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About 10,000 papers for “Exponential function”
Alain Wazner · HAL (Le Centre pour la Communication Scientifique Directe) · 2023
EvènemenTs dEs aRticles d'analyse du contiNU EtDans l'Antichambre de la caverne du Dr Isabelle C, il fit du reste phi K DIck euT une soeur ROSE
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Carl E. Mungan · Physics Education · 2006
Abstract : The exponential function appears in a number of places in introductory physics, such as damped oscillations, radioactive populations, LR and RC circuits, isothermal and adiabatic processes for an ideal gas, and atmospheric pressure as a function of altitude. The purpose of this article is to introduce the exponential function, without using calculus, for the benefit of students in an algebra-based course. The key point is that the exponential is that special function y(x) whose slope at any point x is equal to the value y of the function at that same point.
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Branko Ćurgus · College Mathematics Journal · 2006
Click to increase image sizeClick to decrease image size Additional informationNotes on contributorsBranko ĆurgusBranko Ćurgus (curgus@cc.wwu.edu) received his Ph.D. from the University of Sarajevo, in the former Yugoslavia. His Ph.D. research was done under the advisement of Prof. Heinz Langer at the Technical University Dresden, in the former German Democratic Republic. Branko is currently a professor at Western Washington University in Bellingham. His research papers are mostly in operator theory in Krein spaces. Looking for connections between math and art, he discovered a fascinating fact that the mathematical spirit of Isamu Noguchi's Skyviewing Sculpture (behind him on the photo) is the remarkable number 1 + √2 - ¾π.
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NTUR (臺灣機構典藏) · 2003
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Jacques Sauloy · Graduate studies in mathematics · 2016
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Barbara Saiz de Bustamante · Elsevier eBooks · 1997
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Xiongzhi Liu (22184044), Hao Yang (328526), Yongqiang Qu (22184047) et al. · Figshare · 2025
<div> Accurately determining initial water saturation is essential for assessing reservoir resources and optimizing development, yet conventional J-function methods face challenges such as variability in curve fitting due to sample heterogeneity, less-than-optimal grouping schemes, and limited core sample availability. This study addressed these issues by analyzing 55 J-function curves from the N reservoir in Iraq’s Zagros Basin, identifying permeability as the primary factor influencing curve shape. A novel classification method was developed, categorizing curves into power function and exponential function types based on permeability thresholds. Improved J-function models were established by correlating undetermined coefficients with the reservoir quality index (RQI), enabling continuous, tailored calculations, eliminating the need for sample grouping. Case studies demonstrated that the improved J-function method provides more accurate water saturation (S<sub>w</sub>) estimates in Reservoir N (porosity 0.1–0.27) compared to the Archie equation and conventional J-function: (1) In high-quality intervals (e.g., 3682–3683 m), it yields S<sub>w</sub> = 0.06–0.11, closely matching core-derived irreducible water saturation (0.1), while Archie overestimates S<sub>w</sub> (0.23–0.74); (2) In poor-quality zones (3676.5–3681 m), it agrees with Archie’s S<sub>w</sub> but corrects the conventional J-function’s underestimation by accounting for subtle property variations. These advancements provided a robust framework integrating permeability-based J-function classification, RQI-correlated coefficient models, and continuous saturation calculations, eliminating the need for sample grouping. </div>
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KoheiAbeLab · Zenodo (CERN European Organization for Nuclear Research) · 2025
Initial public release of the Spiral Exponential Function Visualizer. This release provides an interactive Python-based visualization of trajectories generated by the Spiral Exponential Function, a solution of the Spiral Exponential Equation (SEE). Included features Interactive visualization of spiral exponential trajectories in the complex plane Slider control for the angle θ between position and velocity vectors Slider control for time parameter t Optional visualization of derivative directions: position, velocity (θ), acceleration (2θ), jerk (3θ), and snap (4θ) Clear color conventions and external legend for readability Purpose This release is intended as a research and visualization tool to support geometric intuition and exploration of the Spiral Exponential Equation.
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KoheiAbeLab · Zenodo (CERN European Organization for Nuclear Research) · 2025
Initial public release of the Spiral Exponential Function Visualizer. This release provides an interactive Python-based visualization of trajectories generated by the Spiral Exponential Function, a solution of the Spiral Exponential Equation (SEE). Included features Interactive visualization of spiral exponential trajectories in the complex plane Slider control for the angle θ between position and velocity vectors Slider control for time parameter t Optional visualization of derivative directions: position, velocity (θ), acceleration (2θ), jerk (3θ), and snap (4θ) Clear color conventions and external legend for readability Purpose This release is intended as a research and visualization tool to support geometric intuition and exploration of the Spiral Exponential Equation.
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Brian Fisher, Fatma Al-Sirehy · Mathematica Moravica · 2015
The exponential integral ei(λx) and its associated functions ei+(λx) and ei-(λx) are defined as locally summable functions on the real line and their derivatives are found as distributions. The convolutions xr ei+(x) *xsex + and xr ei+(x) *xsex are evaluated.
