Ch 9.Overview of Properties of... Ch 10.The Derivative at a Point Ch 11.The Derivative as a Function Ch 12.Second Derivatives Ch 13.Derivative Applications Ch 14.Finding Derivatives Ch 15.Properties of Definite Integrals Ch 16.Applications of Integrals ...
In this paper we consider the problem of the approximation of definite integrals on finite intervals for integrand functions showing some kind of "pathological" behavior, e.g. "nearly" singular functions, highly oscillating functions, weakly singular functions, etc. In particular, we introduce and ...
On product integration rules for highly oscillatory integrals on a triangle In this paper, we are concerned with a product rule on triangle. After introducing a natural grid configuration, a Lagrange interpolation polynomial of tot... J Gao,Y Jiang - 《Journal of Computational & Applied Mathematic...
A nine-point degree five rule for the numerical approximation of double integrals of analytic functions of complex variables and its error bound have been ... BP Acharya,T Mohapatra - 《Computing》 被引量: 1发表: 1986年 Global error bounds for product cubature rules We describe how global err...
Product integration rules generalizing the Fejer, Clenshaw-Curtis and Filippi quadrature rules respectively are derived for integrals with trigonometric and hyperbolic weight factors. The study puts in evidence the existence of well-cond... ADAM GH.,NOBILE A. - 《Ima Journal of Numerical Analysis》 ...
This derived integral formula is then used to provide formal derivations and new formulae in the form of a summary table of integrals, Table 1. The Lerch function being a special function has the fundamental property of analytic continuation, which enables enables the expansion of the range of ...
Ch 12. L'Hopital's Rule, Integrals & Series in... Ch 13. Analytic Geometry in 3-Dimensions How to Calculate the Volumes of Basic Shapes 7:17 How to Solve Visualizing Geometry Problems 10:41 Vector Dot Product | Formula & Representations 6:21 Cross Product & Right Hand Rule | Formu...
Its history and applications Kurzweil and McShane product integrals J Kurzweil,EJ Mcshane 被引量: 0发表: 2016年 Technically tying applications to a dominant platform in the software market and competition law In the US Microsoft case, the legal rule for assessing technical tying was the rule of ...
We approximate integrals by linear algorithms of the form Ad,N(f)=∑k=1Nakf(xxk), (9) where xx1,xx2,…,xxN are in Dd and a1,a2,…,aN are non-negative integration weights.Footnote 3 The worst-case error of an algorithm is defined by e(Fd,Ad,N)=supf∈Fd‖f‖d≤1|Id(f)...
is the solution of the initial value problem we started with. From the formula det x a e A(s)ds = e x a TrA(s)ds we infer that product integrals are non-singular matrices. We have a composition rule similar to that of ordinary integrals: b a e A(s)ds = b c e A(s)ds c ...