• Journal of the Chungcheong Mathematical Society
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• v.20 no.1
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• pp.11-21
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• 2007

Given a nonlinear function f : $\mathbb{R}{\rightarrow}\mathbb{R}$ that has a simple real zero ${\alpha}$, a new numerical method to be called k-fold pseudo- Halley's method is proposed and it's error analysis is under investigation to confirm the convergence behavior near ${\alpha}$. Under the assumption that f is sufficiently smooth in a small neighborhood of ${\alpha}$, the order of convergence is found to be at least k+3. In addition, the corresponding asymptotic error constant is explicitly expressed in terms of k, ${\alpha}$ and f as well as the derivatives of f. A zero-finding algorithm is written and has been successfully implemented for numerous examples with Mathematica.

• Steel and Composite Structures
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• v.12 no.4
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• pp.303-324
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• 2012

This paper presents the mode-shape analysis of the cross-ply laminated composite cylindrical shallow shells. First, the kinematic relations of strains and deformation are given. Then, using Hamilton's principle, governing differential equations are developed for a general curved shell. Finally, the stress-strain relation for the laminated, cross-ply composite shells are obtained. By using some simplifications and assuming Fourier series as a displacement field, the governed differential equations are solved by the matrix algebra for shallow shells. Employing the computer algebra system called MATHEMATICA; a computer program has been prepared for the solution. The results obtained by this solution are compared with the results obtained by (ANSYS and SAP2000) programs, in order to verify the accuracy and reliability of the solution presented.

• Communications of Mathematical Education
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• v.16
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• pp.109-122
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• 2003

현재 초, 중, 고등학교의 수학교육 현실은 수학 개념의 정확한 이해에 초점을 맞추지 못하고 공식의 암기와 그것을 이용하여 단순한 문제 풀이에 시간을 많이 할애함으로써 수학의 기본적인 개념이나 기호의 정확한 사용법을 인지하지 못하고 계산 기능적인 면으로 치우치는 경향이 많이 나타나며, 문제 풀이의 창의적인 상황이 제시되지 않는 상태에서 교사 중심의 문제풀이 방법에만 의존하고 있다. 이러한 문제점 속에서 창의적인 문제 해결 방안을 구상할 수 있는 사고력의 배양에 소홀함이 있다고 볼 수 있다. 따라서 학생 스스로 의미를 파악하여 학습 할 수 있는 교수 방법이나 학습 방법에 대한 연구는 현실적으로 매우 시급한 상황에 처해있다. 이러한 상황에서 많은 수학교육자들은 학생들이 좀 더 쉽게 수학의 개념에 접근 할 수 있게 하기 위하여 많은 노력을 하고 있다. 그러한 노력 중의 하나로 테크놀러지를 이용한 수학교육을 말 할 수 있는데, 이는 실제로 수학교육에 긍정적인 영향을 준다고 알려져 있다. 본 논문은 현 고등학교 수학I의 등차수열에 관한 내용을 Mathematica를 이용하여 다각수(도형수)로부터 등차수열의 개념을 유도하였다.

• The Pure and Applied Mathematics
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• v.14 no.2 s.36
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• pp.85-90
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• 2007

Arguably the most important internet technology of today is RIA (rich internet application), whose prime advantage is in improving the user experience on the web. However, the scope and variety of the RIA technology demand an eclectic guideline to build the mathematical services such as mathematical text, graphs, and animations. This paper sorts out and simplifies the complicated roadmap of the RIA technologies by presenting three design patterns for exposing the functionality of the CAS (computer algebra system) with the web browser as the user interface platform.

• Journal of the Korean Institute of Electrical and Electronic Material Engineers
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• v.15 no.1
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• pp.37-45
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• 2002

We described a method of resonant mode identification in dielectric-disc loaded cylindrical cavity resonators. The characteristic equations are solved using the ContourPlot graph of Mathematica. Contour graph method uses graphical method. It is comparable with numerical method. The numerical method is very difficult mode identification. The analysis is based on the approximated electromagnetic representation which is only concentrated on the calculation of resonant frequencies, and a mode identification of resonant frequencies has not been covered. However, It is possible to calculate precise resonant frequencies and to identify the mode of resonant frequencies using the contour graph method. The contour graph method is not a method using approximated representation of electromagnetic field variation at the outer area of dielectric in the resonators. It is a method using enact representation.

• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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• 2000.11a
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• pp.267-270
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• 2000

This paper describes measurement of relative permittivity of illite found in young-dong area. A measurement of relative permittivity of illite used to cylindrical cavity resonators with moveable cap. A concentric dielectric-rod inserted cylindrical cavity resonator and an exact field representation of travelling wave mode are introduced for measurement of relative permittivity. The exact electromagnetic fields in cylindrical cavity with concentric dielectric rod is analysed. A relative permittivity of dielectric in cavity is calculated by analyzing the characteristic equation. The characteristic equation is solved by using the ContourPlot graph of Mathematica. We know that the field representation of travelling mode is exact. As a result, relative permittivity of dielectric materials were 7.820 at sample-1 and 7.894 at sample-2.

• Proceedings of the KIPE Conference
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• 2001.07a
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• pp.101-104
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• 2001

This paper represent about design of the controller for battery of a PE drum for power supply using PV Module. Simulation is represents V-I and power characteristic by Mathematica & Pspice 6.0 & Qnet 2.1. Finally, we composed of road surface-signpost system. This system is successfully operating with high clearness lights.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.7 no.6
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• pp.1421-1424
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• 2006

By extending the Mandelbrot set for the complex polynomial $$M={c\in C\;:\; _{k\rightarrow\infty}^{lim}P_c^k(0)\;{\neq}\;{\infty}$$ we define the degree-n bifurcation set. In this paper, we formulate the boundary equation of a period-2 component on the main component in the degree-9 bifurcation set by parameterizing its image. We establish an algorithm constructing a period-2 component in the degree-9 bifurcation set and the typical implementations show the satisfactory result with Mathematica codes grounded on the analysis.

• Journal of the Korean Society for Precision Engineering
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• v.18 no.12
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• pp.88-94
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• 2001

The V-notched crack problem in dissimilar materials can be formulated as an eigenvalue problem. The RWCIM(Reciprocal Work Contour Integral Method) is applied to the determination of the eigenvector coefficients associated with eigenvalues for V-notched cracks in pseudo-isotropic and anisotropic dissimilar materials. The RWCIM algorithm is programed by the commercial numerical program, MATHEMATICA. The numerical results obtained are shown that the RWCIM is a useful method for determining the eigenvector coefficients of V-notched cracks in pseudo-isotropic and anisotropic dissimilar materials.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.11 no.3
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• pp.7-20
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• 2007

We examined the steady state solution for a strongly exothermic mixtures in some class A geometries subjected to different boundary conditions under Arrhenius, Bimolecular and Sensitised reactions. The solution of the governing nonlinear reaction diffusion equation was obtained using the variational method formulation executed in Mathematica package. The paper elucidates the influence of geometry, boundary conditions and types of reaction on the thermal ignition of the reactive mixture. Apart from validating known results in literature, the solution gave further insight into the influence of material properties and conditions on the occurrence of thermal ignition.