics leads to a simple first-order linear differential equation. The corresponding lumped capacity solution can be written T

Dragon curve (1,577 words) [view diff] exact match in snippet view article find links to article

as the Lévy dragon. Having obtained the set of solutions to a linear differential equation, any linear combination of the solutions will, because of the

Morris–Lecar model (992 words) [view diff] exact match in snippet view article find links to article

of the recovery variable can be approximated by a first-order linear differential equation for the probability of channel opening. The Morris–Lecar model

Operational calculus (1,733 words) [view diff] exact match in snippet view article find links to article

}a_{n}{\frac {t^{n}}{n!}}H(t).} Applying this rule, solving any linear differential equation is reduced to a purely algebraic problem. Heaviside went further

Joseph Miller Thomas (668 words) [view diff] exact match in snippet view article find links to article

8 (1941): 391–394. JSTOR 3028551 Equations equivalent to a linear differential equation. Proc. Amer. Math. Soc. 3 (1952) 899–903. MR0052001 Differential

List of topics named after Leonhard Euler (1,721 words) [view diff] exact match in snippet view article find links to article

integrals. Cauchy–Euler equation (or Euler equation), a second-order linear differential equation Cauchy–Euler operator Euler–Maclaurin formula – relation between

Hill differential equation (608 words) [view diff] exact match in snippet view article find links to article

Second order linear differential equation featuring a periodic function

Terminal velocity (2,608 words) [view diff] exact match in snippet view article find links to article

Riccati equation that can be solved by reduction to a second-order linear differential equation, it is easier to separate variables. A more practical form of

Reduction of order (1,610 words) [view diff] exact match in snippet view article find links to article

solution we were looking for. Given the general non-homogeneous linear differential equation y ″ + p ( t ) y ′ + q ( t ) y = r ( t ) {\displaystyle y''+p(t)y'+q(t)y=r(t)}

Control-Lyapunov function (1,668 words) [view diff] exact match in snippet view article find links to article

\left(-{\frac {\kappa }{2}}t\right)} which can then be solved using any linear differential equation methods. Isidori, A. (1995). Nonlinear Control Systems. Springer

Spring (device) (3,365 words) [view diff] exact match in snippet view article

{\displaystyle -kx=m{\frac {d^{2}x}{dt^{2}}}.\,} This is a second order linear differential equation for the displacement x {\displaystyle x} as a function of time

Vector control (motor) (2,639 words) [view diff] exact match in snippet view article

work involves his ability to transform any related machine's linear differential equation set from one with time varying coefficients to another with time

Mary Margaret Speer (575 words) [view diff] exact match in snippet view article find links to article

A note on the solution in series of the general homogeneous linear differential equation. She attended summer programs at the University of Chicago during

Hydrostatic equilibrium (4,416 words) [view diff] exact match in snippet view article find links to article

{\displaystyle \rho _{D}=\rho _{M}-\rho _{B}} satisfies the non-linear differential equation d d r [ r 2 ρ D ( r ) d d r ( k T D ( r ) ρ D ( r ) m D ) ] =

Distributed parameter system (2,216 words) [view diff] exact match in snippet view article find links to article

Y(s)=\int _{0}^{1}W(s,\xi )\,d\xi .} This is an inhomogeneous linear differential equation with ξ {\displaystyle \xi } as the variable, s as a parameter

Omega equation (1,538 words) [view diff] exact match in snippet view article find links to article

Jacobian formalism) gives: Equation (7) is now a diagnostic, linear differential equation for ω {\displaystyle \omega } , which can be split into two terms

Local system (2,681 words) [view diff] exact match in snippet view article find links to article

(f_{1},\dots ,f_{n})^{t}\right\}} i.e., the solutions to the linear differential equation d f i = ∑ Θ i j f j {\displaystyle df_{i}=\sum \Theta _{ij}f_{j}}

T-symmetry (4,422 words) [view diff] exact match in snippet view article find links to article

This form follows whenever the spinor can be described with a linear differential equation that is first-order in the time derivative, which is generally

Self-buckling (1,596 words) [view diff] exact match in snippet view article find links to article

x}\end{aligned}}} We get that the governing equation is the third order linear differential equation with a variable coefficient. The way to solve the problem is

Vortex lattice method (2,043 words) [view diff] exact match in snippet view article find links to article

and φ 2 {\displaystyle \varphi _{2}} are two solutions of the linear differential equation, then the linear combination c 1 φ 1 + c 2 φ 2 {\displaystyle

Stokes flow (3,387 words) [view diff] exact match in snippet view article find links to article

and pressure, and therefore can take advantage of a variety of linear differential equation solvers. With the velocity vector expanded as u = ( u , v , w

Pharmacokinetics (4,312 words) [view diff] exact match in snippet view article find links to article

the change in concentration over time can be expressed as a linear differential equation d C d t = − k el C {\textstyle {\frac {dC}{dt}}=-k_{\text{el}}C}

Chaplygin's theorem (1,084 words) [view diff] exact match in snippet view article find links to article

Yuriy (1967-09-01). "Chaplygin's theorem for a second-order linear differential equation with lagging argument". Mathematical Notes of the Academy of

Nondimensionalization (3,389 words) [view diff] exact match in snippet view article find links to article

{\frac {d\chi }{d\tau }}+\chi =F(\tau ).} The general nth order linear differential equation with constant coefficients has the form: a n d n d t n x ( t

Ramsey–Cass–Koopmans model (3,778 words) [view diff] exact match in snippet view article find links to article

