It is a solid truth in mathematics that the derivative of a function is unique. We want to show that there exist particular functions all of which have the same form but their derivatives are ...

Derivatives of functions are computed using differential calculus. A derivative in calculus is defined as “the rate of change of quantity y with respect to quantity x”. This sounds very similar to the ...

from sympy import * f, g, x = Function('f'), Function('g'), Symbol('x') Derivative(f(g(x)), g(x)).doit() returns Subs(Derivative(f(_xi_0), _xi_0), (_xi_0,), (g(x ...

Abstract: This article uses Maple for the auxiliary tool to study the partial differential problem of two types of two-variables functions. We can obtain the infinite series forms of any order partial ...

The input of the get_GPR function can be "Sobolev", "SE" or "Matern", which corresponds to second-order Sobolev kernel, squared exponential kernel and Matern kernel as the covariance kernel in the ...

The input argument fun refers to an IML module that specifies a function that returns f, a vector of length m for least-squares subroutines or a scalar for other optimization subroutines. The returned ...

Effective formulas for computing the Green's function of an exponentially graded three dimensional material have been derived In previous work. The expansion approach for evaluating the Green's ...

Abstract: In the field of nonstationary signal analysis and processing, the short-time Fourier transform (STFT) is frequently used to convert signals into the time-frequency domain. The instantaneous ...