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Journal articles on the topic 'Differential and integral calculus teaching'

Author: Grafiati

Published: 4 June 2021

Last updated: 14 February 2022

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1

Gray, Allan B., and Charles G. Moore. "Sharing Teaching Ideas: Integral Cubics." Mathematics Teacher 83, no. 5 (May 1990): 370–71. http://dx.doi.org/10.5951/mt.83.5.0370.

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The teacher of differential calculus needs to be able to draw from a store of problems that have neat answers, solutions that are integers. These problems furnish valid items for quizzes or short tests because fundamental concepts involved in the problem can be tested without the student's becoming ensnared in peripheral details.

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Pereira, Breno De Faria Arnaut, Fabiane Mondini, and Luciane Ferreira Mocrosky. "Expondo os índices de permanência e continuidade na disciplina de Cálculo Diferencial e Integral I em cursos de engenharia na UNESP– Câmpus de Guaratinguetá." Revista Brasileira de Educação em Ciências e Educação Matemática 3, no. 3 (December 28, 2019): 841. http://dx.doi.org/10.33238/rebecem.2019.v.3.n.3.23755.

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Resumo: Este texto apresenta resultados de uma pesquisa cujo objetivo foi estudar como se mostram os índices de permanência e continuidade, na disciplina de Cálculo Diferencial e Integral I, na Universidade Estadual Júlio de Mesquita Filho, UNESP – Câmpus de Guaratinguetá. Justificamos a escolha do tema por sua relevância e pelos altos índices de reprovação e evasão que comumente ocorrem nessa disciplina. Os dados foram constituídos entre os anos de 2013 e 2016. Orientados pela interrogação “como estão os índices de permanência e continuidade na disciplina de CDI - I nos cursos de engenharia da FEG/UNESP?, nossa intenção é expor os dados e nossas considerações de modo a subsidiar futuras pesquisas ou ações voltadas para o ensino da disciplina, não se registrindo a este contexto em que a investigação se desenvolve, mas avançando para outros contextos mais abrangentes, permitindo um pensar sobre novas metodologias e abordagens de ensino que sejam capazes de romper o status quo do ensino de Cálculo Diferencial e Integral.Palavras-chave: Cálculo Diferencial e Integral; Educação Matemática; Ensino Superior; Índices de Permanência e Continuidade. A study on permanence and continuity indices in Differential and Integral Calculation I in engineering courses at UNESP - Guaratinguetá CampusAbstract: This paper presents results of a research whose objective was to study how to show the indices of permanence and continuity in the discipline of differential and integral calculus I, at Unesp - Campus de Guaratinguetá. We justify the choice of the theme for its relevance and the high rates of retention and dropout that commonly occur in this discipline. The data were constituted between 2013 and 2016. uided by the question “how are the indices of permanence and continuity in the discipline of CDI - I in engineering courses at FEG / UNESP?”, our intention is to expose the data and considerations in order to support future research or actions aimed at teaching this discipline, not restricting itself to this context in which research develops, but advancing to a broader context, allowing one to think about new teaching methodologies and approaches that are able to break the status quo of differential and integral calculus teaching.Keywords: Differential and integral calculus; Mathematics education; University education; Permanence and Continuity Indices.

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Bigotte de Almeida, Maria Emília, Araceli Queiruga-Dios, and María José Cáceres. "Differential and Integral Calculus in First-Year Engineering Students: A Diagnosis to Understand the Failure." Mathematics 9, no. 1 (December 29, 2020): 61. http://dx.doi.org/10.3390/math9010061.

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Difficulties in the curricular units (CU) of the mathematical science area, particularly those related to differential and integral calculus (DIC), are often found among students of engineering degrees, leading to high failure rates. A research work was developed with the objective of finding the reasons that lead the students to fail in the CU of DIC (CU-DIC) taught in the 1st year of the engineering undergraduate degrees at the Coimbra Engineering Institute (ISEC), in Portugal. Applying a case study methodology, this article will present a current diagnosis with the objective to establish relationships between teaching methods and students’ learning strategies, and besides, we propose to build learning environments that lead to higher success. The analysis of collected data allows us to conclude that the CU-DIC in the ISEC maintain an identical distribution in the hourly load in several engineering degrees, where contents are adjusted to each context taking into account the CUs of each degree. The data analysis found better results in the academic year that includes two examination moments without any relationship between class attendance, dropout and pass rates. We propose some different teaching/learning strategies in CU-DIC and new learning environments that enhance freshmen students’ engagement and participation in their own learning process.

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Vorontsova, Ol’ga R., and Tat’yana A. Chebun’kina. "Assessment of students' psychoemotional state in the process of teaching higher mathematics using colour matrix." Vestnik of Kostroma State University. Series: Pedagogy. Psychology. Sociokinetics 26, no. 4 (February 24, 2021): 196–202. http://dx.doi.org/10.34216/2073-1426-2020-26-4-196-202.

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The article deals with the psychoemotional state of students when studying the modules "Integral calculus" and "Differential equations" in the course of higher mathematics. The factors that affect the degree of assimilation of educational material by first-year students are described, and the causes of emotional (psychological) stress are noted. The study is confirmed by an empirical description, which was conducted using the "colour painting" technique, first used to assess the psychoemotional state of first-year students when studying sections of the higher mathematics course. The proposed method makes it possible to "see" the mood of students on each topic of the module, to track the dynamics of emotional states in the team on the topics of each module and the overall picture of the mood of each individual in the student group. Colour matrix allows recording the emotional response to events (for the authors of the article, these are modules of the course) and finding out how it was perceived by students, who of them is experiencing difficulties. The study of the psychoemotional state of respondents was conducted by means of a questionnaire, where the authors were interested in how the study materials on the topic "Integral calculus" and "Differential equations"affect the students' health/mood. Based on the analysis, the most difficult topics for learning modules were identified, and recommendations were given on their possible forms and methods of teaching.

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Grattan-Guinness, I. "On proving certain optimisation theorems in plane geometry." Mathematical Gazette 97, no. 538 (March 2013): 75–80. http://dx.doi.org/10.1017/s0025557200005441.

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A pleasurable aspect of mathematics and its teaching is to review the diversity of ways in which theorems are proved. Especially in elementary branches, there are various kinds of proof: using (or avoiding) spatial geometry, analytic or coordinate geometry, common algebra, vectors, abstract algebras, matrices, determinants, the differential and integral calculus, and maybe mixtures thereof. Further, sometimes a proof of one kind is elegant while another is clumsy, or one proof of a theorem suggests why it follows while another proof is not perspicuous. There is also the question of whether a proof is direct or indirect (for example, proofby contradiction).

