Most calculus textbooks present this topic as the method of partial fractions. They usually contain a bunch of apparently unrelated examples (sometimes not exhaustive) and do not focus on the purpose of this method. For this reason I have decided to write a few notes about “partial fractions” and I want to focus on what the method is good for and not on examples. Everything that follows is devo...

Simple continued fractions, base-b expansions, Dedekind cuts and Cauchy sequences are common notations for number systems. In this note, first, it is proven that both simple continued fractions and base-b expansions fail to denote real numbers and thus lack logic; second, it is shown that Dedekind cuts and Cauchy sequences fail to join in algebraical operations and thus lack intuition; third, w...

The object of this paper is to establish certain generalized fractional integration and differentiation involving generalized Mittag-Leffler function defined by Salim and Faraj [25]. The considered generalized fractional calculus operators contain the Appell's function $F_3$ [2, p.224] as kernel and are introduced by Saigo and Maeda [23]. The Marichev-Saigo-Maeda fractional calculus operators a...

The Euler-Lagrange equation plays an important role in the minimization problems of the calculus of variations. This paper employs the differential transformation method (DTM) for finding the solution of the Euler-Lagrange equation which arise from problems of calculus of variations. DTM provides an analytical solution in the form of an infinite power series with easily computable components. S...

Background: Enterococci are important gram-positive bacteria causing dental calculus in human beings; however, the role of these bacteria in oral cavity is unclear. The aim of this study was to investigate the presence of Enterococcal Surface Protein (esp) gene in Enterococcus faecalis isolated from dental calculus in the city of Sari, Iran. Materials and Methods: In the present study, 207 den...

we propose a method for medical image denoising using calculus of variations and local variance estimation by shaped windows. this method reduces any additive noise and preserves small patterns and edges of images. a pyramid structure-texture decomposition of images is used to separate noise and texture components based on local variance measures. the experimental results show that the proposed...

we describe a variational problem on a surface under a constraintof geometrical character. necessary and sufficient conditions for the existence ofbifurcation points are provided. in local coordinates the problem corresponds toa quasilinear elliptic boundary value problem. the problem can be consideredas a physical model for several applications referring to continuum medium andmembranes.

Let $A$ be a generator of an analytic semigroup having H{\"o}rmander functional calculus on $X = L^p(\Omega ,Y)$, where $Y$ is UMD lattice. Using methods from Banach space geometry in connection with calculus, we show that for spectral multipliers decaying sufficiently fast at $\infty$, there holds maximal estimate $\| \sup_{t \geq 0} |m(tA)f|\, \|_{L^p(\Omega ,Y)} \lesssim \|f\|_{L^p(\Omega ,Y...

I hate calculus. Which is a lie: secretly love it. enjoy teaching it, drawing intricate diagrams of where the definition derivative comes from, stumping my students on convoluted trigonometric integrals with solutions dependent partial fractions, hammering mnemonics for rules—all joys And enjoyed learning too. Well, not failing it first time, but after that. long undergraduate time spent in rea...