• Title/Summary/Keyword: 정적분

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Comprehending the Symbols of Definite Integral and Teaching Strategy (정적분 기호 이해의 특징과 교수학적 전략)

  • Choi, Jeong-Hyun
    • Journal for History of Mathematics
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    • v.24 no.3
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    • pp.77-94
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    • 2011
  • This study aims to provide a teaching strategy accommodating the symbols of the definite integral and guiding students through the meaning of notations in area and volume calculations, based on characterization as to how students comprehend the symbols used in the Riemann sum formula and the definite integral, and their interrelationship. A survey was conducted on 70 high school students regarding the historical background of integral symbols and the textbook contents designated for the definite integral. In the following analysis, the comprehension was qualified by 5 levels; students in higher levels of comprehension demonstrated closer relation to the history of integral notations. A teaching strategy was developed accordingly, which suggested more desirable student understanding on the concept of definite integral symbols in area and volume calculations.

High School Students' Understanding of Definite Integral (고등학생들의 정적분 개념 이해)

  • Shin, Bo-Mi
    • School Mathematics
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    • v.11 no.1
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    • pp.93-110
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    • 2009
  • This paper provides an analysis of a survey on high school students' understanding of definite integral. The purposes of this survey were to identify high school students' private concept definitiones and concept images on definite integral. Definitions and images, as well as the relation between them of the definite integral concept, were examined in 108 high school students. A questionnaire was designed to explore the cognitive schemes for the definite integral concept that evoked by the students. The students' individual answers were collected through written environment. Four types of the private concept definitiones and concept images were identified in the analysis.

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A Study on Infinitesimal Interpretation of Definite Integral (정적분의 무한소 해석에 대한 고찰)

  • Joung, Youn-Joon;Kang, Hyun-Young
    • School Mathematics
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    • v.10 no.3
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    • pp.375-399
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    • 2008
  • Infinitesimal did not play an explicit role concerning definite integral in the textbook nowadays. But studies which investigate understanding of students on definite integral show that many students comprehend definite integral with infinitesimal. Formally infinitesimal is not taught at mathematics classroom, but many students identify definite integral as infinite sum of infinitesimals. This means that definite integral itself contains some structural elements that allow infinitesimal interpretation. In this study we investigate the role of infinitesimal In the historical development of partition-sum in definite integral, extract didactical issues concerning understanding of definite integral, and analyse Korean mathematics textbooks. Finally we propose some suggestions on the teaching of definite integral which contains the process of refinement intuition.

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A study on the Relationship between Indefinite Integral and Definite Integral (부정적분과 정적분의 관계에 관한 고찰)

  • Joung, Youn-Joon;Lee, Kyeong-Hwa
    • School Mathematics
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    • v.11 no.2
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    • pp.301-316
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    • 2009
  • There are two distinct processes, definite integral and indefinite integral, in the integral calculus. And the term 'integral' has two meanings. Most students regard indefinite integrals as definite integrals with indefinite interval. One possible reason is that calculus textbooks do not concern the meaning in the relationship between definite integral and indefinite integral. In this paper we investigated the historical development of concepts of definite integral and indefinite integral, and the relationship between the two. We have drawn pedagogical implication from the result of analysis.

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An Analysis of the Concept on Mensuration by Parts and Definite Integral (구분구적법과 정적분의 개념 분석)

  • Shin, Bo-Mi
    • Journal of the Korean School Mathematics Society
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    • v.11 no.3
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    • pp.421-438
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    • 2008
  • Understanding the concept of definite integral is based on understanding the concept of mensuration by parts. However, several previous studies pointed out the difficulty on teaching the concept of mensuration by parts. The paper provides some didactic strategies which help teaching the concept of mensuration by part. To teach the concept of definite integral, in the high school curriculum, the relation between definite integral and series is dealt with. However, the paper suggests that importing the concept of series is not indispensable to teach the concept of definite integral. It is proper that definite integral is taught as limit of particular sequence not series.

