scholarly journals Integrability and the Integral of Partial Functions from R into R1

2006 ◽  
Vol 14 (4) ◽  
pp. 207-212
Author(s):  
Noboru Endou ◽  
Yasunari Shidama ◽  
Masahiko Yamazaki
Keyword(s):  
General Expression ◽  
Fundamental Theorem ◽  
Partial Functions ◽  
Integral Calculus ◽  
Fundamental Theorem Of Calculus ◽  
Indefinite Integral

Integrability and the Integral of Partial Functions from R into R1 In this paper, we showed the linearity of the indefinite integral the form of which was introduced in [11]. In addition, we proved some theorems about the integral calculus on the subinterval of [a,b]. As a result, we described the fundamental theorem of calculus, that we developed in [11], by a more general expression.

scholarly journals Fundamental theorem of Wiener calculus

1990 ◽  
Vol 13 (3) ◽  
pp. 443-452
Author(s):  
Chull Park ◽  
David Skoug ◽  
Lawrence Smolowitz
Keyword(s):  
Fundamental Theorem ◽  
Wiener Space ◽  
Wiener Integral ◽  
Integral Calculus ◽  
Indefinite Integral

In this paper we define and develop a theory of differentiation in Wiener spaceC[0,T]. We then proceed to establish a fundamental theorem of the integral calculus forC[0,T]. First of all, we show that the derivative of the indefinite Wiener integral exists and equals the integrand functional. Secondly, we show that certain functionals defined onC[0,T]are equal to the indefinite integral of their Wiener derivative.

scholarly journals Analysis of a criterial examination of integral calculus: the case of a public university of Mexico

2021 ◽  
pp. 1-9
Author(s):  
Maximiliano DE LAS FUENTES-LARA ◽  
Wendolyn Elizabeth AGUILAR-SALINAS ◽  
Araceli Celina JUSTO-LÓPEZ
Keyword(s):  
Fundamental Theorem ◽  
Large Scale ◽  
Public University ◽  
Trigonometric Functions ◽  
Integral Calculus ◽  
Reliable Test ◽  
Fundamental Theorem Of Calculus ◽  
Integration Techniques ◽  
Logarithmic Functions ◽  
Research Show

This research analyzes the quality and results of a criterial and large-scale comprehensive calculus test in the school cycles between 2014 and 2019 to a total of 5367 second-semester students of the engineering careers of a mexican public university. With the results obtained it is observed that the criterial examination of integral calculus is a valid, reliable test with satisfactory power of discrimination and with a majority load of procedural reagents. The results of the research show that the greatest difficulty for students is focused on integration techniques, especially when trigonometric functions are involved. It was also found that the success of students in the ECCI is due to the ability to resolve integrals with hyperbolic, exponential and logarithmic functions, as well as the proper application of the fundamental theorem of calculus and the technique of variable change.

scholarly journals A Teaching Experience through the use of Tasks: Limits and possibilities for learning Mathematics in a university context

2020 ◽  
Vol 22 (2) ◽  
Author(s):  
Alessandro Ribeiro ◽  
Juliana Paulin
Keyword(s):  
Teaching And Learning ◽  
Teaching Practice ◽  
Teaching Experience ◽  
Analysis Data ◽  
University Teaching ◽  
Mathematical Tasks ◽  
Integral Calculus ◽  
Mathematical Concepts ◽  
Fundamental Theorem Of Calculus ◽  
The University

Context: Rethinking mathematics teaching practices in a university context is an emerging research theme. Objectives: In this article, we aim to discuss the limits and possibilities of using mathematical tasks in the teaching and learning processes of the concepts of Derivative, Integral and the Fundamental Theorem of Calculus. Design: The study is based on a qualitative-interpretative perspective of research, with methodological procedures inspired by a Design-Based Research. Environment and participants: The research was developed with students attending a Functions of a Variable class in a public university in the state of São Paulo. Data collection and analysis: Data were collected through mathematical tasks on Differential and Integral Calculus solved by students. The protocols produced were analysed, pointing out the main aspects identified, which led us to organize categories of analysis and dimensions (i) knowledges mobilized and developed by students in relation to mathematical concepts; (ii) main errors and difficulties presented by students in the development of tasks; (iii) limits and possibilities of the practice of exploratory teaching in the university context. Results: The results reveal aspects that characterize a process of resignifying the mathematical concepts discussed with the students and a deepening of their knowledge about the concepts of the DIC. Conclusions: As future notes, we suggest rethinking university teaching practice, since the study indicated possibilities and potentialities of the use of exploratory tasks in the teaching of Differential and Integral Calculus.

scholarly journals Integral transforms of the κ-Hilfer fractional derivative

2021 ◽  
Author(s):  
Felix Costa ◽  
Junior Cesar Alves Soares ◽  
Stefânia Jarosz
Keyword(s):  
Fractional Derivative ◽  
Gamma Function ◽  
Fundamental Theorem ◽  
Beta Function ◽  
Integral Transforms ◽  
Fractional Operators ◽  
Riesz Fractional Derivative ◽  
Hilfer Fractional Derivative ◽  
Fundamental Theorem Of Calculus

In this paper, some important properties concerning the κ-Hilfer fractional derivative are discussed. Integral transforms for these operators are derived as particular cases of the Jafari transform. These integral transforms are used to derive a fractional version of the fundamental theorem of calculus. Keywords: Integral transforms, Jafari transform, κ-gamma function, κ-beta function, κ-Hilfer fractional derivative, κ-Riesz fractional derivative, κ-fractional operators.

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