A Study on Teaching of the Integral Calculus Based on the Lacroix-style Definition of the Definite Integral: Focusing on the Calculus Textbooks in the First Half of the 20th Century

2021 ◽  
Vol 23 (1) ◽  
pp. 189-210
Author(s):  
Youn-joon Joung
Keyword(s):  
20Th Century ◽  
Definite Integral ◽  
Integral Calculus ◽  
Definition Of

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.

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

The Limit Situation And The Narrative Of War (On The Material Of The Novel “My Lieutenant” By Daniil Granin)

2020 ◽  
Vol 6 (1) ◽  
pp. 90-104
Author(s):  
Anatoly S. Kuprin ◽  
Galina I. Danilina
Keyword(s):  
20Th Century ◽  
Scientific Work ◽  
Point Of View ◽  
Continuous Limit ◽  
The Novel ◽  
Term Limit ◽  
Abstract Author ◽  
The Third ◽  
Definition Of

The purpose of this study is the analysis of limit situation in the narrative of war. The material of the study is the novel of Daniil Granin “My Lieutenant” and related texts. In the first part of the paper, the authors explore existing approaches to the term “limit situation” and similar concepts into scientific and philosophical traditions; limits of its applicability in literary studies and its relation to the categories of “narrative instances” and “event”. Proposed a literary-theoretical definition of the limit situation, which can be used in the analysis of fiction texts. Existing approaches to the examination of the situation of war are analyzed: philosophical-existential, psychoanalytic, sociological, literary. In the second part of the paper, the authors propose their method for analyzing limit situations in texts about war, which basis on existing approaches and preserves the text-centric principle of studying the structure of the story. Two interrelated areas of research have been identified: the study of war as a continuous limit situation in the intertextual aspect (the discourse of war); the study of limit situations (death, suffering, guilt, accident) in the narrative of war as part of a specific text. In the third part of the scientific work,the analysis of war as a continuous limit situation results in the study of the concept of “limit” (border) in a fiction text. The role of “limit” (border) concept in the texts about the war is studied, the possible types of limits in the discourse of war are examined. Limit situations in the narrative of war are analyzed on the basis of the novel “My Lieutenant” by Daniil Granin. A review of journalistic and scientific works about the novel revealed both the continuity and the differences between the novel and the “lieutenant” prose of the 20th century. An analysis of the limit situations in the novel revealed their key position in the narrative. These situations are independent of the fiction time, of the fluctuation of the point of view’; the function of the abstract author is to build the narrative as a “directive” immersion of the hero and narrator in these situations.

scholarly journals Patterns of Memory in Askold Melnyczuk’s Novels as an Example of Ukrainian-American Émigré Fiction

2020 ◽  
Vol 47 (2) ◽  
pp. 125-137
Author(s):  
Marta Koval
Keyword(s):  
North America ◽  
20Th Century ◽  
European History ◽  
Family Stories ◽  
Traumatic Memories ◽  
The Past ◽  
History Of ◽  
The Dead ◽  
Definition Of

Although Ukrainian emigration to North America is not a new phenomenon, the dilemmas of memory and amnesia remain crucial in Ukrainian-American émigré fiction. The paper focuses on selected novels by Askold Melnyczuk (What is Told and Ambassador of the Dead) and analyzes how traumatic memories and family stories of the past shape the American lives of Ukrainian emigrants. The discussion of the selected Ukrainian-American émigré novels focuses on the dilemmas of remembering and forgetting in the construction of both Ukrainian and American narratives of the past. The voluntary amnesia of the Ame- rican-born Ukrainians in Melnyczuk’s novels confronts their parents’ dependence on the past and their inability to abandon it emotionally. Memories of ‘the old country’ make them, similarly to Ada Kruk, ambassadors of the dead. The expression becomes a metaphoric definition of those wrapped by their repressed, fragmentary and sometimes inaccessible memories. Crucial events of European history of the 20th century are inscribed and personalized in the older generation’s stories which their children are reluctant to hear. For them, their parents’ memories became a burden and a shame. Using the concept of transgenerational memory, the paper explores the challenges of postmemory, and eventually its failure. 

scholarly journals Imagination in Entrepreneurship: An Inspiration from Heidegger