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Lema Carrera, Miguel. "Empleo de simulaciones dinámicas en matlab como parte del proceso de enseñanza-aprendizaje de las matemáticas con aplicación al cálculo diferencial e integral." Revista Científica y Tecnológica UPSE 5, no. 1 (June 20, 2018): 36–41. http://dx.doi.org/10.26423/rctu.v5i1.306.

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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.

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Lopes, Vanessa Rodrigues, and Suely Scherer. "Cálculo Diferencial e Integral e o Uso de Tecnologias Digitais de Informação e Comunicação: uma Discussão de Pesquisas nos Últimos Onze Anos." Jornal Internacional de Estudos em Educação Matemática 11, no. 2 (September 11, 2018): 145. http://dx.doi.org/10.17921/2176-5634.2018v11n2p145-159.

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Os conceitos de Cálculo Diferencial e Integral são estudados em diversos cursos do Ensino Superior, como por exemplo, Engenharias, Química, Ciência da Computação, Administração, Biologia, Física, Matemática, dentre outros. Nos últimos onze anos, diversas pesquisas foram realizadas com foco nos processos de ensino e/ou de aprendizagem de Cálculo e em muitas se anuncia que foram motivadas pelos índices de reprovação nesta disciplina. Neste artigo, o objetivo é apresentar e analisar pesquisas desenvolvidas nos últimos onze anos, cujo objeto de investigação é o ensino e/ou a aprendizagem de Cálculo em espaço presencial e/ou virtual, no Ensino Superior, com uso de Tecnologias Digitais de Informação e Comunicação (TDIC) e refletir sobre a problemática do ensino e da aprendizagem de Cálculo com uso de TDIC, em especial com momentos à distância, a partir do cenário evidenciado por essas pesquisas. O estudo foi realizado a partir de uma busca no banco de teses e dissertações da Capes e na Biblioteca Digital Brasileira de teses e dissertações, tendo como resultado final vinte pesquisas sobre o tema, que foram analisadas nesse artigo. Esse cenário de pesquisas evidencia que o uso de tecnologias digitais pode ser um caminho para a superação de algumas dificuldades na aprendizagem do Cálculo. E um desafio para pesquisas sobre essa temática/problemática é considerar a possibilidade da aprendizagem móvel, ou M-learning, da aprendizagem ubíqua, ou u-learning, afinal os alunos do Ensino Superior estão cada vez mais com a tecnologia digital em suas mãos, acessível a qualquer momento, em vários espaços.Palavras-chave: Cálculo Diferencial e Integral I. Tecnologia Digital de Informação e Comunicação. Espaço Presencial. Espaço Virtual.AbstractThe concepts of Differential and Integral Calculus are studied in several courses of Higher Education, such as in Engineering, Chemistry,Computer Science, Administration, Biology, Physics, Mathematics, among others. In the last eleven years, several researches have beenconducted focusing on the teaching and / or learning process of Calculus, and in many, it is announced that they were motivated by the failurerates in this discipline. In this article the objective is to present and analyze researches developed in the last eleven years whose object ofresearch is the teaching and / or learning of Calculus in presence and / or virtual space in higher education, using Digital Information andCommunication Technologies ( TDIC), and to reflect on the teaching and learning of Calculus using TDIC, especially with moments at adistance, based on the scenario evidenced by these studies. The study was carried out from a search of the thesis and dissertation bank ofCapes and the Brazilian Digital Library of theses and dissertations, with the result of twenty researches on the subject, which were analyzed inthis article. This research scenario shows that the use of digital technologies can be a way to overcome some difficulties in learning Calculus.And a challenge for research on this issue / problem is to consider the possibility of mobile learning, or M-learning, ubiquitous learning, oru-learning, after all Higher Education students are increasingly with digital technology at their fingertips, Accessible at any time, in variousspaces.Keywords: Differential and Integral Calculus I. Digital Information and Communication Technology. Face-to-Face Space. Virtual Space.

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Oliveira, Júlia, Leonardo Panontim, Vitor Hugo Fonseca, Pedro Gonçalves, Diovana Napoleão, and Marco Alcântara. "Project-Based Learning." International Journal for Innovation Education and Research 9, no. 7 (July 1, 2021): 224–37. http://dx.doi.org/10.31686/ijier.vol9.iss7.3244.

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One of the problems that concerns engineering courses in Brazil is the students low level of motivation in regarding the type of teaching and, as a consequence, low academic performance. This article encourages the introduction of active methods in Engineering teaching, emphasizing the methodologies of Project Based Learning. The approach used was proposing a project for students to analyze important aspects in the production of cylindrical cans. The students applied calculus concepts and developed a model for the optimal dimensions of the cylinder and the utilization of the plates used. Characteristics of two materials used in the manufacture of these cans (tinplate and aluminum) were also gotten. Such aspects are relevant for both environmental sustainability and production costs. Concepts of application of derivatives and Fermat's theorem were used, learned in the discipline of Differential and Integral Calculus, in order to obtain the maximum and minimum values of an established function which relates the dimensions of the can and the amount of material needed. The dimensions obtained theoretically proved to be close to the real values found in cans available on the market. After analyzing the resistance to corrosion, the cost, the decomposition time and the mechanical resistance, it was concluded that the most appropriate material for the production of cans was the tinplate. In this context, teaching with Project Based Learning methodologies may contribute to innovative teaching practices in the training of engineering professionals, overcoming the limitations of traditional teaching methods.

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Trevisan, André Luis, and Eliane Maria de Oliveira Araman. "Argumentos Apresentados por Estudantes de Cálculo em uma Tarefa de Natureza ExploratóriaArguments Presented by Students of Calculus in an Exploratory Task." Educação Matemática Pesquisa : Revista do Programa de Estudos Pós-Graduados em Educação Matemática 23, no. 1 (April 11, 2021): 591–612. http://dx.doi.org/10.23925/1983-3156.2021v23i1p591-612.

