P1 Chapter1.6Maximum and Minimum value of a quadratic function 10:12 1.7解一元二次不等式及特殊不等式 15:30 P1.chapter1.5 Solve complex equations 05:51 P1.chapter1.4 Solve simultanous equations 07:34 P1.Chapter1.3 Solve quadratic equation by formula 07:43 P1 Chapter1.2 Solve quadratic...
By reversing the process in obtaining the derivative of the exponential function, we obtain the remarkable result:∫eudu=eu+K∫eudu=eu+KIt is remarkable because the integral is the same as the expression we started with. That is, eueu....
Expansions of the solutions of the biconfluent Heun equation in terms of incomplete Beta and Gamma functions Considering the equations for some functions involving the first or the second derivatives of the biconfluent Heun function, we construct two expansions of... TA Ishkhanyan,Y Pashayan-Leroy...
The ordinary exponential function solves the initial value problem $$ dy/dx = alpha y,y(0) = y.$$doi:10.1007/978-3-662-11791-0_15K. YosidaYosida, K. : On the integration of the equation of evolution. J. Fac. Sci. Univ. Tokyo, Sect. 1, 9 , 397–402 (1963).K.Yosida.On ...
[10pt] \text{where order of the functions is chosen according to ILATE}\\[15pt] \text{b) Intergation of exponential function}\\[10pt] \int e^{f(x)}dx=\frac{e^{f(x)}}{f'(x)}+C\hspace{90pt}\text{(equation 1)}\\[10pt] \t...
We apply an exponential time integration scheme combined with a central difference scheme on a piecewise uniform mesh with respect to the spatial variable to evaluate a generalized Black-Scholes equation. We show that the scheme is second-order convergent for both time and spatial variables. It is...
We apply an exponential time integration scheme combined with a central difference scheme on a piecewise uniform mesh with respect to the spatial variable to evaluate a generalized Black-Scholes equation. We show that the scheme is second-order convergent for both time and spatial variables. It is...
The ordinary exponential function solves the initial value problem $$dy/dx = \\alpha y,\\quad y(0) = 1.$$ We consider the Diffusion equation $$\\partial u/\\partial t = \\Delta u,where\\Delta =...Yosida, KsakuYosida, K. : On the integration of the equation of evolution. J....
In Section 7.5, for example, we found that exponential growth and decay is m ed by a differential equation of the form dydx = ky , for some constant k Z 0. We have not yet considered differential equations such as dydx = y - x , yet such equations arise frequently in applications. ...
Although at first it may seem counterproductive, let’s now integrate both sides of this equation: ∫h′(x)dx=∫(g(x)f′(x)+f(x)g′(x))dx∫h′(x)dx=∫(g(x)f′(x)+f(x)g′(x))dx.This gives ush(x)=f(x)g(x)=∫g(x)f′(x)dx+∫f(x)g′(x)dxh(x)=f(x)g(x...