Search results for "Integral calculus"

Generalized hypergeometric functions and the evaluation of scalar one-loop integrals in Feynman diagrams

2000

Present and future high-precision tests of the Standard Model and beyond for the fundamental constituents and interactions in Nature are demanding complex perturbative calculations involving multi-leg and multi-loop Feynman diagrams. Currently, large effort is devoted to the search for closed expressions of loop integrals, written whenever possible in terms of known - often hypergeometric-type - functions. In this work, the scalar three-point function is re-evaluated by means of generalized hypergeometric functions of two variables. Finally, use is made of the connection between such Appell functions and dilogarithms coming from a previous investigation, to recover well-known results.

Algebriskā analīze: teorija un uzdevumi

1937

Reālās ģimnāzijas kurss.

Calculus for the intermediate point associated with a mean value theorem of the integral calculus

2020

Abstract If f, g: [a, b] → 𝕉 are two continuous functions, then there exists a point c ∈ (a, b) such that ∫ a c f ( x ) d x + ( c - a ) g ( c ) = ∫ c b g ( x ) d x + ( b - c ) f ( c ) . \int_a^c {f\left(x \right)} dx + \left({c - a} \right)g\left(c \right) = \int_c^b {g\left(x \right)} dx + \left({b - c} \right)f\left(c \right). In this paper, we study the approaching of the point c towards a, when b approaches a.

Properties of the intermediate point from a mean value theorem of the integral calculus - II

2019

Abstract In this paper we consider two continuous functions f, g : [a, b] → ℝ and we study for these ones, under which circumstances the intermediate point function is four order di erentiable at the point x = a and we calculate its derivative.

Diferencialrēķini un integrālrēķini: inženierzinātņu un mehānikas fakultātes studentiem

1941

Integrālie rēķini

1941

Saturs: 1. d. Nenoteiktie integrāli -- 2. d. Noteiktie integrāļi -- Pielikums: Zīmējumi

Exploring Students’ Metacognitive Knowledge: The Case of Integral Calculus

2020

Previous studies of integral calculus have mainly explored students&rsquo

On students' understanding of Riemann sums of integrals of functions of two variables

2018

International audience; APOS (Action-Process-Object-Schema) Theory is used to pose and test a conjecture of mental constructions that may be used to understand the relation between integrals of two variable functions over rectangles and corresponding Riemann sums. Interviews with ten students who had just finished a multivariable calculus course showed that the conjectured mental constructions are necessary.

An Archimedean research theme: the calculation of the volume of cylindrical groins

2010

Starting from Archimedes’ method for calculating the volume of cylindrical wedges, I want to get to describe a method of 18th century for cilindrical groins thought by Girolamo Settimo and Nicolo di Martino. Several mathematicians studied the measurement of wedges, by applying notions of infinitesimal and integral calculus; in particular I examinated Settimo’s Treatise on cylindrical groins, where the author solved several problems by means of integrals.

Propuesta de unidad didáctica del concepto de integral y del cálculo de primitivas

2010

En este Trabajo Fin de Máster se va a proceder a desarrollar una propuesta de unidad didáctica sobre el concepto de integral y el cálculo de primitivas. Ambos temas, en orden contrario, fueron de los que me encargué de desarrollar en mis prácticas. Como trataré más adelante, la forma tradicional de introducir estos temas a los alumnos es comenzar con el cálculo de primitivas o antiderivadas para después, una vez que los alumnos tienen suficiente destreza en el cálculo de las mismas, continuar con el teorema fundamental del cálculo y la regla de Barrow, es decir, las integrales definidas, convirtiéndose dichos conceptos en transparentes para los alumnos y sin llegar a ser asimilados correcta…