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ResumoA presente pesquisa tem como objetivo reconhecer conceitos matemáticos que foram utilizados por estudantes de Cálculo Diferencial e Integral na elaboração de argumentos, na resolução de uma tarefa de natureza exploratória envolvendo representações gráficas. Como referencial teórico, recorremos aos estudos relacionados ao raciocínio matemático e à argumentação, aos episódios de resolução de tarefas e à aprendizagem do conceito de função. A pesquisa segue princípios de uma investigação baseada em design. Para produção de dados, utilizamos gravações em áudio e a produção escrita dos estudantes no trabalho com a tarefa, além do diário de campo dos pesquisadores. Apoiados pelo arcabouço teórico, analisamos os argumentos apresentadas por quatro grupos de estudantes durante a discussão da tarefa. Como resultados, destacamos que os estudantes mobilizam alguns processos de raciocínio (identificar padrão, conjecturar, comparar e justificar) ao elaborarem a descrição do gráfico de funções, recorrendo, para tal, a conceitos matemáticos como (de)crescimento de função, variação da taxa de crescimento, concavidade de um gráfico e assíntota horizontal.Palavras-chave: Ensino de matemática. Ensino de cálculo diferencial e integral. Raciocínio matemático. Argumentação.AbstractThis research aims to analyse arguments developed by students of the Differential and Integral Calculus subject of a public university in Paraná when solving an exploratory task. The theoretical framework is formed by studies related to mathematical reasoning and argumentation, episodes of solving tasks, and learning the concept of function. The research follows the principles of design research. The data were audio recordings and the written production of students working on the task, and the researchers’ field diary. Supported by the theoretical framework, we analysed the arguments presented by four groups of students during the discussion of the task. The result show that students mobilise some reasoning processes (identify pattern, conjecture, compare, and justify) when elaborating the function graph description, using mathematical concepts such as function growth and decrease, rate variation of growth, concavity of a graph, and horizontal asymptote.Keywords: Mathematics teaching. Teaching Differential and Integral Calculus. Mathematical reasoning. Argumentation. ResumenEsta investigación tiene como objetivo analizar los argumentos desarrollados por estudiantes de la asignatura Cálculo Diferencial e Integral de una universidad pública de Paraná al momento de resolver una tarea exploratoria. El marco teórico está formado por estudios relacionados con el razonamiento y la argumentación matemática, episodios de resolución de tareas y aprendizaje del concepto de función. La investigación sigue los principios de la investigación basada en diseño. Los datos fueron grabaciones de audio y la producción escrita de los estudiantes trabajando en la tarea y el diario de campo de los investigadores. Apoyados en el marco teórico, analizamos los argumentos presentados por cuatro grupos de estudiantes durante la discusión de la tarea. El resultado muestra que los estudiantes movilizan algunos procesos de razonamiento (identificar patrón, conjeturar, comparar y justificar) al elaborar la descripción del gráfico de funciones, utilizando conceptos matemáticos como crecimiento y disminución de funciones, tasa de variación de crecimiento, concavidad de una gráfica y asíntota horizontal.Palabras clave: Enseñanza de las matemáticas. Enseñanza del cálculo diferencial e integral. Razonamiento matemático. Argumentación.

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Molon, Jaqueline, and Edson Sidney Figueireo. "CÁLCULO NO ENSINO MÉDIO: UMA ABORDAGEM POSSÍVEL E NECESSÁRIA COM AUXÍLIO DO SOFTWARE GEOGEBRA." Ciência e Natura 37 (August 7, 2015): 156. http://dx.doi.org/10.5902/2179460x14523.

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http://dx.doi.org/10.5902/2179460X14523This article is the result of the dissertation of the Professional Masters in Mathematics in National Network, held in March 2013 at the Federal University of Santa Maria (UFSM). The work aimed to verify the possibility of inclusion in high school, the intuitive ideas of the Differential and Integral Calculus: limits of a function, the average rate of change, instantaneous variation and calculation of areas under the graph of positive functions, limited the x-axis and vertical lines, or even between positive functions in a particular area of the same range. To facilitate the understanding of these ideas, activities were developed using the Software GeoGebra as support learning tool. The activities were applied to an experimental group of students from the first year of High School, combined with the study of quadratic functions. It was found that you can open the horizons within the teaching and learning of mathematics in high school, to the intuitive ideas of calculus. In this work, the objectives of this research will be presented, some proposed activities and the results achieved, and propose developments to deepen and apply the issues discussed here.

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RODRIGUEZ, Maria de Lourdes, Juan Salvador NAMBO DE LOS SANTOS, and Jesús RODRÍGUEZ BUENDÍA. "Socioformation and the Formative Evaluation in Engineering." Revista Romaneasca pentru Educatie Multidimensionala 10, no. 1 (April 2, 2018): 210. http://dx.doi.org/10.18662/rrem/29.

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The society demands nowadays that the educational models of the institutions at the university level focus in an integral formation developing knowledge, skills and competences. Nevertheless, the systems of evaluation are not necessarily according to the requirements and methods of teaching and learning in the classroom. This investigation describes the effect of implementing a checklist as a medium so that the student acquires knowledge and gives feedback on the process of teaching and learning, promoting the integral formation. The checklist was designed under the socioformative approach and was used as a mean for the formative evaluation and shared during a course of differential and integral calculus. The qualitative investigation of analytical and descriptive type was based on the action-investigation, with students of the Career of Engineering on Communications and Electronics of Instituto Politécnico Nacional. Among the obtained results, it turns out that the students had a better academic performance and a change of attitude towards the learning of the mathematics in engineering, because they can take the control and the regulation of it. Concluding, we can say that the instruments of evaluation constructed under the socioformative approach promote the formative and participative evaluation and are a good way to improve the academic performance of the student and to develop competences like the collaborative work, the resolution of problems and the autonomy in the learning. It becomes necessary to continue the research regarding the design of instruments of formative evaluation as a didactic medium and the roles that the teachers and students must follow in order to promote an integral formation from the socioformative approach.

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Fernandes, Beatriz Da Costa, Rodiney Marcelo Braga dos Santos, Regina Maria Pereira de Souza, Jonas Andrade de Sousa, and José Doval Nunes Martins. "Análise do índice de retenção da disciplina Cálculo Diferencial e Integral I no IFPB – Campus Cajazeiras e proposta de intervenção didático-pedagógica a partir do serviço da web ‘Google Sala de Aula’." Revista Principia - Divulgação Científica e Tecnológica do IFPB 1, no. 50 (July 17, 2020): 11. http://dx.doi.org/10.18265/1517-0306a2020v1n50p11-22.

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In this research we point out the problem of the retention rate in the discipline “Differential and Integral Calculus I “(CDI I) which is in the curriculum of the higher education courses of the Federal Institute of Education, Science and Technology of Paraíba, Cajazeiras campus. The research typology used in the study comprises the qualitative-quantitative, descriptive-exploratory approaches and case study. The results obtained present the general performance data of students of 32 classes of the discipline in the years 2014 and 2017; the brief profile of the students of class 2018.2, in effect during the period of this research and an experience of pedagogical intervention through the use of the web service ‘Google Classroom’. We infer, however, that if this teaching strategy continues from its setting to its expansion, there will possibly be an expansion of the study dynamics of the subjects involved.

