• 대한수학회논문집
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• 제31권1호
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• pp.115-129
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• 2016

Fractional calculus operators have been investigated by many authors during the last four decades due to their importance and usefulness in many branches of science, engineering, technology, earth sciences and so on. Saigo et al. [9] evaluated the fractional integrals of the product of Appell function of the third kernel $F_3$ and multivariable H-function. In this sequel, we aim at deriving the generalized fractional differentiation of the product of Appell function $F_3$ and multivariable H-function. Since the results derived here are of general character, several known and (presumably) new results for the various operators of fractional differentiation, for example, Riemann-Liouville, $Erd\acute{e}lyi$-Kober and Saigo operators, associated with multivariable H-function and Appell function $F_3$ are shown to be deduced as special cases of our findings.

• 한국수학교육학회지시리즈E:수학교육논문집
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• 제24권1호
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• pp.259-282
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• 2010

본 연구자들은 이 논문에서 다변수미적분학 수업에 적용한 변형 무어교수법(Modified Moore Method)을 소개하고, 이 교수법을 적용한 수업에서 학습에 대한 학생들의 인식변화와 학습 효과를 관찰하여 효과적인 교수 학습을 논의하였다. 본 연구는 3주 기간의 여름계절학기 강좌로 개설된 다변수미적분학 수업을 수강한 15명의 학생들을 대상으로 실시되었다. 학생들의 능동적 예습을 안내하기 위하여 주요 수학 개념에 관련된 단계별로 구조화된 발문 형식의 예습자료를 미리 제시하였다. 수업 중 학생들의 소그룹 협력학습 과정과 발표를 관찰하고, 매 수업 후반에 작성한 학생들의 강의일지와 학기말에 실시한 설문 조사를 분석한 결과에 의하면, 학생들은 스스로 탐구하여 발견하는 학습을 통하여 주제 개념에 대하여 보다 깊이 이해할 수 있음을 인식하게 되었고, 동료와의 토론 및 상호 가르침을 통하여 다양한 내용의 학습과 반성적 사고를 경험할 수 있었다.

• 한국수학교육학회지시리즈D:수학교육연구
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• 제16권3호
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• pp.195-206
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• 2012

We adopt a spirit of Problem based learning to the class of Multivariable Calculus in a school of scientifically talented students and observed effects of our teaching-learning method in the Spring Semester of 2010. Twelve students who enrolled in this class participated in this research. We have proceeded with classroom experiment for the half of semester after midterm exam so that the students could compare our teaching-learning method with usual traditional one in the subject of multivariable calculus. Especially, we investigated changes in the learning attitude and cognitive development of the students toward definition and theorem of mathematics. Each group of 4 students worked on a sheet of our well-designed structured problems of several steps in each class and presented how they understood the way of constructing new definition and related theorems. Instructor's role in this research was to guide students' activities as questioner so that students could attain the clear meanings of definitions and theorems by themselves. We firstly analyzed students' process of mathematization of definition through observing their discussions and presentations as well as their achievements in the quizzes and final exams. Secondly, we analyzed students' class-diaries collected at the end of each class in addition to pre/post surveys.