scholarly journals Fractional Line Integral

Mathematics ◽  
2021 ◽  
Vol 9 (10) ◽  
pp. 1150
Author(s):  
Gabriel Bengochea ◽  
Manuel Ortigueira
Keyword(s):  
Fundamental Theorem ◽  
Piecewise Linear ◽  
Directional Derivatives ◽  
Definite Integral ◽  
Integral Calculus ◽  
Regular Curve ◽  
Line Integral ◽  
Linear Path ◽  
Definition Of

This paper proposed a definition of the fractional line integral, generalising the concept of the fractional definite integral. The proposal replicated the properties of the classic definite integral, namely the fundamental theorem of integral calculus. It was based on the concept of the fractional anti-derivative used to generalise the Barrow formula. To define the fractional line integral, the Grünwald–Letnikov and Liouville directional derivatives were introduced and their properties described. The integral was defined for a piecewise linear path first and, from it, for any regular curve.

scholarly journals Fractional Line Integral

2021 ◽  
Author(s):  
Gabriel Bengochea ◽  
Manuel Ortigueira
Keyword(s):  
Fundamental Theorem ◽  
Directional Derivatives ◽  
Definite Integral ◽  
Integral Calculus ◽  
Regular Curve ◽  
Line Integral ◽  
Definition Of

This paper proposes a definition of fractional line integral, generalising the concept of fractional definite integral. The proposal replicates the properties of the classic definite integral, namely the fundamental theorem of integral calculus. It is based on the concept of fractional anti-derivative used to generalise the Barrow formula. To define the fractional line integrals the Gr\"unwald-Letnikov and Liouville directional derivatives are introduced and their properties described. The integral is defined first for broken line paths and afterwards to any regular curve

scholarly journals Empleo de simulaciones dinámicas en matlab como parte del proceso de enseñanza-aprendizaje de las matemáticas con aplicación al cálculo diferencial e integral.

2018 ◽  
Vol 5 (1) ◽  
pp. 36-41
Author(s):  
Miguel Lema Carrera
Keyword(s):  
Learning Process ◽  
Definite Integral ◽  
Integral Calculus ◽  
Dynamic Simulations ◽  
Student Community ◽  
Basic Ideas ◽  
Definition Of ◽  
Teaching Learning ◽  
Disk Method ◽  
Geometric Definition

     La matemática en todos los tiempos ha tenido como principal fuente de inspiración la visualización, jugando un papel importante en el desarrollo de conceptos, nociones e ideas básicas del cálculo diferencial e integral. El presente trabajo proporciona herramientas y métodos básicos de uso relativamente sencillo, desarrollados en el paquete computacional MATLAB, trabajando temas como la definición geométrica de derivada, la integral definida y cálculo de volúmenes de revolución utilizando el método de discos, que permite obtener resultados muy poderosos en simulaciones dinámicas “animadas” que sirvan de soporte y recurso didáctico facilitador en el proceso de enseñanza-aprendizaje del cálculo. Modificando y renovando en una primera instancia la forma tradicional de enseñanza de esta asignatura en los primeros años del ciclo básico universitario en esta institución y porque no del país, además, se espera que este trabajo, permita desterrar el paradigma entorno a la comunidad estudiantil, que ha relacionado al cálculo matemático con una idea pura y completamente algebraizada, estática y memorística. ABSTRACT The mathematics of all time has had as the main source of inspiration the visualization, playing an important role in the development of concepts, notions and basic ideas of the differential and integral calculus. The present work provides tools and basic methods of use relatively simple, developed in the computational package Matlab, working topics such as the geometric definition of derivative, the definite integral and calculation of volumes of revolution using the disk method, which allows to obtain very powerful results in "animated" dynamic simulations that serve as support and facilitating didactic resource in the teaching-learning process of calculus. Modifying and renewing in the first instance the traditional way of teaching this subject in the first years of the basic university cycle in this institution and why not in the country, in addition, it is expected that this work, to banish the paradigm around the student community, that has related to the calculus with a pure and completely algebraic, static and rote idea.