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Damy, Abelardo, and Maria Guadalupe Lomeli Plascencia. "Interdisciplinary block of learning challenges." Contemporary Educational Researches Journal 10, no. 1 (February 29, 2020): 21–27. http://dx.doi.org/10.18844/cerj.v10i1.4611.

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The Block of Sciences is a project that includes the contents of Differential and Integral Calculus and Mechanics around learning challenges that students solve along the semester. It becomes evident the development of not only disciplinary but also transversal competencies, so that students learn the contents and solve the challenges. In the concerning to the teaching work, there exist changes due to the fact that a very close communication among the team members during the full semester is necessary. The professor’s role in a subject transforms into a learning facilitator or guide in order to create an appropriate environment to produce a better and more meaningful learning. In addition, there is a supervising professor for the challenges, who supports the students through all the process. With respect to the students, they have a key and active role, and as a consequence, they get a more significant learning. Keywords: Competencies, educational innovation, multidisciplinary blocks, teamwork, Tec21.

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Bisognin, Eleni, Vanilde Bisognin, and Etiane Bisognin Rodrigues. "A Learning Trajectory to the Understanding of the Curve Length Concept." Acta Scientiae 21, no. 3 (July 19, 2019): 24–40. http://dx.doi.org/10.17648/acta.scientiae.v21iss3id5030.

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In this article, we present results of a research study focusing on the analysis of a hypothetical learning trajectory carried out with students taking a mathematics teaching degree. The aim of this study was to examine students’ understanding of the concept of curve length. The qualitative research was carried out with nine students participating in a course on Differential and Integral Calculus discipline of a private university in which that content was approached. The data were obtained through records of the students' worked out solutions, notes from observation recorded in the teacher's field diary and audio recordings made during the course development. From the analysis of the results, it can be inferred that the students showed gaps in their previous knowledge and difficulties on how to use that knowledge in the construction of new concepts; however, evidence was observed that the planned hypothetical learning trajectory facilitated, in part, the understanding of the concept of curve length.

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Retzlaff, Eliani, Rozelaine De Fatima Franzin, Rosangela Ferreira Prestes, and Antonio Vanderlei dos Santos. "Acompanhamento pedagógico com o software mathcad prime como contribuição na perspectiva da aprendizagem significativa." Revista Brasileira de Educação em Ciências e Educação Matemática 2, no. 2 (August 31, 2018): 303. http://dx.doi.org/10.33238/rebecem.2018.v.2.n.2.19887.

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Resumo: Existe uma variedade de softwares disponíveis que podem ser usados na Educação Básica e Superior como recursos didáticos para apoiar, reforçar ou complementar as aulas, de forma dinâmica, propiciando situações para uma aprendizagem significativa. O artigo propõe-se analisar o potencial didático do Software Mathcad Prime como contribuição dessa aprendizagem. Nesse sentido, utilizou-se o Estudo de Funções, pela dificuldade apresentada pelos alunos na compreensão de conceitos, propriedades e análise gráfica, bem como na resolução de problemas. A utilização desse recurso nas atividades dos componentes curriculares de Fundamentos de Matemática “A”, Física Geral “A” e Cálculo Diferencial e Integral I, sob a forma de acompanhamento pedagógico, pode favorecer e fortalecer o ensino da Matemática. Os resultados dessa pesquisa mostram que a mediação do software pode promover diferentes abordagens e situações de aprendizagem que envolvem relações conceituais e a utilização de modelos que se ajustam a solução de problemas reais colaborando para o desenvolvimento de estruturas mentais de forma coordenada.Palavras-chave: Aprendizagem significativa; Estudo de Funções; Software Mathcad Prime. Pedagogical follow-up with the mathcad prime software as a contribution to the perspective of meaningful learningAbstract: There are a variety of softwares available that can be used in basic and higher education as teaching resources to support, reinforce or complement classes, dynamically strengthening for meaningful learning. The article proposes to analyze the didactic potential of Mathcad Prime Software as a contribution of this learning. In this sense, the Study of Functions was used, due to the difficulty presented by the students in understanding concepts, properties and graphic analysis, as well as in solving problems. The use of this resource in the activities of the curricular components of Fundamentals of Mathematics A, General Physics A and Differential and Integral Calculus I, in the form of pedagogical accompaniment, can support and strengthen the teaching of Mathematics The results of this research show that software mediation can promote different approaches and learning situations that involve conceptual relationships and the use of models that adjust to the solution of real problems collaborating for the development of mental structures in a coordinated way.Keywords: Meaningful learning; Function Study; Mathcad Prime software.

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Flowers, M. J., and R. L. Wallis. "Differential and Integral Calculus." Mathematical Gazette 69, no. 447 (March 1985): 58. http://dx.doi.org/10.2307/3616467.

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Acosta, Daniel J., and Randall Wills. "CLASSROOM INTEGRAL CALCULUS: SOME USEFUL DIGRESSIONS WHEN TEACHING INTEGRAL CALCULUS*." PRIMUS 12, no. 1 (January 2002): 75–86. http://dx.doi.org/10.1080/10511970208984019.

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Bisognin, Vanilde, and Eleni Bisognin. "Compreensão do conceito de taxa de variação por professores em formação continuada." Revista Brasileira de Educação em Ciências e Educação Matemática 2, no. 1 (May 3, 2018): 27. http://dx.doi.org/10.33238/rebecem.2018.v.2.n.1.19379.

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Resumo: Neste trabalho, são apresentados resultados de uma pesquisa que tem como objetivo analisar como professores em formação continuada, participantes da disciplina de Fundamentos de Cálculo Diferencial de um curso de Mestrado em Ensino de Matemática, interpretam e relacionam as informações explicitadas pelas diferentes representações do conceito de taxa de variação. Para tanto foi aplicada uma sequência de atividades sobre as diferentes representações do conceito de taxa de variação e as respostas das questões foram analisadas e categorizadas. Os resultados apontam que, apesar de terem trabalhado o conceito de taxa de variação em seus cursos de licenciatura em Matemática, alguns professores ainda apresentam dificuldades para compreender esse conceito e relacionar suas diferentes representações. Pela análise dos dados, considera-se que as atividades propostas proporcionaram a evolução da ideia intuitiva de taxa de variação e favoreceram a compreensão desse conceito pelos participantes da pesquisa.Palavras-chave: Taxa de variação; Formação de professores; Imagem de conceito; Definição de conceito. Comprehension of the variation rate concept by teachers in continued trainingAbstract: In this work, results of a research are presented that aim to analyze how teachers in continuous formation, participants in the discipline of Fundamentals of Differential and Integral Calculus of a Master course in Mathematics Teaching, interpret and relate the information explained by the different representations of the concept of rate of variation. For this, a sequence of activities was applied on the different representations of the concept of rate of variation and the answers of the questions were analyzed and categorized. The results show that, although they have worked on the concept of rate of variation in their undergraduate courses in Mathematics, some teachers still find it difficult to understand this concept and to relate their different representations. By analyzing the data, it is considered that the proposed activities provided the evolution of the intuitive idea of rate of variation and favored the understanding of this concept by the research participants.Keywords: Rate of variation; Teacher training; Concept image; Definition of concept.

