京都大学 / 0048 / 新制・課程博士 / 博士(情報学) / 甲第19121号 / 情博第567号 / 新制||情||100(附属図書館) / 32072 / 京都大学大学院情報学研究科複雑系科学専攻 / (主査)教授 木上 淳, 教授 磯 祐介, 教授 西村 直志 / 学位規則第4条第1項該当 / Doctor of Informatics / Kyoto University / DFAM

京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第20153号 / 理博第4238号 / 新制||理||1609(附属図書館) / 京都大学大学院理学研究科数学・数理解析専攻 / (主査)教授 坂上 貴之, 教授 上田 哲生, 教授 國府 寛司 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

京都大学 / 0048 / 新制・課程博士 / 博士(工学) / 甲第21754号 / 工博第4571号 / 新制||工||1712(附属図書館) / 京都大学大学院工学研究科機械理工学専攻 / (主査)教授 西脇 眞二, 教授 北村 隆行, 教授 小森 雅晴 / 学位規則第4条第1項該当 / Doctor of Philosophy (Engineering) / Kyoto University / DFAM

No description available.

In this dissertation, a new numerical method for solving the fractional dynamical systems, is presented. We first introduce Riemann-Liouville fractional integral operator for hybrid functions. Then we will show the spectral accuracy of the present method for solving fractional-order differential equations, and we will extend the present method for solving nonlinear fractional integro-differential equations, fractional Bagley-Torvik equation, distributed order fractional differential equations, two-dimensional fractional partial differential equations, and fractional optimal control problems. In all cases, we will show the rate of convergence is more than some existing numerical methods which were used to solve these kind of problems in the literature. Illustrative examples are included to demonstrate the validity and applicability of the technique.

In this dissertation, a new numerical method for solving fractional calculus problems is presented. The method is based upon the fractional Taylor vector approximations. The operational matrix of the fractional integration for the fractional Taylor vector is introduced. This matrix is then utilized to reduce the solution of the fractional calculus problems to the solution of a system of algebraic equations. This method is used to solve fractional differential equations, Bagley-Torvik equations, fractional integro-differential equations, and fractional duffing problems. Illustrative examples are included to demonstrate the validity and applicability of this technique.

No description available.

京都大学 / 新制・課程博士 / 博士(工学) / 甲第24581号 / 工博第5087号 / 新制||工||1974(附属図書館) / 京都大学大学院工学研究科材料工学専攻 / (主査)教授 田中 功, 教授 安田 秀幸, 教授 中村 裕之 / 学位規則第4条第1項該当 / Doctor of Philosophy (Engineering) / Kyoto University / DFAM

No description available.

This is a case study using qualitative methods to analyze how a first semester calculus student named Mark makes sense of the derivative and the role of the classroom practice in his understanding. Mark is a bright yet fairly average student who successfully makes sense of the derivative and retains his knowledge and understanding. The study takes place within a collaborative, student-centered, task-based classroom where the students are given opportunity to explore mathematical ideas such as rate of change and accumulation. Mark's sense making of the derivative is analyzed in light of his use of physics, Mark as a visual learner, the representations he used to make sense of the derivative using Zandieh's (2000) framework for representations of derivatives, and his conceptions of the limit over time. Classroom practice allowed Mark to exercise his agency and explore tasks in ways that were personally meaningful. The findings in this study contribute new details about how calculus students might solve tasks, develop strategies, and communicate with each other.