07:35 A RIDICULOUSLY AWESOME INTEGRAL int sin(x)sinh(x) from 0 to infinity 13:20 One of THE craziest & most beautiful integrals in existence【存在的最疯狂和最美丽的积分之一】 09:55 A stellar integral solved using some wonderful complex analysis【一个恒星积分用一些奇妙的复分析】 20:29 A ...
Energy and double differential cross section datadoi:10.1007/s12648-017-1079-yRajput, MayankVala, SudhirsinhSrinivasan, R.Abhangi, M.Subhash, P. V.Pandey, B.Rao, C. V. S.Bora, D.Springer IndiaIndian Journal of Physics
y' - y \tan x = \cos x Solve the differential equation. y'' - y' - 6y = x + \cos x Find a solution to the following oridnary differential equation [sinh, y] \frac {dy}{dx} + cosh^2 y cos^2 x = 0 Solve differential equation (16+cot^2 x) \frac{dy}{dx}...
To solve the PDE problem, a feedforward neural network (FNN) [11] is used to approximate the solution function as (2)u(x)=F(x,θ),where θ represents all the trainable parameters of the FNN. To train the FNN with physics, the physics-informed loss function is formulated as (3)L(...
x +sin 2 x = 1 and cosh 2 x +sinh 2 x = 1 and the addition formulas in mind since they are especially useful when antidifferentiating. 9. Evaluation after Differentiation To evaluate Df at a particular number, say x =17, use the evaluation bar notation: “ x=17 ” or if the var...
Rate of Change & Tangents 变化率分为:平均变化率 (average rate of change) 与瞬时变化率 (instantaneousrate of change) 割线(secant) 对应平均变化率,切线 (tangent) 对应瞬时变化率 Concept of Limits f(x)f(x)在x0x0处的极限为LL,意味着limx→x−0f(x)=limx→x+0f(x)=Llimx→x0−f(x)...
[tex]\frac{\partial u}{\partial y}=\frac{x}{\sqrt{1+y^2}}[/tex] for a function [itex]u(x,y,z)[/itex] [tex]u(x,y,z)=x\int \frac{dy}{\sqrt{1+y^2}}[/tex] let [itex]y=\sinh v[/itex] [tex]u(x,y,z)=x\int \frac{\cosh v\: dv}{\sqrt{1+\sinh ^2v}...
(.) We get the lower solution XL(t) = [– cosh(t) + sinh(t), cosh(t) – sinh(t)] and upper solu- tion XU(t) = [– cosh(t) + sinh(t), cosh(t) – sinh(t)] for the integral equation (.) cor- responding to problem (.),...
Proposition 3 Let A ∈ W (Zn, X) be a rich operator. Then A is locally invert- ible at infinity on lp(Zn, X) for some p ∈ (1, ∞) if and only every limit operator Ah of A is invertible on one of the spaces lp(Zn, X) with p ∈ [1, ∞]. 2.2 Pseudodifferential ...
\quad \gamma(t)=\cosh (\alpha t) u+\sinh (\alpha t) v.for any \alpha \in \mathbb{R}, is a geodesic, and these are all the geodesic on the hyperbolic plane. If \alpha \neq 0, the image of \gamma is just the intersection of H^n with the plane spanned by u, v. Note ...