2019 ◽  
Vol 1 (01) ◽  
Author(s):  
Usman Talat ◽  
Kirk Chang
Keyword(s):  
20Th Century ◽  
Business Success ◽  
Opportunity Identification ◽  
Current Article ◽  
Definition Of

Entrepreneur's imagination has crucial implication on business success and management. Despite its espoused importance, imagination is still undervalued and deserves more academic attention. The current article aims to provide a novel perspective on imagination informed by Heidegger (1889-1976; widely acknowledged to be one of the most original philosophers of the 20th century). Specifically, the article has clarified the definition of imagination in entrepreneurship and risen constructs align with the proposed conception. Under the microscope of Heidegger’s theory, entrepreneur’s imagination co-operates ventures successfully by incorporating notions of webs of significance, authenticity, spontaneity, heroes and moods, which guide opportunity identification and exploration in markets. The article has offered new insights to the knowledge of entrepreneur's imagination. From a pragmatic viewpoint, inferential leaps are possible because entrepreneurs practice against a background of webs of significance they own - which they relationally, linguistically and pragmatically - share across institutional frames. Implications of the findings on management are discussed. 

scholarly journals Aproximación teórica y práctica a una propuesta de gestión conjunta: el archivo y la biblioteca de la familia Belmonte-Chico de Guzmán

2019 ◽  
Author(s):  
Camino Sánchez Oliveira
Keyword(s):  
20Th Century ◽  
Management System ◽  
Private Ownership ◽  
Design Elements ◽  
15Th Century ◽  
Definition Of ◽  
Siglo Xx ◽  
A Current

ENGLISH: The paper presents a current research and examines the design elements of a Familiar Heritage Documentary Collection, composed by bibliographical (a library) and archival (a family archive) collections, and, with enough frequency, a collection of objects related to the activities of the generators of these kind of heritage. The objective is to reflect on the definition of an integrator management system, with particular reference to patrimonial conceptualization and organisation documental systems. It is exposed The experience of managing a particular case of private ownership: the library and archive of the Belmonte-Chico de Guzmán family. We refer to a historical collection, of bibliographic and archival character, contributed and generated by the members of the different generations, branches and houses that compose this Castilian family of noble origin, throughout several centuries (from the end of the 15th century to the beginning of the 20th century). SPANISH: Se presenta parte de una investigación en curso, cuyo objetivo es definir y reflexionar sobre los elementos que fundamentan un sistema de gestión de lo que se ha denominado como un Fondo Documental Patrimonial Familiar (FDPF), compuesto por un fondo bibliográfico (una biblioteca), un fondo archivístico (un archivo familiar) y, con bastante frecuencia, una colección de objetos materiales relacionados con las actividades de los generadores del FDPF. El objetivo es reflexionar sobre la definición de un sistema de gestión conjunto en base a su conceptualización patrimonial, a su procesamiento documental y a su funcionalidad, así como atender al tipo de centro a cargo de dicho patrimonio. Se expone la experiencia de gestión de un caso particular de titularidad privada: la biblioteca y el archivo de la familia Belmonte-Chico de Guzmán. Nos referimos a un fondo histórico, de carácter bibliográfico y archivístico, aportado y generado por los miembros de las distintas generaciones, ramas y casas que componen esta familia castellana de origen nobiliario- hidalgo, a lo largo de varios siglos (desde finales del s. XV hasta inicios del siglo XX).

scholarly journals The traditional figures of women in Sardinian cinema

2020 ◽  
Vol 11 ◽  
pp. 17-27
Author(s):  
Ewa Baszak
Keyword(s):  
20Th Century ◽  
Point Of View ◽  
Main Character ◽  
Internal Point ◽  
Grazia Deledda ◽  
Definition Of

In this article I focus my attention on the archetype of women in Sardinian cinema. First of all, I explain the definition of the cinematographic movement which dominates Sardinia and I try to find the answer if Sardinian cinema cinema sardo exists. The next part of this paper shows the division of the cinema in Sardinia into two categories: seen from an external perspective by authors originating off the island and its culture, defined as hetero-representation, and seen from an internal point of view, developed by directors born and culturally raised in Sardinia, defined as self-representation.In the second part of the paper, I write about the term il deleddismo, which means the picture of Sardinia seen by the writer Grazia Deledda. Gianni Olla uses this term with reference to the cinema, il deleddismo cinematografico, as a way to enter the Sardinian world from the cinematic point of view. In early Sardinian cinema, stereotypes aimed at educating society and in the case of women by the merits of 20th-century ideology — to show them how they should behave. In recent decades this has not changed completely, but the figure of the modern woman is more often shown as the main character, who possesses far more power than her predecessors.