The Evaluation of ∫abdxx2 and ∫abdxx

1971 ◽  
Vol 64 (7) ◽  
pp. 605-606
Author(s):  
Norman Schaumberger
Keyword(s):  
Positive Integer ◽  
Fundamental Theorem ◽  
Definite Integral ◽  
Fundamental Theorem Of Calculus ◽  
Definition Of

Prior to the introduction of the fundamental theorem of calculus, it is a Common practice to use the definition of the definite integral to evaluate integrals of the form . These calculations are usually limited to cases in which k is a positive integer but are rarely extended to values larger than 3.

Mesh duality and Legendre duality

1990 ◽  
Vol 428 (1875) ◽  
pp. 351-377 ◽  
Keyword(s):  
Piecewise Linear ◽  
Voronoi Tessellation ◽  
Tangent Plane ◽  
Linear Functions ◽  
Piecewise Linear Functions ◽  
Dual Transformation ◽  
Delaunay Mesh ◽  
Definition Of

We describe a sense in which mesh duality is equivalent to Legendre duality. That is, a general pair of meshes, which satisfy a definition of duality for meshes, are shown to be the projection of a pair of piecewise linear functions that are dual to each other in the sense of a Legendre dual transformation. In applications the latter functions can be a tangent plane approximation to a smoother function, and a chordal plane approximation to its Legendre dual. Convex examples include one from meteorology, and also the relation between the Delaunay mesh and the Voronoi tessellation. The latter are shown to be the projections of tangent plane and chordal approximations to the same paraboloid.

scholarly journals Determination of the Starting Point in Time Series for Trend Detection Based on Overlapping Trend

2016 ◽  
Vol 16 (6) ◽  
pp. 98-110
Author(s):  
Gao Xuedong ◽  
Gu Kan
Keyword(s):  
Time Series ◽  
Piecewise Linear ◽  
Negative Influence ◽  
Trend Detection ◽  
Computational Accuracy ◽  
Starting Point ◽  
Time Series Studies ◽  
Definition Of ◽  
Stage Characteristic

Abstract The traditional time series studies consider the time series as a whole while carrying on the trend detection; therefore not enough attention is paid to the stage characteristic. On the other hand, the piecewise linear fitting type methods for trend detection are lacking consideration of the possibility that the same node belongs to multiple trends. The above two methods are affected by the start position of the sequence. In this paper, the concept of overlapping trend is proposed, and the definition of milestone nodes is given on its base; these way not only the recognition of overlapping trend is realized, but also the negative influence of the starting point of sequence is effectively reduced. The experimental results show that the computational accuracy is not affected by the improved algorithm and the time cost is greatly reduced when dealing with the processing tasks on dynamic growing data sequence.

A Multi-Purpose Off-Line Path Planner Based on an A* Search Algorithm

1996 ◽  
Author(s):  
Arturo L. Rankin ◽  
Carl D. Crane
Keyword(s):  
Search Algorithm ◽  
Piecewise Linear ◽  
Autonomous Mobile Robot ◽  
Linear Path ◽  
Shortest Distance ◽  
Computer Controlled ◽  
Turning Radius ◽  
Minimum Turning Radius ◽  
Path Planner ◽  
Line Path

Abstract Efficient navigation of an autonomous mobile robot through a well-defined environment requires the ability of the robot to plan paths. An efficient and reliable planar off-line path planner has been developed that is based on the A* search method. Using this method, two types of planning are accomplished. The first uses a map of all known obstacles to determine the shortest-distance path from a start to goal configuration. The second determines the shortest path along a network of predefined roads. For the most complicated environment of obstacles and roads, a near-optimal piecewise-linear path is found within a few seconds. The planner can generate paths for robots capable of rotation about a point as well as car-like robots that have a minimum turning radius. For car-like robots, the planner can generate forward and reverse paths. This software is currently implemented on a computer controlled Kawasaki Mule 500 all-terrain vehicle and a computer controlled John Deere 690 excavator.

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