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A Case Study on Team Project in Calculus for Medicine - Numerical Methods of Integration - (의대생을 위한 미분적분학 팀프로젝트 사례 - 정적분의 수치채산법을 중심으로 -)

  • Min, Sook
    • Communications of Mathematical Education
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    • v.26 no.2
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    • pp.155-176
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    • 2012
  • In this paper, we present a practical and essential method of using team projects for calculus. We, specifically, take into account the team project that calculate the volume of lung represented on CT scan images. We have demonstrated that the process of analyzing the images in a team project encourage studying numerical methods of integration for calculus. Also, we have used various technological programs(MATLAB, MATHEMATICA, MS Excel) to solve the team project.

Computional Errors in the Elements of Stiffness Matrix for Tapered Members (선형변단면부재(線型變斷面部材)의 강도(剛度)매트릭스들의 계산상(計算上) 오차(誤差))

  • Lee, Yong Woo
    • KSCE Journal of Civil and Environmental Engineering Research
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    • v.5 no.2
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    • pp.35-39
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    • 1985
  • The closed form of the stiffness matrix is derived in terms of closed forms of intergrals for analyses of plane frame members containing linerly tapered members with the cross section of thin-walled tube. The series expansion forms of these are also developed to study the errors in the closed form of the stiffness matrix. The useful limits of the closed form of integrals are defined in terms of the relative taper.

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A study for Build the Concept Image about Natural Logarithm under GeoGebra Environment (GeoGebra 환경에서 정적분을 이용한 자연로그의 개념이미지 형성 학습 개선방안)

  • Lee, Jeong-Gon
    • Journal for History of Mathematics
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    • v.25 no.1
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    • pp.71-88
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    • 2012
  • The purpose of this study is to find the way to build the concept image about natural logarithm and the method is using definite integral in calculus under GeoGebra environment. When the students approach to natural logarithm, need to use dynamic program about the definite integral in calculus. Visible reasoning process through using dynamic program(GeoGebra) is the most important part that make the concept image to students. Also, for understand mathematical concept to students, using GeoGebra environment in dynamic program is not only useful but helpful method of teaching and studying. In this article, about graph of natural logarithm using the definite integral, to explore process of understand and to find special feature under GeoGebra environment. And it was obtained from a survey of undergraduate students of mathmatics. Also, relate to this process, examine an aspect of students, how understand about connection between natural logarithm and the definite integral, definition of natural logarithm and mathematical link of e. As a result, we found that undergraduate students of mathmatics can understand clearly more about the graph of natural logarithm using the definite integral when using GeoGebra environment. Futhermore, in process of handling the dynamic program that provide opportunity that to observe and analysis about process for problem solving and real concept of mathematics.

Teachers' Opinions on Differences of Detail Learning Content According to High School Textbooks - Focused on Utilizing of Definite Integral - (고등학교 교과서 내용 영역별 세부 학습내용 차이에 대한 교사 의견 조사: 정적분의 활용을 중심으로)

  • Yang, Seong Hyun
    • School Mathematics
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    • v.17 no.4
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    • pp.555-570
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    • 2015
  • General and subject guideline for new curriculum are confirmed and plan to announced on September 2015. The development of instructional materials according to them will proceed. Because textbooks have the role and function to determine and control the direction and scope of teaching and learning, Textbook plays a very important role in the situation where teachers and students meet. Thus we get a significant effect depending on the structure of textbook. In this study, we analyzed differences of detail learning content according to high school textbooks focused on utilizing of definite integral. After creating the questionnaire based on it, The survey was conducted targeting for 369 high school mathematics teachers belong to 14 education offices of cities and provinces are polled out by accidental sampling method. Analyzing the results of the survey, We searched various teaching and learning method that arise due to differences of detail learning content according to high school textbooks and thereby it explored the impact on students' mathematics learning. Through this, Our intention is to offer implication about the structure of textbook detail learning contents and to derive the improvements about textbook compilation system.

A Study on the Performance of Multiple GPU's (다중 GPU의 성능에 대한 연구)

  • Kim, Yerim;Kim, Youngtae
    • Proceedings of the Korea Information Processing Society Conference
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    • pp.49-50
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    • 2016
  • 본 논문에서는 다중 GPU의 효율성을 알아보기 위하여 정적분 계산을 이용하여 원주율(${\pi}$)를 계산하는 CUDA 프로그램을 구현하였으며, 다중 GPU를 사용하기 위해서는 병렬처리 라이브러리인 MPI를 사용하였다. 실험 결과 GPU의 수에 비례하여 성능이 선형으로 증가함을 보였다.