• 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.

• Honam Mathematical Journal
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• v.2 no.1
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• pp.25-35
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• 1980

Vector치(値) 함수(函數)의 Vector치(値) 적분론(積分論)에는 많은 연구(硏究)가 되어 왔으나, 본(本) 논문(論文)에서는 그 가운데 Bochner 적분론(積分論)에 대(對)해서 연구(硏究)하고 Bochner 부정적분(不定積分)에 의(依)한 Vector치(値) 측도(測度)의 표현(表現)에 관(關)한 Radon-Nikodym 정리(定理)에 대(對)해서 연구(硏究)하였다.

• Communications of Mathematical Education
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• v.36 no.1
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• pp.39-57
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• 2022

This study aims to design an integral instruction method that follows the Abstraction in Context (AiC) framework proposed by Hershkowitz, Schwarz, and Dreyfus to help students in acquiring in-depth understanding of the relationship between indefinite integrals and definite integrals and to analyze how the students' understanding improved as a result. To this end, we implemented lessons according to the integral instruction method designed for eight 11th grade students in a science high school. We recorded and analyzed data from graded student worksheets and transcripts of classroom recordings. Results show that students comprehend three knowledge elements regarding relationship between indefinite integral and definite integral: the instantaneous rate of change of accumulation function, the calculation of a definite integral through an indefinite integral, and The determination of indefinite integral by the accumulation function. The findings suggest that the AiC framework is useful for designing didactical activities for conceptual learning, and the accumulation function can serve as a basis for teaching the three knowledge elements regarding relationship between indefinite integral and definite integral.

• Journal of Korean Society of Transportation
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• v.1 no.1
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• pp.64-81
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• 1983

소비자 행태에 관한 신고전 경제이론을 통행수요의 분석에 그대로 적용하는데 문제 가 되는 특기 사항으로는 운임이외에 통행시간과 같은 서어비스 질도 통행수단의 선택에 영 향을 미친다는 점과 특정 두지점간의 통행에서 동일한 소비자도 여러 수송수단을 이용한다 는 점을 들수 있다. 본 연구의 주제는 이와같은 통행수요의 독특한 특성을 반영할 수 있는 소비자의 효용최대화모형의 설정과 이 모형에서 유도된 수요함수의 구조를 분석함에 있다. 상술하면, 통행시간 가치의 불확실성 아래에서 효용을 극대화하는 의사결정문제를 Stochastic Programming 모형으로 표현하였다. 또한 이 모형에서 유도된 특성 통행수단의 수요함수는 이 수단이 가장 유리한 시간가치의 범위에 대한 부정적분으로 표현되며 이 적분 범위와 피적분함수는 모든 경쟁수단의 운임과 통행수단의 함수로 정의됨을 증명하였다. 또 한 수요함수는 통행수요에 관한 통계분석모형에서 묵시적으로 가정되고 있는 통행수단간 대 체성(Property of gross substitute)과 대각방향우세성(Property of diagonal dominance)등의 특성을 가지고 있음을 보여 주었다.

• The Journal of the Convergence on Culture Technology
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• v.9 no.6
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• pp.957-966
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• 2023

In this paper, we propose a new real-time adaptive PID temperature control technique. This is a technique that prevents overshoot by introducing a model that represents the control object. To prevent excessive integration that causes overshoot, integral control adjusts the integral gain to track the heat loss of the model in real time. In the conventional PID control, the integration was dependent on proportional control and the gain was fixed to a constant. As a result, applying two gains that mismatch each other could cause excessive overshoot. However, the proposed adaptive control actively eliminates overshoot so that the integral control amount does not always exceed the heat loss. The cause of overshoot in PID control is integration. Basically, proportional control does not cause overshoot. Therefore, according to the proposed technique, adaptive PID control without the need for tuning experiments can be realized.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.59 no.3
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• pp.623-629
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• 2010

In this paper, a new robust variable structure controller based on a nonlinear integral type sliding surface is presented for the control of uncertain systems with mismatched uncertainties and disturbance. A nonlinear integral type sliding surface is suggested for removing the reaching phase. After its ideal sliding dynamics is obtained, the two design methods are presented. A corresponding control input is proposed to satisfy the closed loop stability in the sense of Lyapunov and the existence condition of the sliding mode on the nonlinear integral type sliding surface, which will be investigated in Theorem 1. Through a design example and simulation study, the usefulness of the proposed controller is verified.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.18 no.2
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• pp.113-121
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• 2005

In order to resolve a common numerical integration inaccuracy of meshfree methods, we introduce an improved natural clement method called Petrov-Galerkin natural element method(PG-NEM). While Laplace basis function is being taken for the trial shape function, the test shape function in the present method is differently defined such that its support becomes a union of Delaunay triangles. This approach eliminates the inconsistency of tile support of integrand function with the regular integration domain, and which preserves both simplicity and accuracy in the numerical integration. In this paper, the validity of the PG-NEM is verified through the representative benchmark problems in 2-d linear elasticity. For the comparison, we also analyze the problems using the conventional Bubnov-Galerkin natural element method(BG-NEM) and constant strain finite clement method(CS-FEM). From the patch test and assessment on convergence rate, we can confirm the superiority of the proposed meshfree method.

• Korean Journal of Cognitive Science
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• v.4 no.2
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• pp.85-114
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• 1994

One of the major research topics in the area of the development of intelligent tutoring system(ITS)is the control of instructional mechanism consisting of lesson plans,curriculum plans,and discourse plans.This paper describes a method of building the lesson plans among these three instructional plans based on the case-based planning.It is more efficient to retrieve the lesson plan from the plan memoru than to generate it whenever an instructional goal is selected.The retrieved lesson plan may be modified to build more adaptive plan for the current goal.We have developed a lesson plan generator that has such capabilities as a component of an ITS for teching indefinite intergration.We also have devised a description language to represeint the generalized form for the given arithmetic expression as an instructional goal and a curriculum tree to represent the lesson units required to master the subject matter.The result of this research could be used either by a developer of the lesson plan generator in the other area of ITS or by human teacher as a curriculum in the actual class.

• The Mathematical Education
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• v.56 no.4
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• pp.387-405
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• 2017

The purpose of this study is to investigate the change of students 'perception and expression about the motion of object following distance function $={x \atop 3}$ and distance function $y=\frac{x^3}{3}+3$ according to the necessity of research on students' perception and expression about integral constant. In this paper, we present the recognition and the expression of the difference of the constant in the relationship between the distance function and the speed function of the students, while examining the process of constructing the speed function and the inverse process of the distance function. This provides implications for the relationship between the derivative and the indefinite integral corresponding to the inverse process. In particular, in a teaching experiment, a constructive activity was performed to analyze the motion of two distance functions, where the student had a difference of the constant term. At this time, the students used the expression 'starting point' for the constants in the distance function, and the motion was interpreted by using the meaning. This can be seen as a unique 'students' mathematics' in the process of analyzing the motion of objects. These scenes, in introducing the notion of the relation between differential and indefinite integral, it is beyond the comprehension of the integral constant as a computational procedure, so that the learner can understand the meaning of the integral constant in relation to the motion of the object. It is expected that it will be a meaningful basic research on the relationship between differential and integral.

• 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.