• East Asian mathematical journal
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• v.18 no.1
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• pp.111-125
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• 2002

Many different families of infinite series were recently observed to be summable in closed forms by means of certain operators of fractional calculus(that is, calculus of integrals and derivatives of any arbitrary real or complex order). In this sequel to some of these recent investigations, the authors present yet another instance of applications of certain fractional calculus operators. Alternative derivations without using these fractional calculus operators are shown to lead naturally a family of analogous infinite sums involving hypergeometric functions.

• The Mathematical Education
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• v.48 no.3
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• pp.213-234
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• 2009

College students have a diverse educational background with the recent multiplicity in university admissions standards and procedures. As a result, their mathematical preparation and performance varies widely. Teaching calculus to such a diverse student group is a demanding task. Differentiated curriculum has been conducted for the university calculus course in Yonsei university for the past five years. A case study on the differentiated curriculum in Yonsei university is presented for the curriculum improvement. With its ideal purpose, the differentiated curriculum has created issues and problems in practice. As an alternative to the ideal differentiated curriculum, this study shows that a computer-based approach using a numerical software could give aids to overcoming the difficulty of inadequately prepared students in the learning process while mathematically sophisticated students could keep interested in the course. This study also presents the useful topics in calculus that can be implemented for computer-based calculus education and provides guidelines for the effective usage.

• Communications of the Korean Mathematical Society
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• v.12 no.2
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• pp.457-466
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• 1997

We give a formula related to fractional calculus which may be useful in solving some fractional linear differential equations. We also give a brief survey of the history of the fractional calculus.

• Journal of Pharmacopuncture
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• v.12 no.3
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• pp.61-72
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• 2009

Objectives : This experimental study was performed to investigate the safety and efficacy of Bovis Calculus pharmacopuncture solution manufactured with freezing dryness method to use eye drop. To identify the use of it as eye drop, the eye irritation test of rabbits and the antibacterial test of Staphylococcus aureus, Staphylococcus epidermidis, Pseudomonas aeruginosa, Aspergillus niger, Fusarium oxysporum, and Candida albicans were performed. Methods : 1. The eye irritation test of this material was performed according to the Regulation of Korea Food & Drug Administration(2005. 10. 21, KFDA 2005-60). After Bovis Calculus pharmacopuncture solution was administered in the left eye of the rabbits, eye irritation of the cornea, iris and conjunctiva was observed at 1, 2, 3, 4 & 7day. 2. After administering Bovis Calculus pharmacopuncture solution on bacterial species(Staphylococcus aureus, Staphylococcus epidermidis, Pseudomonas aeruginosa, Aspergillus niger, Fusarium oxysporum, Candida albicans) which cause Keratitis, MIC(Minimum Inhibition Concentration) and the size of inhibition zone were measured. Anti-bacterial potency was also measured using the size of inhibition zone. Results : 1. After Bovis Calculus pharmacopuncture solution was administered in the left eye of the rabbits, it was found that none of nine rabbits have abnormal signs and weight changes. 2. After Bovis Calculus pharmacopuncture solution was medicated in the left eye of the rabbits, no eye irritation of the cornea, iris and conjunctiva was observed at 1, 2, 3, 4 & 7day. 3. There was no response to MIC on bacterial species(Staphylococcus aureus, Staphylococcus epidermidis, Pseudomonas aeruginosa, Aspergillus niger, Fusarium oxysporum, Candida albicans) after Bovis Calculus pharmacopuncture solution was medicated. Conclusions : The present study suggests that Bovis Calculus pharmacopuncture solution is a nontoxic and non-irritant medicine, which does not cause eye irritation in rabbits, but dosen't have antibacterial effects on bacterial species(Staphylococcus aureus, Staphylococcus epidermidis, Pseudomonas aeruginosa, Aspergillus niger, Fusarium oxysporum, Candida albicans) which cause Keratitis. These study result recommends that more research on other herbal medicines of eye drop for Keratitis are required.

• Journal of Acupuncture Research
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• v.24 no.4
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• pp.125-142
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• 2007

calculus pharmacopuncture. Porcine skin including fat tissue after treated Fel ursi and Bovis calculus pharmacopuncture by means of the dosage dependent variation are investigated the histologic changes after injection of these pharmacopuncture. Results: Following results were obtained from the preadipocyte proliferation and lipolysis of adipocyte and histologic investigation of fat tissue. 1. Fel ursi and Bovis calculus pharmacopuncture showed the effect of decreased preadipocyte proliferation on the high dosage($1mg/m{\ell}$). 2. Fel ursi pharmacopuncture showed the effect of decreased the activity of glycerol-3-phosphate dehydrogenase (GPDH) on the high dosage($1mg/m{\ell}$) and Bovis calculus pharmacopuncture significantly showed from $0.1mg/m{\ell}$ concentration. 3. Fel ursi pharmacopuncture was not showed the effect of lipolysis, but Bovis calculus pharmacopuncture was increased the effect of lipolysis in all concentration significantly. 4. Investigated the histological changes in porcine fat tissue after treated Fel ursi and Bovis calculus pharmacopuncture, we knew that these pharmacopuncture was showed significant activity to the lysis of cell membranes in all concentration. Conclusion : These results suggest that Fel ursi and Bovis calculus pharmacopuncture efficiently induces diminish proliferation of preadipocyte and lipolysis in adipose tissue.

