A few sections on Green`s functions in 1D
... In Figure 21.2 we see conceptually the behavior of the ramp function, the Heaviside function, the delta function, and the derivative of the delta function. We write the differential equation for the Green function. G�� (x|ξ) + p(x)G� (x|ξ) + q(x)G(x|ξ) = δ(x − ξ) we see that only the G�� (x|ξ) term c ...
... In Figure 21.2 we see conceptually the behavior of the ramp function, the Heaviside function, the delta function, and the derivative of the delta function. We write the differential equation for the Green function. G�� (x|ξ) + p(x)G� (x|ξ) + q(x)G(x|ξ) = δ(x − ξ) we see that only the G�� (x|ξ) term c ...
Stochastic models for relativistic diffusion
... which cannot be reached by a single particle without exceeding the speed of light c. The resulting stochastic process is a Gaussian diffusion with the superluminal locations excluded. The process avoids the sharp fronts in the usual telegrapher’s equation 共19兲, but is also non-Markovian. An alternat ...
... which cannot be reached by a single particle without exceeding the speed of light c. The resulting stochastic process is a Gaussian diffusion with the superluminal locations excluded. The process avoids the sharp fronts in the usual telegrapher’s equation 共19兲, but is also non-Markovian. An alternat ...
Algebra 2 5.5 Completing the Square Name: Essential Question
... Third step, complete the perfect square trinomial. (Remember that whatever you do to one side of the equation, you must also do to the other side) ...
... Third step, complete the perfect square trinomial. (Remember that whatever you do to one side of the equation, you must also do to the other side) ...
Differential equation
A differential equation is a mathematical equation that relates some function with its derivatives. In applications, the functions usually represent physical quantities, the derivatives represent their rates of change, and the equation defines a relationship between the two. Because such relations are extremely common, differential equations play a prominent role in many disciplines including engineering, physics, economics, and biology.In pure mathematics, differential equations are studied from several different perspectives, mostly concerned with their solutions—the set of functions that satisfy the equation. Only the simplest differential equations are solvable by explicit formulas; however, some properties of solutions of a given differential equation may be determined without finding their exact form.If a self-contained formula for the solution is not available, the solution may be numerically approximated using computers. The theory of dynamical systems puts emphasis on qualitative analysis of systems described by differential equations, while many numerical methods have been developed to determine solutions with a given degree of accuracy.