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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