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Kelly Hoffman (11336036), David Holcomb (10319240), Stacie Reckling (17199933) et al. · Figshare · 2023
<div><p>Wastewater surveillance emerged during the COVID-19 pandemic as a novel strategy for tracking the burden of illness in communities. Previous work has shown that trends in wastewater SARS-CoV-2 viral loads correlate well with reported COVID-19 case trends over longer time periods (i.e., months). We used detrending time series to reveal shorter sub-trend patterns (i.e., weeks) to identify leads or lags in the temporal alignment of the wastewater/case relationship. Daily incident COVID-19 cases and twice-weekly wastewater SARS-CoV-2 viral loads measured at 20 North Carolina sewersheds in 2021 were detrended using smoothing ranges of ∞, 16, 8, 4 and 2 weeks, to produce detrended cases and wastewater viral loads at progressively finer time scales. For each sewershed and smoothing range, we calculated the Spearman correlation between the cases and the wastewater viral loads with offsets of -7 to +7 days. We identified a conclusive lead/lag relationship at 15 of 20 sewersheds, with detrended wastewater loads temporally leading detrended COVID-19 cases at 11 of these sites. For the 11 leading sites, the correlation between wastewater loads and cases was greatest for wastewater loads sampled at a median lead time of 6 days before the cases were reported. Distinct lead/lag relationships were the most pronounced after detrending with smoothing ranges of 4–8 weeks, suggesting that SARS-CoV-2 wastewater viral loads can track fluctuations in COVID-19 case incidence rates at fine time scales and may serve as a leading indicator in many settings. These results could help public health officials identify, and deploy timely responses in, areas where cases are increasing faster than the overall pandemic trend.</p></div>
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vvhdsirfb · Zenodo (CERN European Organization for Nuclear Research) · 2024
&lt;pre&gt;&lt;code&gt;\n&lt;p&gt;&lt;strong&gt;derivative of exponential function pdf&lt;/strong&gt;&lt;br&gt;&lt;/p&gt;\n&lt;p&gt;Rating: 4.8 / 5 (4930 votes)&lt;br&gt;&lt;/p&gt;\n&lt;p&gt;Downloads: 30484&lt;br&gt;&lt;br&gt;&lt;/p&gt;\n &lt;p&gt;= = = = = \n&lt;strong&gt;&lt;a href="https://myvroom.fr/21Nr9y?keyword=derivative of exponential function pdf" target="_blank"&gt;CLICK HERE TO DOWNLOAD&lt;/a&gt;&lt;/strong&gt;\n = = = = = &lt;br&gt;&lt;br&gt;&lt;/p&gt;\n&lt;p&gt;&lt;br&gt;&lt;br&gt;&lt;br&gt;&lt;br&gt;&lt;/p&gt;\n&lt;p&gt;&lt;br&gt;&lt;br&gt;&lt;br&gt;&lt;br&gt;&lt;/p&gt;\n&lt;p&gt;&lt;br&gt;&lt;br&gt;ExamplesFind the derivative of the following functionsx. b0(t), we'll need to return to the definition of the derivative. ∆t) − f(x)=e−x g. = ex 2⎛ ⎝2x 2−1⎞ ⎠ x First we'll explore the derivative of our function graphicallyEnter the function as y1 and the numerical derivative (nDeriv) as y2 on your calculatorGraph the function In this section, we explore derivatives of exponential and logarithmic functions. (b) g(t) =()t. General Graphs of exponential functions and logarithmsThe derivative of axand the de nition of eDerivatives of LogarithmsLimits involving exponentials and Differentiation of Exponential Functions Graph fx() ex on the graphing calculator then use the nderiv function to graph its derivative. Find the derivative ofh(x)=xe2x. f(x)=e x2+e. As we discussed in Introduction to Functions and Graphs, exponential functions play an Derivative of exponential functions. In order to find. Example Applying the Natural Exponential Function A colony of mosquitoes has an initial population Derivative of exponential function. the Differentiate the following functions. = ex 2⎛ ⎝2x 2−1⎞ ⎠ x2 Simplify. f(x)=log e (7x−2) f. b(t) = 2t. Functions. Derivative of the inverse function. In this section we'd like to consider the derivatives of exponential and logarithmic functions. The natural exponential function can be considered as "the easiest function in Calculus courses" since the derivative of ex is ex. The exponential function with base e, is the only function (other than the trivial zero The reason for the above definition of e should now be clear. If. f(x) is a one-to-one function (i.e. General Exponential Function ax. The natural exponential function can be considered as "the easiest function in Calculus courses" since the derivative of ex is ex. f(x)=ln(ex +x3) h. +. (a) f(x) = 5xex (b) g(t) =()t Question: What rule do you have to use to take the derivative of a function of the form The most basic exponential function in calculus has base e: y = f(x) = ex. In fact, the only functions with this Use the derivative of the natural exponential function, the quotient rule, and the chain rule. f(x)=ln(exx3) i. b(t. y′ = ⎛ ⎝e x2·2⎞ ⎠x·x−1·exx2 Apply the quotient rule. f(x)=ln x2 +1 x3 −x General Exponential Function ax. Assuming the formula for ex, you can obtain the formula for the derivative of any other base a &gt;by noting that y = ax is equal to elnax = exlna Derivatives of Exponential and Logarithmic Functions. dy duuu dx dx ee EX) Differentiate each CalculusLia Vas. Derivatives of Exponential, Logarithmic and Trigonometric. The derivative of the exponential function is just the function