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Sauerheber, Richard D., and Brandon Muñoz. "Teaching demonstration of the integral calculus." International Journal of Mathematical Education in Science and Technology 51, no. 4 (May 24, 2019): 631–42. http://dx.doi.org/10.1080/0020739x.2019.1614689.

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Vinogradov, A. M., and L. Vitagliano. "Iterated differential forms III: Integral calculus." Doklady Mathematics 75, no. 2 (April 2007): 177–80. http://dx.doi.org/10.1134/s1064562407020019.

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Igliori, Sonia Barbosa Camargo, Celina Aparecida Almeida Pereira Abar, and Marcio Vieira De Almeida. "Continuidade e diferenciabilidade de funções reais: uma proposta de estudo dessas noções com a utilização do computador." Revemop 1, no. 1 (January 10, 2019): 24. http://dx.doi.org/10.33532/revemop.v1n1a2.

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<p>Este artigo objetiva analisar a utilização dos computadores no ensino da noção de continuidade e diferenciabilidade de funções de uma variável real. A relação é abordada no caso de funções contínuas e não diferenciáveis em um intervalo real, por meio de um exemplo que foi encontrado em um artigo escrito por David Tall e utilizado para evidenciar uma forma pela qual o computador pode auxiliar no ensino e aprendizagem dos conceitos do Cálculo Diferencial e Integral quando materiais didáticos e significativos são produzidos. Elementos da teoria de Tall sobre as vantagens dos computadores na Educação, bem como a importância histórica do desenvolvimento de um exemplo de função contínua e não diferenciável são apresentados neste artigo. Além disso, é explorado o caso de uma função definida por um limite de uma série de funções. Também são apresentados comando e ferramentas que estão disponíveis no <em>software</em> GeoGebra. Como resultado, são apresentadas ferramentas que, possivelmente, podem contribuir com a prática, bem como avançar com a Educação Matemática no ensino superior.</p><p><strong>Palavras-chave: </strong>Diferenciabilidade. Continuidade. Didática. Computadores. Ensino Superior.</p><p><strong><br /></strong></p><p><strong>Continuity and differentiability of real functions: a proposal for the study of these notions with the use of the computer</strong></p><p><strong></strong>His paper aims at analyzing the use of computers when teaching differentiability and continuity in real-valued functions. The relation is approached in the case of a non-differentiable continuous real interval through an example is found in an article written by David Tall and is used to evidence a way in which a computer helps the learning and teaching of concepts of Differential and Integral Calculus when didactic and meaningful materials are produced. Elements of Tall’s theory on the advantages of the use of computers in Education, as well as the historical importance of the development of an example of a continuous non-differentiable function are presented in this paper. In addition, a case of a function defined as limit to a series of functions is explored. In addition, commands and tools, which are available in the software GeoGebra, are presented. As a result, we present tools, which will hopefully contribute to the practice as well as advancements in Mathematics Education at higher education level.</p><p><strong>Keywords: </strong> Differentiability. Continuity. Didactic. Computers<strong>. </strong>Higher Education level.</p><p><strong><br /></strong></p><p><strong>Continuidad y diferenciabilidad de funciones reales: una propuesta de estudio de esas nociones con la utilización del ordenador</strong></p><p><strong></strong>Este artículo tiene como objetivo analizar la utilización de las computadoras en la enseñanza de la noción de continuidad y diferenciabilidad de funciones de una variable real. La relación es abordada en el caso de funciones continuas y no diferenciables en un intervalo real, por medio de un ejemplo que fue encontrado en un artículo escrito por David Tall y utilizado para evidenciar una forma por la cual el ordenador puede auxiliar en la enseñanza y aprendizaje de los conceptos del Cálculo Diferencial e Integral cuando se producen materiales didácticos y significativos. Los elementos de la teoría de Tall sobre las ventajas de las computadoras en la Educación, así como la importancia histórica del desarrollo de un ejemplo de función continua y no diferenciable se presentan en este artículo. Además, se explora el caso de una función definida por un límite de una serie de funciones. También se presentan comandos y herramientas que están disponibles en el software GeoGebra. Como resultado, se presentan herramientas que, posiblemente, pueden contribuir con la práctica, así como avanzar con la Educación Matemática en la enseñanza superior.</p><p><strong>Palabras clave:</strong> Diferenciabilidad. Continuidad. Didáctica. Las computadoras. Enseñanza superior.</p>

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COCKETT, J. R. B., and J. S. LEMAY. "Integral categories and calculus categories." Mathematical Structures in Computer Science 29, no. 2 (February 5, 2018): 243–308. http://dx.doi.org/10.1017/s0960129518000014.

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Differential categories are now an established abstract setting for differentiation. However, not much attention has been given to the process which is inverse to differentiation: integration. This paper presents the parallel development for integration by axiomatizing an integral transformation, sA: !A → !A ⊗ A, in a symmetric monoidal category with a coalgebra modality. When integration is combined with differentiation, the two fundamental theorems of calculus are expected to hold (in a suitable sense): a differential category with integration which satisfies these two theorems is called a calculus category.Modifying an approach to antiderivatives by T. Ehrhard, we define having antiderivatives as the demand that a certain natural transformation, K: !A → !A, is invertible. We observe that a differential category having antiderivatives, in this sense, is always a calculus category.When the coalgebra modality is monoidal, it is natural to demand an extra coherence between integration and the coalgebra modality. In the presence of this extra coherence, we show that a calculus category with a monoidal coalgebra modality has its integral transformation given by antiderivatives and, thus, that the integral structure is uniquely determined by the differential structure.The paper finishes by providing a suite of separating examples. Examples of differential categories, integral categories and calculus categories based on both monoidal and (mere) coalgebra modalities are presented. In addition, differential categories which are not integral categories are discussed and vice versa.

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Almeida, Lourdes Maria Werle de, and Tania Camila Kochmanscky Goulart. "Recursos Semióticos em Atividades de Modelagem Matemática." Jornal Internacional de Estudos em Educação Matemática 13, no. 3 (January 12, 2021): 286–97. http://dx.doi.org/10.17921/2176-5634.2020v13n3p286-297.

