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Derivative and Differential
The concepts of the derivative and the differential of a function are defined and several examples are given. The notion of a differential operator...
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Derivative Analysis
After adding a new specific analytical protocol, this chapter applies the theory and methodological tools described in the first and second parts of...
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The Derivative
We start by introducing the concept of “derivative” of a function defined on a subset of...
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Basic Derivative Rules
The definition of the derivative function given in M-Box 10.2 is time-consuming to apply to every function...
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Lie Group and Lie Derivative
This chapter begins with a brief review of Lie groups and their Lie algebras. Subsequently, it introduces the notion of the Lie derivative, its...
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The Derivative Graphically
In the previous chapter we estimated the slope of the tangent line at one specific point. We now take a qualitative look at the slopes of tangent...
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Deformable derivative in complex domain
In this article, we are proposing a limit-based definition, which we have termed as complex deformable derivative . The complex deformable derivative...
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Derivative-Free Methods for Unconstrained Optimization
In this chapter we introduce some classes of optimization methods that do not use derivatives of the objective function. After a short introduction,...
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The Idea of the Derivative
In Chapter 4 we estimated that in 2017...
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The Derivative
The idea of derivative appears in the XVIIth Century in the work of Pierre de Fermat and others, in general in relation to questions like: How do the...
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The Derivative
In studying SIR and other phenomena in Chap. 1, we contented ourselves with an intuitive, or heuristic, understanding of what a rate of change...
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Conformable fractional derivative in commutative algebras
In this paper, an analog of the conformable fractional derivative is defined in an arbitrary finite-dimensional commutative associative algebra....
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The Time Derivative
It is the aim of this chapter to define a derivative operator on a suitable L 2-space, which will be used as the derivative with respect to the...
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Oblique Derivative Problems for Elliptic Equations in Conical Domains
The aim of our book is the investigation of the behavior of strong and weak solutions to the regular oblique derivative problems for second order...
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Construction of Jacobi forms using adjoint of the Jacobi–Serre derivative
In the article, we study the Oberdieck derivative defined on the space of weak Jacobi forms. We prove that the Oberdieck derivative maps a Jacobi...
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Analytic Resolving Families of Operators for Linear Equations with Hilfer Derivative
We study linear differential equations with the Hilfer derivative and a closed operator A in a Banach space with Cauchy type conditions. We obtain a...
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Extremal Problems for a Polynomial and Its Polar Derivative
AbstractThis paper considers the well known Erdős–Lax and Turán-type inequalities that relate the uniform norm of a univariate complex coefficient...
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Returning to the Janowski Subordination of the Derivative of the Holomorphic Function
AbstractWe find a sharp estimate for the pre-Schwarzian derivative on the class of holomorphic functions in the unit disk with derivatives...
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Combined Derivative Estimators
We discuss combinations of simulation-based derivative estimators using infinitesimal perturbation analysis (IPA) and the likelihood ratio method...
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A Pro Rata Definition of the Fractional-Order Derivative
In this paper a novel definition of the fractional-order derivative operator will be introduced. This operator will be called “pro rata” due to its...