• Communications of Mathematical Education
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• v.30 no.1
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• pp.47-65
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• 2016

The purpose of this paper is to compare the effects on the students' academic achievement and satisfaction level in a Calculus course taught by two different teaching modes, blended learning and face-to-face learning. The comparison analysis was made for Calculus 2 course in H university in South Korea offered in the Spring semester of the year 2015. Calculus 2 is a Calculus course designed for the first year students who plan to choose their majors in Engineering. There were two sections of the Calculus course taught in a blended learning mode and one in a conventional face-to-face learning mode. All these three sections including e-learning parts were taught by the author. We discuss some meaningful differences in the effects by the two different teaching modes.

• Journal of Pharmacopuncture
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• v.11 no.3
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• pp.105-111
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• 2008

Objective: The aim of this study is to investigate the safety of Fel Ursi, Bovis Calculus & Moschus pharmacopuncture solution manufactured with freezing dryness method to use eye drop. Methods: The eye irritation test of this material was performed according to the Regulation of Korea Food & Drug Administration(2005. 10. 21, KFDA 2005-60). After Fel Ursi, Bovis Calculus & Moschus pharmacopuncture solution was applied eyewash in the left eye of the rabbits, the author observed eye irritation of the cornea, iris, conjunctiva at 1, 2, 3, 4 & 7day. Results: 1. After Fel Ursi, Bovis Calculus & Moschus pharmacopuncture solution was applied eyewash in the left eye of the rabbits, there wasn t physical problem at 9 rabbits. 2. After Fel Ursi, Bovis Calculus & Moschus pharmacopuncture solution was applied eyewash in the left eye of the rabbits, there wasn't eye irritation of the cornea, iris, conjunctiva at 1, 2, 3, 4 & 7day. Conclusions: In this study, it was observed that Fel Ursi, Bovis Calculus & Moschus pharmacopuncture solution didn't induced eye irritation in rabbits.

• Journal for History of Mathematics
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• v.23 no.3
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• pp.45-56
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• 2010

Sequent Calculus is a symmetrical version of the Natural Deduction which Gentzen restructured in 1934, where he presents 'Hauptsatz'. In this thesis, we will examine why the Cut-Elimination Theorem has such an important status in Proof Theory despite of the efficiency of the Cut Rule. Subsequently, the dynamic side of Curry-Howard correspondence which interprets the system of Natural Deduction as 'Simply typed $\lambda$-calculus', so to speak the correspondence of Cut-Elimination and $\beta$-reduction in $\lambda$-calculus, will also be studied. The importance of this correspondence lies in matching the world of program and the world of mathematical proof. Also it guarantees the accuracy of program.

• Journal of Educational Research in Mathematics
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• v.8 no.2
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• pp.495-507
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• 1998

This article intends to review what problems the terms in calculus have and how those problems are caused. For this purpose We make examinations on the considerations in the analysis of mathematical terminology, which includes the problems of general and technical terms, the meaning and the boundary of words, their consistency, the name and meaning, concept and their concept images, translations and qwerty effects. And in chapter 3, We analyse the textbook which are currently used, through which I was able to find out that the terms in calculus have some problems, In other words, the key terms such as "differentiable", "differential coefficient", "differential" have their roots in the term "differential" but the term "derived function" is very distinct from other terms and thus obstructs the consistency of terms. And the central term "differential" is being used without clear definition. In particular, the fact that "differential", when used in its arbitrary definition, has the image of "splitting minutely" can be an obstacle to understanding the exact concepts of calculus. In chapter 4, We make a review on the history of calculus and the term "differential" currently used in modern mathematics so that I can identify the origin of the problem connected with the usage of the term "differential". We should recognize the specified problems and its causes and keep their instructional implications in mind. Furthermore, following researches and discussions should be made on whether the terminology system of calculus should be reestablished and how the reestablishment should be made.e terminology system of calculus should be reestablished and how the reestablishment should be made.

• Journal of Educational Research in Mathematics
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• v.19 no.1
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• pp.123-142
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• 2009

Dynamic context is considered as a source for intuitive understanding on the calculus. The relation between the area under time-velocity graph and distance is the base of the dynamic contexts which are treated in the integral calculus. The fundamental theorem of calculus has originated in dynamic contexts. This paper investigated the fundamental theorem of calculus via the relation between the area under time-velocity graph and distance. And we analyzed mathematics textbooks and the understanding of students. Finally we suggest some proposal for the teaching of the fundamental theorem of calculus.