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ResumoNeste artigo dirigimos nossa atenção à questão: quais recursos semióticos são ativados em atividades de modelagem matemática e como eles colaboram para o desenvolvimento da atividade? Nossas argumentações são fundamentadas, por um lado, em um quadro teórico que considera características da modelagem matemática bem como elementos relativos ao uso de recursos semióticos em atividades de ensino e aprendizagem e a constituição de pacotes semióticos. Por outro lado, consideramos uma pesquisa empírica em que atividades de modelagem matemática são desenvolvidas por alunos de uma disciplina de Cálculo Diferencial e Integral em um curso de Ciência da Computação. A pesquisa tem natureza qualitativa com cunho interpretativo. As análises nos permitem inferir que os alunos fazem uso de recursos semióticos de naturezas diversas de modo que se constituem pacotes semióticos relativamente às ações dos alunos nas diferentes fases do desenvolvimento de uma atividade de modelagem matemática. A ativação dos recursos semióticos bem como a sua colaboração para o desenvolvimento da atividade de modelagem matemática é ao mesmo tempo sincrônica e diacrônica de modo que não é possível afirmar especificamente quando um recurso atua de forma isolada ou conjuntamente com outros para potencializar a comunicação e organizar o pensamento. O que se pode concluir é que diferentes recursos semióticos atuam de maneira colaborativa para fomentar estas ações. Palavras-chave: Educação Matemática. Modelagem Matemática. Recurso Semiótico. Pacote Semiótico. AbstractIn this article we focus our attention on the question: what semiotic resources are activated in mathematical modeling activities and how do they collaborate in the development of the activity? Our arguments are based, on the one hand, on a theoretical framework that considers characteristics of mathematical modeling as well as elements related to the use of semiotic resources in teaching and learning activities. On the other hand, we consider an empirical research in which mathematical modeling activities are developed by students from a Differential and Integral Calculus discipline in a Computer Science course. From a qualitative research and interpretive nature, the analyzes allow us to infer that students make use of semiotic resources of different natures so that they constitute semiotic packages in relation to students' actions in the different phases of the development of a modeling activity mathematics. The activation of semiotic resources as well as their collaboration for the development of the mathematical modeling activity is both synchronous and diachronic so that it is not possible to state specifically when a resource acts in isolation or in conjunction with others to enhance communication and organize the thought. What can be concluded is that different semiotic resources work collaboratively to foster these actions. Keywords: Mathematical Education. Mathematical Modeling. Semiotic Resource. Semiotic Package

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Karaçuha, Serkan, and Christian Lomp. "Integral calculus on quantum exterior algebras." International Journal of Geometric Methods in Modern Physics 11, no. 04 (April 2014): 1450026. http://dx.doi.org/10.1142/s0219887814500261.

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Hom-connections and associated integral forms have been introduced and studied by Brzeziński as an adjoint version of the usual notion of a connection in non-commutative geometry. Given a flat hom-connection on a differential calculus (Ω, d) over an algebra A yields the integral complex which for various algebras has been shown to be isomorphic to the non-commutative de Rham complex (in the sense of Brzeziński et al. [Non-commutative integral forms and twisted multi-derivations, J. Noncommut. Geom.4 (2010) 281–312]). In this paper we shed further light on the question when the integral and the de Rham complex are isomorphic for an algebra A with a flat Hom-connection. We specialize our study to the case where an n-dimensional differential calculus can be constructed on a quantum exterior algebra over an A-bimodule. Criteria are given for free bimodules with diagonal or upper-triangular bimodule structure. Our results are illustrated for a differential calculus on a multivariate quantum polynomial algebra and for a differential calculus on Manin's quantum n-space.

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Márquez Albés, Ignacio, and F. Adrián F. Tojo. "Displacement Calculus." Mathematics 8, no. 3 (March 14, 2020): 419. http://dx.doi.org/10.3390/math8030419.

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In this work, we establish a theory of Calculus based on the new concept of displacement. We develop all the concepts and results necessary to go from the definition to differential equations, starting with topology and measure and moving on to differentiation and integration. We find interesting notions on the way, such as the integral with respect to a path of measures or the displacement derivative. We relate both of these two concepts by a Fundamental Theorem of Calculus. Finally, we develop the necessary framework in order to study displacement equations by relating them to Stieltjes differential equations.

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Guzman Cabrera, Rafael, M. Guía-Calderón, J. J. Rosales-García, A. González-Parada, and J. A. Álvarez-Jaime. "The differential and integral fractional calculus and its applications." Acta Universitaria 25, no. 2 (May 2015): 20–27. http://dx.doi.org/10.15174/au.2015.688.

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Atangana, Abdon, and Seda İğret Araz. "New concept in calculus: Piecewise differential and integral operators." Chaos, Solitons & Fractals 145 (April 2021): 110638. http://dx.doi.org/10.1016/j.chaos.2020.110638.

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Fabian, Andrew, and Hieu D. Nguyen. "Paradoxical Euler: Integrating by Differentiating." Mathematical Gazette 97, no. 538 (March 2013): 61–74. http://dx.doi.org/10.1017/s002555720000543x.

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Every student of calculus learns that one typically solves a differential equation by integrating it. However, as Euler showed in his 1758 paper (E236),Exposition de quelques paradoxes dans le calcul intégral(Explanation of certain paradoxes in integral calculus) [1], there are differential equations that can be solved by actually differentiating them again. This initially seems paradoxical or, as Euler describes it in the introduction of his paper:Here I intend to explain a paradox in integral calculus that will seem rather strange: this is that we sometimes encounter differential equations in which it would seem very difficult to find the integrals by the rules of integral calculus yet are still easily found. not by the method of integration. but rather in differentiating the proposed equation again; so in these cases, a repeated differentiation leads us to the sought integral.

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PARVATE, ABHAY, and A. D. GANGAL. "CALCULUS ON FRACTAL SUBSETS OF REAL LINE — II: CONJUGACY WITH ORDINARY CALCULUS." Fractals 19, no. 03 (September 2011): 271–90. http://dx.doi.org/10.1142/s0218348x11005440.