itself. Use the derivative of the natural exponential function, the quotient rule, and the chain rule. Assuming the formula for ex; you can obtain the formula for the derivative of any other base a &gt;by noting that y = ax is equal to elnax = exlna: Use chain rule and the formula for derivative of ex to obtain that y0 = exlna ln a = ax ln a: Thus. a. Question: What rule do you have to use to take the derivative of a function of the form f(x) = af(x)? f(x)=ex7 c. (a) f(x) =ex. For any positive real number a, d dx [ax] = ax lna: In particular, d dx [ex] = ex: For example, d dx [2x] = 2x lnThe second formula follows from the rst, since lne =In modeling problems involving exponential growth, the base a of the exponential function can often be chosen to be anything, so, due to Derivative of exponential functions. Con sider a dynamical system for bacteria population, with a closed form solution given by. y′ = ⎛ ⎝e x2·2⎞ ⎠x·x−1·exx2 Apply the quotient rule. f(x)=ln(2x3) b. f(x)=ln(11x7) d. Find the derivative of the following functions. the derivative of ax is ax ln a: Derivative of the inverse function As a special case of the exponential rule, we have a very nice formula for taking the derivative of ex: DERIVATIVE OF ex: d (ex) = ex: dx.&lt;/p&gt;&lt;/code&gt;&lt;/pre&gt;
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Marlene Milgram · Mathematics of Computation · 1985
The generalized integro-exponential function is defined in terms of the exponential integral (incomplete gamma function) and its derivatives with respect to order.A compendium of analytic results is given in one section.Rational minimax approximations sufficient to permit the computation of the first six first-order functions are reported in another section.
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James K. Peterson · Cognitive science and technology · 2016
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Patricia Sureda, Rita Otero · International Electronic Journal of Mathematics Education · 2019
The construction of the exponential function of a real exponent from the definition of the powers of a real number, and its properties, requires the notion of successions, a decimal approximation of a rational number, convergence, and limit of a function. In Argentina, this construction would exceed what could be taught at the secondary level, but it provides advanced students of teachers in mathematics, and teachers in practice, the possibility of discussing what happens in the case of irrational exponents of the type aπ, or discuss the validity of the properties of this type of power.
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Oliver Nagy · Digital Repository (National Repository of Grey Literature) · 2017
Title: Exponential function and Mayer expansion Author: Oliver Nagy Department: Department of Mathematical Analysis Supervisor: doc. RNDr. Miloš Zahradník, CSc., Department of Mathematical Analysis Abstract: The unifying topic of this thesis is cluster expansion in statistical phy- sics. It is divided into three chapters. In the first one we present the necessary mathematical apparatus - selected topics from combinatorics, graph theory and theory of generating functions. The second one is an introduction to cluster expan- sion and abstract polymer model. Finally, in the third chapter we show a new resummation method for partition function of hard-core repulsive abstract poly- mer model. In this resummation we make use of cancellations of terms in partition function to rewrite the sum of clusters to a sum of quilted clusters, or alternati- vely as a sum of "bunches". The methods we use in this final chapter are original and may lead to some new results. Keywords: binomial and multinomial formula; power series; inclusion-exclusion principle; cluster expansion. iii
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Barbosa, Maria do Céu, Soares, João L. C. · Portuguese National Funding Agency for Science, Research and Technology (RCAAP Project by FCT) · 2005
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M. Ya. Likhttsinder, O. A. Katsyuba, P. Lange · Measurement Techniques · 1970
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Manoj Kumar Sharma · Multimedia Tools and Applications · 2026
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Tkachuk Vladimir V. · Commentationes Mathematicae Universitatis Carolinae · 2020
Given a Tychonoff space $X$ and an infinite cardinal $\kappa$, we prove that exponential $\kappa$-domination in $X$ is equivalent to exponential $\kappa$-cofinality of $\,C_p(X)$. On the other hand, exponential $\kappa$-cofinality of $X$ is equivalent to exponential $\kappa$-domination in $C_p(X)$. We show that every exponentially $\kappa$-cofinal space $X$ has a $\kappa^+$-small diagonal; besides, if $X$ is $\kappa$-stable, then $nw(X) \leq \kappa$. In particular, any compact exponentially $\kappa$-cofinal space has weight not exceeding $\kappa$. We also establish that any exponentially $\kappa$-cofinal space $X$ with $l(X) \leq\kappa$ and $t(X) \leq \kappa$ has $i$-weight not exceeding $\kappa$ while for any cardinal $\kappa$, there exists an exponentially $\o$-cofinal space $X$ such that $l(X) \geq \kappa$.
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