With the continuous development of the fuzzy set theory, neutrosophic set theory can better solve uncertain, incomplete and inconsistent information. As a special subset of the neutrosophic set, the ...single-valued neutrosophic set has a significant advantage when the value expressing the degree of membership is a set of finite discrete numbers. Therefore, in this paper, we first discuss the change values
of single-valued neutrosophic numbers when treating them as variables and classifying these change values with the help of basic
operations. Second, the convergence of sequences of single-valued neutrosophic numbers are proposed based on subtraction
and division operations. Further, we depict the concept of single-valued neutrosophic functions (SVNF) and
study in detail their derivatives and differentials. Finally, we develop the two kinds of indefinite integrals of SVNF
and give the relevant examples.
We shall discuss three methods of inverse Laplace transforms. A Sinc-Thiele approximation, a pure Sinc, and a Sinc-Gaussian based method. The two last Sinc related methods are exact methods of ...inverse Laplace transforms which allow us a numerical approximation using Sinc methods. The inverse Laplace transform converges exponentially and does not use Bromwich contours for computations. We apply the three methods to Mittag-Leffler functions incorporating one, two, and three parameters. The three parameter Mittag-Leffler function represents Prabhakar’s function. The exact Sinc methods are used to solve fractional differential equations of constant and variable differentiation order.
A generalization of the Schwarz–Christoffel mapping to multiply connected polygonal domains is obtained by making a combined use of two preimage domains, namely, a rectilinear slit domain and a ...bounded circular domain. The conformal mapping from the circular domain to the polygonal region is written as an indefinite integral whose integrand consists of a product of powers of the Schottky-Klein prime functions, which is the same irrespective of the preimage slit domain, and a prefactor function that depends on the choice of the rectilinear slit domain. A detailed derivation of the mapping formula is given for the case where the preimage slit domain is the upper half-plane with radial slits. Representation formulae for other canonical slit domains are also obtained but they are more cumbersome in that the prefactor function contains arbitrary parameters in the interior of the circular domain.
In this paper we develop a stochastic calculus with respect to a Gaussian process of the form Bt= ∫t
0K(t, s) dWs, where W is a Wiener process and K(t, s) is a square integrable kernel, using the ...techniques of the stochastic calculus of variations. We deduce change-of-variable formulas for the indefinite integrals and we study the approximation by Riemann sums. The particular case of the fractional Brownian motion is discussed.
It is known that in the construction of the numerical methods for solving of the initial-value problem of ODE in basically used the methods which have applied to the calculation of the definite ...integrals. Here for the computing of definite integrals propose to use the methods which have used in solving of the initial-value problem for the ODEs. The definite integrals express by the indefinite integrals which are the solutions of the above-mentioned problems. For the construction of more exact methods for calculation of the definite integrals here propose to use forward-jumping (advanced) methods and the hybrid methods. Here establishes some connection between the Gauss and hybrid methods. And also have determined some necessary conditions for which the coefficients of the proposed methods have to satisfy. Constructed stable methods with the degree
p
≤ 8. Shown that, how received here results can be applied to the computing of the double integrals. For this aim, determines some connection between double integrals and single definite integrals. By using this relation have constructed methods which are applied to calculate the double integrals. Advantages of this method illustrated by calculation of model double integral by the constructed here methods.
An accessible, streamlined, and user-friendly approach to calculus
Calculus is a beautiful subject that most of us learn from professors, textbooks, or supplementary texts. Each of these resources ...has strengths but also weaknesses. InCalculus Simplified, Oscar Fernandez combines the strengths and omits the weaknesses, resulting in a "Goldilocks approach" to learning calculus: just the right level of detail, the right depth of insights, and the flexibility to customize your calculus adventure.
Fernandez begins by offering an intuitive introduction to the three key ideas in calculus-limits, derivatives, and integrals. The mathematical details of each of these pillars of calculus are then covered in subsequent chapters, which are organized into mini-lessons on topics found in a college-level calculus course. Each mini-lesson focuses first on developing the intuition behind calculus and then on conceptual and computational mastery. Nearly 200 solved examples and more than 300 exercises allow for ample opportunities to practice calculus. And additional resources-including video tutorials and interactive graphs-are available on the book's website.
Calculus Simplifiedalso gives you the option of personalizing your calculus journey. For example, you can learn all of calculus with zero knowledge of exponential, logarithmic, and trigonometric functions-these are discussed at the end of each mini-lesson. You can also opt for a more in-depth understanding of topics-chapter appendices provide additional insights and detail. Finally, an additional appendix explores more in-depth real-world applications of calculus.
Learning calculus should be an exciting voyage, not a daunting task.Calculus Simplifiedgives you the freedom to choose your calculus experience, and the right support to help you conquer the subject with confidence.
· An accessible, intuitive introduction to first-semester calculus
· Nearly 200 solved problems and more than 300 exercises (all with answers)
· No prior knowledge of exponential, logarithmic, or trigonometric functions required
· Additional online resources-video tutorials and supplementary exercises-provided
We study the algebraicity of Stark-Heegner points on a modular elliptic curve E. These objects are p-adic points on E given by the values of certain p-adic integrals, but they are conjecturally ...defined over ring class fields of a real quadratic field K. The present article gives some evidence for this algebraicity conjecture by showing that linear combinations of Stark-Heegner points weighted by certain genus characters of K are defined over the predicted quadratic extensions of K. The non-vanishing of these combinations is also related to the appropriate twisted Hasse-Weil L-series of E over K, in the spirit of the Gross-Zagier formula for classical Heegner points.
We compute the explicit formula of the Bergman kernel for a nonhomogeneous domain { $(z_{1},z_{2})\in {\Bbb C}^{2}\colon |z_{1}|^{4/q_{1}}+|z_{2}|^{4/q_{2}}<1$ for any positive integers q₁ and q₂. We ...also prove that among the domains $D_{p}\coloneq \{(z_{1},z_{2})\in {\Bbb C}^{2}\colon |z_{1}|^{2/p_{1}}+|z_{2}|^{2p_{2}}<1\}$ in ℂ² with p = (p₁, p₂) ∈ ℕ², the Bergman kernel is represented in terms of closed forms if and only if p = (p₁, 1), (1, p₂), or p = (2,2).
The present work consists of a solution of exercises proposed in the book Differential and Integral Calculus, Seventh Edition, McGraw Hill, corresponding to indefinite integrals applying the Method ...of Substitution and Change of Variable. So that the students of sciences and engineering can have an additional document that allows them to speed up the learning process corresponding to the resolution of this integral type where the most significant contribution to the demonstration of the obtained results is through the inverse process called Derivation. To develop skills in the students, such as empowerment of the need to verify a result in a mathematical operation, as well as to consolidate the existing links between Integral and Differential Calculus as inverse operations.
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