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Calculus on fractals, or Fα-calculus, developed in a previous paper, is a calculus based fractals F ⊂ R, and involves Fα-integral and Fα-derivative of orders α, 0 < α ≤ 1, where α is the dimension of F. The Fα-integral is suitable for integrating functions with fractal support of dimension α, while the Fα-derivative enables us to differentiate functions like the Cantor staircase. Several results in Fα-calculus are analogous to corresponding results in ordinary calculus, such as the Leibniz rule, fundamental theorems, etc. The functions like the Cantor staircase function occur naturally as solutions of Fα-differential equations. Hence the latter can be used to model processes involving fractal space or time, which in particular include a class of dynamical systems exhibiting sublinear behaviour. In this paper we show that, as operators, the Fα-integral and Fα-derivative are conjugate to the Riemann integral and ordinary derivative respectively. This is accomplished by constructing a map ψ which takes Fα-integrable functions to Riemann integrable functions, such that the corresponding integrals on appropriate intervals have equal values. Under suitable conditions, a restriction of ψ also takes Fα-differentiable functions to ordinarily differentiable functions such that their values at appropriate points are equal. Further, this conjugacy is generalized to one between Sobolev spaces in ordinary calculus and Fα-calculus. This conjugacy is useful, among other things, to find solutions to Fα-differential equations: they can be mapped to ordinary differential equations, and the solutions of the latter can be transformed back to get those of the former. This is illustrated with a few examples.

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Raposo, Álvaro P. "The Algebraic Structure of Quantity Calculus II: Dimensional Analysis and Differential and Integral Calculus." Measurement Science Review 19, no. 2 (April 1, 2019): 70–78. http://dx.doi.org/10.2478/msr-2019-0012.

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Abstract In a previous paper, the author has introduced and studied a new algebraic structure which accurately describes the algebra underlying quantity calculus. The present paper is a continuation of that one, which extends the purely algebraic study by adding two more ingredients: an order structure and a topology. The goal is to give a solid justification of dimensional analysis and differential and integral calculus with quantities.

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David M. Bressoud. "Historical Reflections on Teaching the Fundamental Theorem of Integral Calculus." American Mathematical Monthly 118, no. 2 (2011): 99. http://dx.doi.org/10.4169/amer.math.monthly.118.02.099.

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Faraj, Ahmad, Tariq Salim, Safaa Sadek, and Jamal Ismail. "Generalized Mittag-Leffler Function Associated with Weyl Fractional Calculus Operators." Journal of Mathematics 2013 (2013): 1–5. http://dx.doi.org/10.1155/2013/821762.

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This paper is devoted to study further properties of generalized Mittag-Leffler functionEα,β,pγ,δ,qassociated with Weyl fractional integral and differential operators. A new integral operatorℰα,β,p,w,∞γ,δ,qdepending on Weyl fractional integral operator and containingEα,β,pγ,δ,q(z)in its kernel is defined and studied, namely, its boundedness. Also, composition of Weyl fractional integral and differential operators with the new operatorℰα,β,p,w,∞γ,δ,qis established.

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Kalanov, Temur Z. "Logical analysis of the foundations of differential and integral calculus." Indian Journal of Science and Technology 4, no. 12 (December 20, 2011): 1786–89. http://dx.doi.org/10.17485/ijst/2011/v4i12.35.

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Da Silva Filho, João Inácio. "An Introduction to Paraconsistent Integral Differential Calculus: With Application Examples." Applied Mathematics 05, no. 06 (2014): 949–62. http://dx.doi.org/10.4236/am.2014.56090.

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Cerri, Cristina, and Maria Cristina Bonomi Barufi. "Differential and integral calculus III through WebCT: analysis of results." International Journal of Mathematical Education in Science and Technology 34, no. 3 (January 2003): 335–41. http://dx.doi.org/10.1080/0020739031000078758.

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Wang, Na, and Yanqin Yang. "Research on the numerical solution and dynamic properties of nonlinear fractional differential equations." Lifelong Education 7, no. 2 (August 4, 2018): 42. http://dx.doi.org/10.18282/le.v7i2.776.

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<p>Fractional calculus is an important branch of mathematical analysis, which is specialized in the study of the mathematical properties and applications of arbitrary order integral and differential, and is the extension of the traditional integral calculus. At present, fractional integral and derivative operators are mainly used to calculate fractional calculus, among which the most famous ones are Riemann-Liouville fractional integral and derivative, Caputo fractional derivative, Grümwald-Letnikov fractional integral and derivative, etc. At present, the numerical algorithm of finite difference scheme is mainly used to solve the approximate solution of the equation, to solve the fractional differential equation. Through the finite difference of time fractional order or space fractional order, the approximate solution of the equation is obtained, and the stability, convergence and compatibility of the scheme are checked, and the convergence order and estimation error are calculated. At present, the theory and method of nonlinear fractional differential equation are widely used in the study of various intermediate processes and critical phenomena in finance, physics and mechanics, which can better fit some natural physical processes and dynamic system processes.</p>

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Meilasari, Venty. "PENGEMBANGAN BAHAN AJAR KALKULUS INTEGRAL DENGAN PENDEKATAN APTITUDE TREATMENT INTERACTION (ATI) BERBANTU MACROMEDIA FLASH." Eksponen 10, no. 1 (April 27, 2020): 31–39. http://dx.doi.org/10.47637/eksponen.v10i1.173.

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ABSTRACT The difficulty of students in understanding the material in the integral calculus print book is one factor that makes student learning outcomes low. The difference in students' abilities is one of the considerations in developing process. This study aims to develop integral calculus teaching material using the aptitude treatment interaction (ATI) approach assisted by Macromedia flash. This research belongs to the development research. The instruments used in this study were questionnaires and tests. Indicators of the results of this study are teaching materials declared worthy of use and students who get optimal learning outcomes> 75%. The stages in the study consisted of ten stages that began with discovering potentials and problems to mass production. The results of the study showed that the integral calculus teaching material made was feasible to use. As many as 79% of students achieve optimal learning outcomes.

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Razzaghi, Mohsen. "Hybrid approximations for fractional calculus." ITM Web of Conferences 29 (2019): 01001. http://dx.doi.org/10.1051/itmconf/20192901001.

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In this paper, a numerical method for solving the fractional differential equations is presented. The method is based upon hybrid functions approximation. The properties of hybrid functions consisting ofblock-pulse functions and Taylor polynomials are presented. The Riemann-Liouville fractional integral operator for hybrid functions is given. This operator is then utilized to reduce the solution of the initial value problems for fractional differential equations to a system of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the technique.

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Tasman, Fridgo, and Defri Ahmad. "PEMAHAMAN MAHASISWA TERHADAP INTEGRAL SEBAGAI ANTI TURUNAN, SUATU DESAIN RISET PADA KALKULUS INTEGRAL." JURNAL EKSAKTA PENDIDIKAN (JEP) 1, no. 1 (September 11, 2017): 9. http://dx.doi.org/10.24036/jep/vol1-iss1/28.