Sakāmvārda kā valodas vienības īpašības

2020 ◽  
pp. 14-23
Author(s):  
Olga Billere
Keyword(s):  
20Th Century ◽  
Semantic Structure ◽  
Complex Sentences ◽  
Part Of Speech ◽  
Art Forms ◽  
Definition Of ◽  
Empirical Material

The existence of various approaches to attributing the proverb to different branches of linguistics is due to the narrow, often intuitive, understanding of its meaning as an ancient, generalized and transmitted one of folk descent. The similarity with units of paremiology, as defined in explanatory and terminological dictionaries, brings even more confusion to the issue of delimiting recited forms. Indeed, aphorisms, apophthegms, maxims are semantically and structurally very similar to proverbs because, like proverbs, they are concise, often self-sufficient statements of an instructive nature, which are read, understood, and interpreted independently of the surrounding text. All these recited forms also have a stable syntactic and semantic structure, and, at first glance, it is difficult to judge which of the expressions is an aphorism, a maxim, an apothegm, and which a proverb. Thus, analyzing the features of the proverb as a language unit, that is, its similarity with other oral art forms, semantic and syntactic completeness and autonomy, and its bipartite structure, as well as determining common and different features of paremiological units, the most complete definition of the proverb and criteria for delimiting recited forms may be found. Here, autonomy means the feature of a unit to be in any part of speech, and completeness – the unit’s functioning as a self-sufficient expression. The attention is also paid to the bipartite structure, as most units (approx. 65%) are rhythmically constructed compound or complex sentences. The research is based on French, Russian, and Latvian theoretical and empirical material; the sources of the units are dictionaries and collections of proverbs in three languages compiled in the 20th century.

Supra-constitutional norms in constitutional law

2021 ◽  
Vol 30 (1) ◽  
pp. 100-127
Author(s):  
Dmitry Shustrov
Keyword(s):  
International Law ◽  
20Th Century ◽  
Natural Law ◽  
Constitutional Law ◽  
The Other ◽  
Constitutional Court ◽  
Definition Of ◽  
First Time ◽  
Positive Character ◽  
Constitutional Changes

The idea of supra-constitutionality was formulated in the science of constitutional law in the second quarter of the 20th century and associated with the names of M.Hauriou and K.Schmitt, who for the first time noticed the possibility of the existence of norms that are higher than the constitution. This article is an attempt to give the doctrine of supra-constitutionality an actual theoretical and dogmatic meaning in the context of the study of the material limits of constitutional changes. The doctrine of supra-constitutionality claims to play an important role in explaining that unchangeable norms can exist in constitutional law and that they cannot be excluded, changed, limited, overcome, affected by the other sources of constitutional law, including the constitution itself. Supra-constitutionality is viewed as a characteristic of unchangeable constitutional norms that constitute the material limits of constitutional changes. Supra-constitutionality presupposes the existence of norms that surpass the rest of the constitutional norms and predetermine their content through the definition of what can, should and should not be included in the constitution or excluded from it. The basis of constitutional supra-constitutionality is the argument of hierarchical differentiation. In addition to recognizing unchangeable constitutional norms as supra-constitutional, the article raises the question of the existence of natural law and international law supra-constitutional norms. Natural law supra-constitutional norms have an external and non-positive character. They are not enshrined in the constitution, but stem from a reasonably understood concept of what is due in the most civilized societies, which is determined by the constitutional court. International law supra-constitutionality is understood as the superiority of the norms of international law over the constitution. It has an external and positive character. International law supra-constitutionality can cause political objections from opponents of the absolute rule of international law. Supra-constitutional constitutional, natural and international law norms can come into conflict with each other. The paradox of the doctrine of supra-constitutionality lies in the fact that it creates a hierarchy of norms within the constitution itself, distinguishing between simple and supra-constitutional constitutional norms, or distinguishes certain non-positive norms that are outside the constitution, as having priority over the constitution, or puts some norms of international law over all norms of national law, including the constitution. The purpose of the doctrine of supra-constitutionality is to preserve the inviolable fundamental (natural or generally recognized) values, which justifies its logical flaws and paradoxicality.

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