Abstract: In this paper, we first extend the Wirtinger derivative which is defined for complex functions to hyperbolic functions, and derive the hyperbolic gradient operator yielding the steepest ...

Abstract: Back-propagation algorithm is one of the key stages of neural network training. At this stage, the derivation of an activation function is employed to ...

SIAM Journal on Numerical Analysis, Vol. 31, No. 3 (Jun., 1994), pp. 655-679 (25 pages) The accuracy of numerical approximations to piecewise smooth solutions of hyperbolic partial differential ...

Provides a review of pre-calculus, algebra and trigonometry integrated with the second half of Calculus I. Inverse trig functions and their derivative, logarithmic functions and their derivative, ...

This course is a continuation of MATH*1200. It is a theoretical course intended primarily for students who need or expect to pursue further studies in mathematics, physics, chemistry, engineering and ...

ABSTRACT: In this paper, we consider the generalized Korteweg-de-Vries (KdV) equations which are remarkable models of the water waves mechanics, the shallow water waves, the quantum mechanics, the ion ...

Different from the construction process of the traditional finite difference method, we derive a large class of high-accuracy methods for approximating derivatives. Since Taylor expansion is avoided, ...