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The low learning outcomes and student’s difficulties in understanding calculus courses, espe-cially integral topic, encourage us as researcher to design a calculus lesson for first year students by using realistic mathematical approach (Realistic Mathematics Education). For that we try to design a series of instructional activities starting from understanding integral as an anti derivative. The in-structional activity is designed and developed based on the learning process that occurs in the class-room by involving 30 first year students in FMIPA UNP. The classroom learning compared with our Hypothetical Learning Trajectory (HLT). The results of teaching experiment show that students' un-derstanding of derivative plays important role in understanding the integrals, in general students have difficulty in communicating their ideas in determining the anti-derivative of a function. Through class-room discussions students can get ideas and discuss it in determining the anti-derivative of a function. Based on these results it is recommended to conduct classroom discussions to build students' under-standing in studying calculus especially integral as an anti derived.

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Holevo, A. S. "Exponential formulae in quantum stochastic calculus." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 126, no. 2 (1996): 375–89. http://dx.doi.org/10.1017/s0308210500022794.

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The rigorous definition of time-ordered exponentials, solving quantum linear stochastic differential equations, is extended to Boson and Fermion stochastic calculi with infinitely many degrees of freedom. The relation to the classicalmultiplicative stochastic integral, solving the Doleans exponential equation, is discussed.

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Tarabrin, Gennady. "The Study on the Differential and Integral Calculus in Pseudoeuclidean Space." Journal of Applied Mathematics and Physics 05, no. 09 (2017): 1739–49. http://dx.doi.org/10.4236/jamp.2017.59147.

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Pramuditya, S. A., H. Sulaiman, and Wahyudin. "Development of instructional media game education on integral and differential calculus." Journal of Physics: Conference Series 1280 (November 2019): 042049. http://dx.doi.org/10.1088/1742-6596/1280/4/042049.

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Mizraji, E. "Differential and integral calculus for logical operations. A matrix-vector approach." Journal of Logic and Computation 25, no. 3 (May 11, 2014): 613–38. http://dx.doi.org/10.1093/logcom/exu020.

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Kakehi, Tomoyuki. "Integral Geometry on Grassmann Manifolds and Calculus of Invariant Differential Operators." Journal of Functional Analysis 168, no. 1 (October 1999): 1–45. http://dx.doi.org/10.1006/jfan.1999.3459.

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Usta, Fuat, and Mehmet Sarikaya. "On generalization conformable fractional integral inequalities." Filomat 32, no. 16 (2018): 5519–26. http://dx.doi.org/10.2298/fil1816519u.

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The main issues addressed in this paper are making generalization of Gronwall, Volterra and Pachpatte type inequalities for conformable differential equations. By using the Katugampola definition for conformable calculus we found some upper and lower bound for integral inequalities. The established results are extensions of some existing Gronwall, Volterra and Pachpatte type inequalities in the previous published studies.

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Zhukovsky, K. "Solution of Some Types of Differential Equations: Operational Calculus and Inverse Differential Operators." Scientific World Journal 2014 (2014): 1–8. http://dx.doi.org/10.1155/2014/454865.

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We present a general method of operational nature to analyze and obtain solutions for a variety of equations of mathematical physics and related mathematical problems. We construct inverse differential operators and produce operational identities, involving inverse derivatives and families of generalised orthogonal polynomials, such as Hermite and Laguerre polynomial families. We develop the methodology of inverse and exponential operators, employing them for the study of partial differential equations. Advantages of the operational technique, combined with the use of integral transforms, generating functions with exponentials and their integrals, for solving a wide class of partial derivative equations, related to heat, wave, and transport problems, are demonstrated.

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Котов and P. Kotov. "Modern aspects of integration of nonresonance differential equations with limited right part functions in problems of electrodynamics and astrophysics." Modeling of systems and processes 7, no. 1 (August 8, 2014): 27–30. http://dx.doi.org/10.12737/4951.

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A constructive approach is offered for integration of nonresonance real differential equations with limited functions in the right part considering the famous foundations of differential and integral calculus of measurable function of diagnosable parameters.

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Mendezabal, Marie Jean, and Darin Jan Tindowen. "Improving students' attitude, conceptual understanding and procedural skills in differential calculus through Microsoft mathematics." Journal of Technology and Science Education 8, no. 4 (July 9, 2018): 385. http://dx.doi.org/10.3926/jotse.356.

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This study examined the effects of using Microsoft Mathematics on students’ attitude, conceptual understanding, and procedural skills in Differential Calculus. A quasi-experimental research design was used in which two different learning environments were compared. The participants of the study were two classes of Electrical Engineering students enrolled in Differential Calculus course, assigned randomly as control and experimental groups with 30 students in each group. The control group was taught using the traditional approach of teaching Differential Calculus while the experimental group was taught the same lessons using the Microsoft Mathematics embedded activity sheets. The experimental group learned through exploration and discovery of various concepts. The findings indicated that the participants had little understanding of the concepts and processes of Calculus prior to the conduct of the study. A significant improvement in their performances was noted after the experimentation. This suggests that the use of Microsoft Mathematics in teaching and learning Differential Calculus improves students’ conceptual understanding and procedural skills. It is also found that the use of Microsoft Mathematics in teaching and learning calculus is equally effective as the traditional approach. In terms of attitude, the experimental group demonstrated a “favorable” to “very highly favorable” attitude along the five (5) domains of the MTAS. A significant difference exists between the pretest and posttest attitude of the subjects on the domain “learning Mathematics with technology”.

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Tilahun, Kelelaw, Hagos Tadessee, and D. L. Suthar. "The Extended Bessel-Maitland Function and Integral Operators Associated with Fractional Calculus." Journal of Mathematics 2020 (June 23, 2020): 1–8. http://dx.doi.org/10.1155/2020/7582063.

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The aim of this paper is to introduce a presumably and remarkably altered integral operator involving the extended generalized Bessel-Maitland function. Particular properties are considered for the extended generalized Bessel-Maitland function connected with fractional integral and differential operators. The integral operator connected with operators of the fractional calculus is also observed. We point out important links to known findings from some individual cases with our key outcomes.

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Jirakulchaiwong, Sansumpan, Kamsing Nonlaopon, Jessada Tariboon, Sotiris K. Ntouyas, and Hwajoon Kim. "On (p,q)-Analogues of Laplace-Typed Integral Transforms and Applications." Symmetry 13, no. 4 (April 9, 2021): 631. http://dx.doi.org/10.3390/sym13040631.

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Abstract:

In this paper, we establish (p,q)-analogues of Laplace-type integral transforms by using the concept of (p,q)-calculus. Moreover, we study some properties of (p,q)-analogues of Laplace-type integral transforms and apply them to solve some (p,q)-differential equations.

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