) k − c {\displaystyle {\dot {k}}=f(k)-(n+\delta )k-c} A non-linear differential equation akin to the Solow–Swan model but incorporates endogenous consumption

List of African-American mathematicians (7,592 words) [view diff] exact match in snippet view article find links to article

(1968). Oscillation and comparison theorems for second order linear differential equation. Lincoln, Nebraska: University of Nebraska. OCLC 36986587. Weddington

Cramer's rule (4,123 words) [view diff] exact match in snippet view article find links to article

rule is used to derive the general solution to an inhomogeneous linear differential equation by the method of variation of parameters. Consider the linear

Air bearing (3,274 words) [view diff] exact match in snippet view article find links to article

lubricant has to be considered as compressible, leading to a non-linear differential equation to be solved. Numerical methods such as Finite difference method

Sturm–Liouville theory (4,722 words) [view diff] exact match in snippet view article find links to article

Sturm–Liouville equation. Consider a general inhomogeneous second-order linear differential equation P ( x ) y ″ + Q ( x ) y ′ + R ( x ) y = f ( x ) {\displaystyle

Hypergeometric function (6,920 words) [view diff] exact match in snippet view article find links to article

is given by Riemann's differential equation. Any second order linear differential equation with three regular singular points can be converted to the hypergeometric

Stability derivatives (3,324 words) [view diff] exact match in snippet view article find links to article

of the equations of motion yields a second order homogeneous linear differential equation in the angle of attack β {\displaystyle \beta } : d 2 β d t 2

Timeline of electrical and electronic engineering (4,531 words) [view diff] exact match in snippet view article find links to article

Pierre-Simon Laplace developed the Laplace transform to transform a linear differential equation into an algebraic equation. Later, his transform became a tool

Linear time-invariant system (5,902 words) [view diff] exact match in snippet view article find links to article

time-varying and/or nonlinear case. Any system that can be modeled as a linear differential equation with constant coefficients is an LTI system. Examples of such

Heat transfer (8,475 words) [view diff] exact match in snippet view article find links to article

often reduces the complexity of the equations to one first-order linear differential equation, in which case heating and cooling are described by a simple

Verlet integration (5,506 words) [view diff] exact match in snippet view article find links to article

example for this task is the exponential function. Consider the linear differential equation x ¨ ( t ) = w 2 x ( t ) {\displaystyle {\ddot {x}}(t)=w^{2}x(t)}

Trace operator (4,669 words) [view diff] exact match in snippet view article find links to article

{\textstyle u_{0}} , a technique which can be applied to any linear differential equation. By the Riesz representation theorem there exists a unique solution

Laplace transform (9,453 words) [view diff] exact match in snippet view article find links to article

and electrical engineering. The Laplace transform reduces a linear differential equation to an algebraic equation, which can then be solved by the formal

Aircraft flight dynamics (8,502 words) [view diff] exact match in snippet view article find links to article

{\alpha }}} These may be manipulated to yield as second order linear differential equation in α {\displaystyle \alpha } : d 2 α d t 2 − ( Z α m U + M q

Systems biology (9,938 words) [view diff] exact match in snippet view article find links to article

complex challenges associated with network inference. Piecewise-linear differential equation models (PLDE): The model is composed of a piecewise-linear representation

Hahn–Banach theorem (12,640 words) [view diff] exact match in snippet view article find links to article

method of a priori estimates. Suppose that we wish to solve the linear differential equation P u = f {\displaystyle Pu=f} for u , {\displaystyle u,} with

Bessel function (12,307 words) [view diff] exact match in snippet view article find links to article

synthesis, Kaiser window, or Bessel filter). Because this is a linear differential equation, solutions can be scaled to any amplitude. The amplitudes chosen

List of numerical analysis topics (8,335 words) [view diff] exact match in snippet view article find links to article

problems: Linear-quadratic regulator — system dynamics is a linear differential equation, objective is quadratic Linear-quadratic-Gaussian control (LQG)

Generating function (14,462 words) [view diff] exact match in snippet view article find links to article

(or function) F(z) is said to be holonomic if it satisfies a linear differential equation of the form c 0 ( z ) F ( r ) ( z ) + c 1 ( z ) F ( r − 1 ) (

Debye–Hückel theory (7,543 words) [view diff] exact match in snippet view article find links to article

e^{x}\approx 1+x} for 0 < x ≪ 1 {\displaystyle 0<x\ll 1} ) to create a linear differential equation.: Section 2.4.2 D&H say that this approximation holds at large

Maass wave form (8,499 words) [view diff] exact match in snippet view article find links to article

differentiation, which is allowed since f is smooth in y . We get a linear differential equation of second degree: y 2 ∂ 2 ∂ y 2 a n ( y ) + ( 1 4 − ν 2 − 4 π

Meijer G-function (10,023 words) [view diff] exact match in snippet view article find links to article

unit circle |z| = 1. The G-function satisfies the following linear differential equation of order max(p,q): [ ( − 1 ) p − m − n z ∏ j = 1 p ( z d d z

Loewy decomposition (7,132 words) [view diff] exact match in snippet view article find links to article

of the function space containing the solution of a reducible linear differential equation L y = 0 {\displaystyle Ly=0} . For operators of fixed order the

Lagrangian coherent structure (10,382 words) [view diff] exact match in snippet view article find links to article

The classic way of computing Lyapunov exponents is solving a linear differential equation for the linearized flow map ∇ F t 0 t ( x 0 ) {\displaystyle